EPA-R2-72-053
NOVEMBER 1972           Environmental Protection Technology Series
 Initial Mixing  in
 Coagulation  Processes
                                   Office of Research and Monitoring
                                   U.S. Environmental Protection Agency
                                   Washington, D.C. 20460

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            RESEARCH REPORTING SERIES
Research reports of the  Office  of  Research  and
Monitoring,  Environmental Protection Agency, have
been grouped into five series.  These  five  broad
categories  were"established to facilitate further
development  and  application   of   environmental
technology.   Elimination  of traditional grouping
was  consciously  planned  to  foster   technology
transfer   and  a  maximum  interface  in  related
fields.  The five series are;

   1.  Environmental Health Effects Research
   2.  Environmental Protection Technology
   3.  Ecological Research
   H.  Environmental Monitoring
   5.  Socioeconomic Environmental Studies

This report has been assigned to the ENVIRONMENTAL
PROTECTION   TECHNOLOGY   series.    This   series
describes   research   performed  to  develop  and
demonstrate   instrumentation,    equipment    and
methodology  to  repair  or  prevent environmental
degradation from point and  non-point  sources  of
pollution.  This work provides the new or improved
technology  required for the control and treatment
of pollution sources to meet environmental quality
standards..

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                                              EPA-R2-72-053
                                              November 1972
        INITIAL MIXING IN COAGULATION PROCESSES
                            by

                  Richard J. Stenquist
                     Warren J. Kaufman
                      Project 17030 DLX
                      Project Officer

                    Dr.  Sidney A. Hannah
         National Environmental Research Center
             Environmental Protection Agency
                 Cincinnati, Ohio  45268
                        Prepared for

           OFFICE OF  RESEARCH AND MONITORING
         U.S. ENVIRONMENTAL PROTECTION AGENCY
                WASHINGTON, D. C. 20460
For sale by the Superintendent of Documents, U.S. Government Printing Office
           Washington, D.C., 20402 - Price $2.25

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            EPA Review Notice
This report has been reviewed by the Environ-
mental Protection Agency and approved for
publication.  Approval does not signify that the
contents  necessarily reflect the views and policies
of the Environmental Protection Agency, nor does
mention  of trade names or commercial products
constitute endorsement or recommendation for
use.
                         u

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                               ABSTRACT
This investigation was undertaken with the objective of determining the
importance of the initial mixing step in water and wastewater treatment
processes and determining whether increasing the rapidity of the initial
mixing could improve process performance.  The principal process con-
sidered was alum coagulation-flocculation of a kaolin suspension in water.
The initial mixing device under consideration was a biplane, square-mesh
grid of bars placed in a turbulent flow, tubular reactor; a 2-in. pipe
was used in the present studies.  Studies were made using a single electrode
"point" conductivity probe and NaCl solution tracer to determine what para-
meters affect the mixing which occurs in the turbulent flow field down-
stream from a grid, and from these results a general mixing model was
developed.  The relation between initial mixing and process performance
was studied by using two of the grids from the mixing studies as initial
mixing devices in coagulation of a kaolin suspension.

This report was submitted by University of California Sanitary Engineering
Research Laboratory, College of Engineering and School of Public Health,
Berkeley, California, in fulfillment of Project 17030 DLX under the
sponsorship  of the Environmental Protection Agency.
                                 iii

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                          CONTENTS


Section                                                        Page

    I      Summary and Conclusions                             1

   II      Recommendations                                     5

   III      Introduction                                          7

   IV      Review of Fundamental Theory:  Turbulence,
           Mixing and  Coagulation                               11

   V      Mixing Studies: Apparatus and Methods               47

   VI      Mixing Studies: Results and Analysis                 71

  VII      Initial Mixing and Alum Coagulation —
           Flocculation                                         91

 VIII      Acknowledgments                                   115

   IX      Appendices                                         117

   X      Glossary                                           151

   XI      References                                         157

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                         FIGURES


                                                         PAGE

 1      MEAN AND FLUCTUATING  COMPONENTS
        OF VELOCITIES                                    i3

 2      LONGITUDINAL AND LATERAL CORRELATION
        FUNCTIONS AND LATERAL MICROSCALE, \ ,
        FOR ISOTROPIC TURBULENCE            g         15

 3      DECAY OF  TURBULENCE AS MEASURED BY VARIOUS
        INVESTIGATORS                                    22

 4      INTEGRAL  SCALE OF TURBULENCE AS
        MEASURED BY VARIOUS INVESTIGATORS             23

 5      UNIVERSAL FORMS OF SCALAR AND VELOCITY
        SPECTRA                                           29

 6      CONCENTRATION OF VARIOUS ALUMINUM
        SPECIES IN EQUILIBRIUM WITH FRESHLY
        PRECIPITATED Al(OH)3                              36

 7      EFFECT OF COLLOID CONCENTRATION ON
        COAGULANT REQUIRED FOR DESTABILIZATION
        (AT CONSTANT  pH)                                  40

 8      FRACTIONAL CONVERSION AS A FUNCTION OF
        ACCOMPLISHED MIXING                             45

 9      ILLUSTRATION  OF CONDUCTIVITY PROBE           51

10      SINGLE ELECTRODE CONDUCTIVITY PROBE         52

11      PROBE IN PLACE IN TUBULAR REACTOR             52

12      BLOCK DIAGRAM FOR TEKTRONIX TYPE 3C66
        CARRIER AMPLIFIER                                54

13      AC BRIDGE CIRCUIT                                55

14      PROBE CONNECTED IN PARALLEL WITH
        120-OHM RESISTOR                                  57

15      TYPICAL CALIBRATION CURVE FOR SINGLE
        ELECTRODE CONDUCTIVITY PROBE                 59

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                     FIGURES (Continued)


                                                         PAGE

16      ELECTRONIC EQUIPMENT FOR MIXING
        EXPERIMENTS                                     60

17      SCHEMATIC ILLUSTRATION OF EXPERIMENTAL
        SETUP FOR MIXING EXPERIMENTS                  61

18      CUTAWAY VIEW OF INJECTION MANIFOLD
        AND GRID SECTION                                63

19      CUTAWAY VIEW OF PROBE SECTION                64

20      MULTIPLE-ORIFICE GRID                          66

21      INJECTION MANIFOLD AND GRID SECTION           66

22      HEAD LOSS COEFFICIENTS FOR SQUARE-
        MESH GRIDS                                        69

23      DECAY OF CONCENTRATION FLUCTUATIONS
        DOWNSTREAM FROM A GRID                        72

24      a1 vs. QT FOR GRID WITH M/d = 4                   75

25      EFFECT OF SCALE OF  TURBULENCE ON
        SCALAR  DECAY RATE                              77

26      EFFECT OF THE NUMBER OF ORIFICES ON
        SCALAR  DECAY RATE                              79

27      INVERSE RELATIONSHIP  BETWEEN NUMBER
        OF SOURCES AND a FOR GRIDS WITH M/d =4        80

28      EFFECT OF CHANGING ORIENTATION OF
        TRACER INJECTION SYSTEM ON SCALAR
        DECAY RATE                                      82

29      RESULTS OBTAINED FROM GEOMETRICALLY
        SIMILAR GRIDS                                     84

30      EFFECT  OF VARYING M                            85

31      GENERAL MIXING MODEL:  RESULTS FOR
        SEVEN GRIDS                                      90
                               vi i

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                     FIGURES (Continued)
32      EFFECT OF SEGREGATION ON COAGULATION-
        FLOCCULATION JAR TESTS

33      RELATION OF pH AND ALKALINITY AT
        "OPTIMUM" ALUM DOSAGES

34      INITIAL MIXING APPARATUS FOR CONTINUOUS
        FLOW COAGULATION-FLOCCULATION STUDIES

35      EFFECT OF INITIAL MIXING DEVICE ON
        FLOCCULATION PERFORMANCE: SINGLE
        COMPARTMENT, T = 5 MIN                        106

36      EFFECT OF INITIAL MIXING DEVICE ON
        FLOCCULATION PERFORMANCE: TWO
        COMPARTMENTS, T = 10 MIN                      107

37      EFFECT OF INITIAL MIXING DEVICE ON
        FLOCCULATION PERFORMANCE: THREE
        COMPARTMENTS, T = 15 MIN                      108

38      EFFECT OF SEGREGATION ON COAGULATION-
        FLOCCULATION: CONTINUOUS FLOW TESTS       109

39      EFFECT OF INITIAL MIXING ON FLOCCULATION
        PERFORMANCE:  COMPARISON BETWEEN FLASH
        MIXER AND NO INITIAL MIXING UNIT, ALKALINITY
        = 70 mg/l                                         110

40      SEGREGATION JAR TESTS FOR VARIOUS
        SEGREGATION TIMES -ALUM COAGULATION
        OF  RAW SEWAGE                                  113
                               vui

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                             TABLES


No.                                                            Page

 1       Types of Reactions Involved in Hydrolysis
         ofAl(III)                                               38

 2       Grid Characteristics                                   65

 3       Head Loss Through Grids at Various Velocities         70

 4       Aggregation Rate Coefficients for Continuous
         Flow Experiments                                      109

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                            SECTION 1

                  SUMMARY AND CONCLUSIONS
The purpose of this investigation has been to determine criteria for
the design of turbulent flow, tubular reactors for the initial mixing of
chemicals in water treatment processes using a biplane grid to inject
the chemical and produce the turbulence.  Initial mixing  is important
because certain physical-chemical  reactions,  if they occur before the
mixing of the chemical with the main stream,  are detrimental to pro-
cess performance.  Use of a grid initial mixer can provide a  more
rapid mixing of the chemical with the waste stream.  The principal
process under consideration was alum coagulation-flocculation of
turbid suspensions  in the clarification of surface waters.  Other pro-
cesses considered were  wastewater chlorination and chemical
coagulation of wastewater with alum or ferric  chloride.

A salt solution tracer and a single electrode conductivity probe used
in conjunction with  an AC bridge amplifier and an rms  voltmeter were
utilized to determine the parameters governing the mixing which occurs
when a tracer  is  injected into a tubular reactor through multiple
orifices.  An attempt was made  to correlate the results to allow pre-
diction of the mixing characteristics for other grids.

Two of the grids used in the mixing studies v/ere then utilized as
initial mixing units  in a pilot-scale  coagulation-flocculation of a kaolin
suspension,  and the results •were compared with those  obtained using
a flash mixer.  It was  possible to attain some  understanding of the
time of mixing necessary to obtain  better process performance.   It
should be emphasized that while  the prediction of mixing produced by
larger grids may be possible,  the larger grids will necessarily pro-
duce greater times  of mixing  and poorer process performance.  Part
of the  prototype  design problem  will be the construction of a fairly
fine grid rnesh in relatively large conduits.

Attempts were also made to determine whether the initial mixing
step is important in coagulation  or  chlorination of wastewater.
Specific conclusions follow.
MIXING EXPERIMENTS

Sections V and VI describe  experiments  intended to ascertain the
parameters which determine the degree  of mixing downstream from
a grid in a turbulent flow, tubular  reactor-  A summary of the results
is as follows;

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1.    Mixing in a grid type tubular reactor takes place in two stages.
      The first, termed wake-mixing,  takes place in a region very
      close to the grid bars as the tracer spreads out across^the^cross-
      section of the reactor.  The rms concentration fluctuation just
      downstream from the wake-mixing region may be less than 1%
      °f the calculated  initial rms concentration fluctuation, a^ =
      AT-y/QT/QM>.  However,  beyond the region of wake-mixing, the
      "point" concentration may still vary considerably from the
      spatial mean concertratioru  The second stage occurs in a region
      which begins at a point  several grid bar diameters downstream
      from the grid.  In this region isotropic turbulence and scalar
      fields exist,  and the decay of rms concentration fluctuations with
      time or distance from the grid can be plotted as a straight line
      on log-log paper.

2.    The scale of  turbulence has a definite effect on the scalar decay
      rate  in the region where isotropic turbulence is present   beyond
      the region of wake-mixing.  For  example, small grid bars result
      in a lower rate of decay than large bars, and the scale of turbulence
      is proportional to the grid bar diameter.

3.    The number of tracer injection orifices  per unit area of reactor
      cross-section does not appear to have a marked effect on the
      rate  of scalar decay. It does, however,  greatly influence the
      extent of wake-mixing and will be important when large conduits
      are considered for tubular reactors in prototype treatment plants.

4.    The direction of tracer injection (upstream or downstream)
      has a marked influence on the rate of  scalar decay (and also on
      the wake-mixing),  it being greatest when the injection orifices
      face  upstream.  As the turbulent flow field is essentially  inde-
      pendent of the manner in which the tracer is introduced, it
      must be concluded that the scalar decay rate must be dependent
      on characteristics of the scalar field —possibly the scale of
      segregation.

5,    Scalar decay downstream from a grid follows the relation

                          a1 n             _
                         	S. = <*" (x/d)"a
                           A

      where a' is the rms  concentration fluctuation, A is the mean
      concentration of the  tracer mixed with the main flow, ns is the
      number of orifices per unit area of reactor  cross-section,  a"
      is a coefficient which depends on the method of scalar injection,
      x is the distance downstream from the grid, d is the grid bar
      diameter, and a is the scalar decay rate which is dependent on
      the method of scalar injection and the grid bar diameter.

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      It appears that head losses incurred by grid mixing devices can
      be kept to less than 6 in. providing the M/d ratio,  the ratio of
      the center-to-center bar spacing to bar diameter,  is greater
      than about 3. 0 (solidity  less than approximately 50%).  Allowable
      head loss, of course, will depend on the specific details  of each
      situation.
TREATMENT  PROCESSES

The effect of initial mixing in three treatment processes, alum coagula-
tion of a kaolin suspension,  chlorination of wastewater, and chemical
coagulation of  wastewater, was  studied.  The conclusions for each
process  are given below:


Alum Coagulation of a Kaolin Suspension

7.    The crucial "reactions" which occur are very rapid.  This was
      demonstrated by the fact that in a continuous flow experiment,
      a high-speed flash mixer produced turbidity removals which were
      no better than those obtained when the alum feed solution was
      added directly to the first compartment of the pilot-scale
      flocculator, a very poor initial mixing situation.

8.    Performance  was  improved by using grid initial mixers (d = 1/8 in. ,
      M/d =4) in a  2-in. diameter tubular reactor.   One grid had 24
      tracer injection orifices; the other had 4.  The  value of ns,
      the injection orifice density, for  each was 7. 60 in. "2 and 1. 27 in."?
      respectively.   Improvement in performance over,  that of a flash
      mixer was obtained  with both grids,  and the 24-orifice grid per-
      formed better than the  4-orifice grid.  From the results obtained,
      it can be estimated that an orifice density of at  least 1. 0 in. ~z  is
      needed to effect a  significant improvement in performance.  From
      both a structual aspect and from consideration of  head  loss inside
      the grid bars, this fine a grid for a prototype plant may be some-
      what difficult  to construct.   Such techniques as  placing smaller
      grids  within larger grids would probably be necessary.

9.    It was found that the alkalinity of the raw water had a strong
      influence on the importance of the initial mixing step, the effect
      of  rapid mixing increasing  with increasing alkalinity.   This may
      be  due to the buffering  effect of the  alkalinity (the reaction rates
      and products appear to be  pH dependent),  or it may be  due to more
      direct action of the bicarbonate ion.   Jar tests which simulate slow
      and rapid initial mixing were utilized to demonstrate the effect of
      the alkalinity.   The  effect  was also  seen in the continuous flow
      experiments.

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Chemical Coagulation of Wastewater

10.    To determine whether the initial mixing step may be important
      in chemical coagulation of sewage, segregation jar tests
      similar to those used with kaolin were done with sewage using
      alum as the coagulant.   It was found that,  as with alum coagula-
      tion of a kaolin suspension,  the  rapid initial mixing did provide
      better  results.  More importantly, the  crucial reactions in
      sewage are  apparently  much slower than is the  case with kaolin
      suspensions.  This means that it is not necessary  to have the
      high scalar  injection orifice density required in the other pro-
      cess, and the resultant design difficulties  may not occur.

11.    While these results may be  extrapolated to include ferric
      chloride coagulation of sewage,  it has been found in other work
      that  in lime coagulation of sewage, the  initial mixing step does
      not appear to be critical.
Chlorination of Wastewater

12.    Several experiments (described in Appendices A and B) were
      done in order to determine if the initial mixing might be a
      crucial step  in that treatment process.   The results indicated
      that while at short contact times an improvement in performance
      (as measured by coliform survival ratio) can be found,  at
      contact times similar  to those found in practice no difference in
      performance could be  discerned. It does appear from the work
      of others that a. tubular (plug flow) reactor, as opposed to a
      back-mixed reactor,  may improve performance.

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                           SECTION II

                      RECOMMENDATIONS


The recommendations resulting from this study can be divided into
two general areas:  1) designing a grid for full-scale  plant experi-
ments and 2)  continuing studies of the  wake-mixing phenomenon.

The present investigation has shown that in pilot-scale operations,
initial mixing is an important step in alum coagulation-flocculation
of a clay suspension.   It remains to be shown that sufficiently rapid
mixing can be  effected in a full-scale treatment plant to provide  a
significant  improvement in performance.  Future studies in initial
mixing should  be directed toward this objective.

From the present studies it appears that wake-mixing may  be critical.
From the results obtained it can be estimated that an injection orifice
density of at least 1. 0 in. ~2  is needed to obtain a significant improve-
ment in performance.  The grid, however, must be fine enough to
allow the orifices to be spread evenly across the reactor cross-section.
With M/d = 3,  1/2-in. O. D.  bars  spaced 1-1/2 in.  center-to-center
would  be required for a biplane grid.  An orifice would be located
halfway between each grid bar intersection.   A grid consisting of one
row of bars would necessitate  1/2-in. bars spaced i in. center-to-
center (solidity = 50%).

It •would be  desirable  to have grids with orifice densities greater than
1 in. ~2.  To accomplish this, finer grids will have to  be constructed.
Placing  small  grids (e.g., 1/4-in. bars spaced 1/2-in. center-to-
center) within  larger  grids (e. g. ,  1-1/2-in.  bars spaced 6-in. center-
to-center) used to feed the coagulant into the  smaller bars is one way
of attacking the problem.

In such a demonstration it would be desirable to keep the head loss to
less than about 6 in.   Solidities between approximately 25% and 50%
•will usually accomplish this.

Since the effect of initial mixing depends upon the alkalinity of the
water, any plant-scale projects should be done with a  water of high
alkalinity, preferably greater than 100 mg/i.

One area of possible exploration is the use of grids at more than one
point along a tubular reactor.  It should be noted,  however,  that this
simulates backmixing, and if backmixing is detrimental to process
performance, the expected improvement may not be realized.

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Use of grid Initial mixers for other treatment processes should also
be considered.  It seems that rapid initial mixing can result in a
significant Improvement In chemical  coagulation of wastewater, a
process which is often found in advanced waste treatment schemes.
It is believed that the injection orifice density need not be as great as
that required for coagulation of kaolin suspensions.  While it appears
from the present investigation that the Initial mixing step in waste -
water disinfection Is not as  critical as first believed, the conclusions
reached are  only tentative,  and further research in this area merits
consideration.

Improvements in wake-mixing should be developed.  For example,
it was found  that when the tracer injection orifices faced upstream
wake-mixing provided less reduction In the concentration fluctuations.
Perhaps  mixing could be improved by placing the orifices so that the
chemical would enter at right angles to the flow.  Using square grid
bars  instead of round bars might Improve  performance.  It appears
that wake-mixing is the critical step, and  any improvement in this
area will probably  improve process performance.

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                           SECTION III

                         INTRODUCTION
In any water or wastewater treatment process which requires the
addition of chemicals,  the initial mixing step is often a poorly designed
aspect of the treatment scheme.  This has been largely due to ignorance
concerning the importance of initial mixing and the lack of any basic
rational design criteria.  In some respects it has been "essentially an
art" [  1] , and  most designs  have been made on the basis of personal
experience,  intuition,  and trial and  error.

Much of the contemporary mixing literature in the field of  sanitary
engineering has been confined to  the study of rotating impellor type
mixers and development of model laws applicable to  them.  Most
initial mixing units have been flash mixers;  short residence time
CSTR's utilizing high-speed impellers to produce homogeneous mixtures
through convective dispersion and turbulent mixing.

It is believed that a different type of mixer which reduces quickly the
segregation between the added  chemical  and the water stream can be  of
great importance in improving  the performance of water and  waste-
water treatment facilities.   When the chemical is added to  the water
stream,  certain crucial physical-chemical reactions, if  completed be-
fore segregation is eliminated, can  result in less than optimal per-
formance or the use of greater quantities of chemical than actually
needed.  In many processes a flash mixer cannot provide the required
very rapid rate of mixing.

Another  feature of the  flash  mixer is backmlxing — mixing between
fluid elements  which have been present  in the reactor for different
lengths of time.  A result is that reactants entering the mixer may
"react" with previously formed "reaction" products rather than with the
constituents of the water stream  which are of concern.   A  specific
example is aluminum sulfate coagulation-flocculation of a turbid
•water in which the alum entering the backmixed reactor can react with
previously formed floes instead of with turbidity-producing particles.

A tubular reactor with  characteristics close to plug flow would eliminate
the backmixing.  A type of tubular reactor which is fairly amenable to
analysis has a  square mesh  grid  of bars  placed normal to the axis.
As the flow passes through the  grid, turbulence is produced which can
be utilized to mix the two fluid  streams.   Orifices drilled in hollow
grid bars can be used to  inject  chemicals into the water stream.   This
allows the chemical to  be released at many points across the cross-
section of the pipe which may be  an important consideration in quickly

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reducing segregation.  Grids have been used extensively in studies
involving turbulence, and there have been a few studies  involving
mixing with such devices.
OBJECTIVES

The principal objective of this investigation was to develop criteria
for the design of turbulent  flow, tubular reactors, utilizing a biplane
grid to inject a reactant and to produce turbulence.  This objective
gives  rise to three related questions:

i.    What parameters of the turbulent flow field, the scalar (tracer
       or treatment chemical)  field,  and the  scalar material determine
      the "goodness of mixing" downstream from a grid initial mixer
       (e. g. , molecular diffusivity and intensity of turbulence may  be
       important factors)?  Implicit in this question is the necessity
      of defining "goodness of mixing, "

2.    What physical parameters should be used for design and scale -
      up of such initial mixers (e. g. , mean flow velocity,  grid bar
      diameter and grid solidity)?

3.    What level of "goodness of mixing" is necessary, and how
       rapidly must this be  achieved in order to attain a given level
      of performance?  It will be necessary to relate the level and
       rapidity of mixing directly to process performance.   This
       is a question which the present investigation answers only
      partially.  Most of the effort of this study was directed toward
      objectives 1 and 2.  However,  certain conclusions will be drawn
      from experiments performed with three treatment processes:
      alum coagulation-flocculation of a kaolin suspension in water,
      chemical coagulation of wastewater (with alum or ferric chloride),
      and chlorination of wastewater.
ORGANIZATION OF REPORT

Section IV is a review of turbulence.- mixing, and coagulation and
flocculation theory and experiments pertaining to this investigation.
A  short review of research involving the initial mixing step in sanitary
engineering is also  given.

Sections V and VI cover the experiments done to determine the parameters
which affect the degree of mixing downstream from a grid in a turbulent
flow, tubular  reactor (objectives 1  and 2).  A single electrode conductivity
probe was used to determine the root-mean-square concentration
fluctuations produced by  various grids.  An attempt was  made to
correlate these results in a manner which allows prediction of the
"goodness of mixing" produced by any square mesh grid.   Also covered
are experiments to  determine head or energy loss which results from

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grids being placed in a tubular reactor.   In some instances,  the
allowable head loss will be restricted to not more than a few inches,
while in others  several feet may be available.

In Section VII experiments are described which reveal the importance
of the initial mixing step in alum coagulation-flocculation of a kaolin
suspension in water.  Two of the grids studied in experiments  described
in Sections V and VI were used as initial mixing devices in a pilot-
scale study.  Results  produced by them were compared with results
obtained with a  flash mixer and "with no initial mixing unit.  The effect
of alkalinity of the raw water on the importance of the initial mixing
step was also studied.  Jar tests which can be used to determine the
significance of  initial  mixing for a given process  and raw water are
described.  Also  covered is alum coagulation-flocculation of waste-
water.

Appendices A and B cover the experiments concerned with initial
mixing  and chlorination of wastewater.  This aspect is presented
in appendices because the experiments were limited in nature and
the  conclusions drawn are tentative.

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                            SECTION IV

     REVIEW OF FUNDAMENTAL THEORY:  TURBULENCE,
                   MIXING AND COAGULATION


ISOTROPIC  TURBULENCE

Turbulence  is a phenomenon associated with a fluid flowing at a high
Reynolds number.  This fluid may be the atmosphere or water flowing
in a river.   The conditions under which turbulence occurs are very
diverse.  Its defining characteristic is random fluctuations of the fluid
velocity.  Hmze [ 2] has defined turbulence in the following way: "Tur-
bulent motion is an irre'gular condition of flow in which the various
quantities show a random variation with time  and space coordinates,
so that statistically distinct average values  can be  discerned. "  This
report will be primarily concerned with a particular type of turbulence -
that produced by water flowing through a biplane  grid of bars placed
in the cross  -section of the pipe.   As will be seen,  this type,  (isotropic,
decaying  turbulence) is  fairly amenable to theoretical analysis,  can be
simply produced in the laboratory,  and has been extensively studied.

The concept of turbulence in a particular system is very  closely
associated with the energy being dissipated  in that  system.  In ordinary
pipe flow, for example, an energy loss will occur due to  •wall friction,
and this energy  is lost from  the system through the dissipation of heat.
Approximately half of the energy  lost from the flow produces heat
directly through internal viscous  friction associated with gradients Ln
the flow.  The other half of the energy goes first to turbulence pro-
duction and then to heat.  In  grid-produced turbulence probably most
of the energy goes into turbulence production.

Turbulence  is a random phenomenon; a Fourier  analysis  of the instan-
taneous velocity fluctuations at a  point in a turbulent flow field will
show that the fluctuations can be associated with a  range  of frequencies.
The lowest frequencies  will be determined by the geometry of the
physical system, while  the highest frequencies will be dominated by
viscosity effects.  These velocity fluctuations are related closely to
the kinetic energy of turbulence.   The turbulent  kinetic energy is
distributed over the range of frequencies with a  distribution termed
the energy spectrum.  It has been found that energy introduced into a
system at lower frequencies  is dissipated by viscosity at higher fre-
quencies.  This  results in a  transfer  of energy from lower to higher
frequencies.    The form of the  energy spectrum and the laws governing
the transfer  of energy have been studied extensively in order to under-
stand better  the  phenomenon of turbulence.

A qualitative picture of turbulence has only limited value, and a more
detailed quantitative description is necessary.  For a more complete
                                  11

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coverage of the topics discussed herein, reference is made to Hinze
[ 2],  Lee [ 3],  Brodkey [ 4],  and  Batchelor [ 5].

If a grid is placed in a pipe through which water (or any fluid) is
flowing, turbulence will be produced downstream.  Because energy is
added only at one point, the turbulence will decay with time (and
distance downstream) because of the action of viscosity.  Homogeneous
turbulence is that which does not change itr character with translation
with a set of coordinate axes.  Isotropy, a stronger condition which
includes homogeneity,  occurs if the character  of the turbulence is
such that its statistical features do not change  with rotation or reflection
of a set of coordinate axes.  While turbulence produced by  a grid decays
in the downstream direction,  isotropic turbulence is closely approximated
in these experimentSj and comparison between them and  isotropic theory
shows good agreement.
Root-Mean-Square Velocity and Correlations

If the velocity in the direction of flow downstream from the grid is
measured with a hot-wire anemometer,  it will be found to consist of a
mean and a fluctuating component:  U1  = U1  + ut (Figure 1).

An important parameter of turbulence is the root-mean-square velocity
fluctuation:
                            u{  =Vuf
(i)
where the overbar indicates averaging.  This is called the "intensity
of turbulence. "

Isotropy requires that all three components of the rms velocity
fluctuations be equal,  i. e.

                        u< =U{  =u<2 =ui    .                    (2)


The nature of isotropic turbulence also requires that there be no cross
velocity term,  that is
                        u2 = ut u3  = u2u3  = 0   .                (3)

These terms are the Reynold's stresses and are the contribution of
the turbulent motion to the total shear  stress.  In isotropic turbulence
there is no shear  stress and no gradients of mean velocity.

Taylor [  6] first pointed out that in turbulent flow there will be a
statistical correlation between the fluctuating velocities  at two points
                                 12

-------
             0
             o
             o
       U,
                                                              u,
FIGURE 1.  MEAN AND FLUCTUATING COMPONENTS OF VELOCITY
 a small distance apart, with correlation decreasing as the separation
 distance increases.  A statistical analysis can be made by studing
 the mean product of the fluctuating velocity components at the two
 points.

 Correlation tensors and correlation functions  can be defined by con-
 sidering the fluctuating velocities at two points separated by a dis-
 tance  r.
                                  13

-------
Two correlation functions  are widely used in the study of turbulence;
The longitudinal correlation function, f(r), and the lateral correlation
function, g(r),
                             u (x)  u  (x+r)
                        ,  >    n    n
                       g(r) = —         	
                                  u'2
The subscript r denotes that the velocity fluctuation is measured in
the same direction as the vector r"   The subscript^ indicates the
velocity fluctuation is measured normal to vector r,   Batchelor [ 5]
has shown that only one scalar function is necessary to specify the
velocity correlation at two points in  isotropic turbulence-   Therefore
g(r) and f(r) cannot be independent.   They are related by

                                            (\
                                       l^rM      •              (6)

If the separation distance is  reduced to zero, the values of f(r) and
g(r) become unity.  As the separation distance is increased,  the
correlation functions  decrease (see Figure 2).

In defining the above correlation tensors and functions, a  Eulerian
viewpoint has been taken with the correlation between velocities at
two fixed points in the flow field separated by a  distance r considered.
It is also possible to define Lagrangian correlation functions which
would correlate the velocity  fluctuations of a fluid particle at two
different times along  its path of travel, For a more complete dis-
cussion  of Lagrangian correlations see Hinze [ 2] or Brodkey [4]


Scales
The correlation functions given by Equations (4) and (5) can be used
to define certain scales of turbulence,   The longitudinal and lateral
integral scales are defined respectively as
                                 CD
                                   f(r) dr
                                i
                              o-
                                  CO
                         L   =   f  g(r) dr
                          5  n J
(8)
                                    14

-------
      1. 0
   FIGURE 2.   LOGITUDINAL AND LATERAL CORRELATION
       FUNCTIONS AND LATERAL  MICROSCALE,  \ ,  FOR
                     ISOTROPIC  TURBULENCE
                         g
These scales can be considered measures of the longest distance which
results in a finite correlation between the velocity fluctuations at the
two points.   In turbulent flow, attempts are often made to relate L£
and Lg to the geometry of the system.  For example,  in pipe flow L£
may be taken as  a certain fraction of the pipe diameter.  In grid-
produced turbulence attempts have been made to relate L.. to the bar
spacing or bar diameter.

Since f(r) a.nd g(r) are related by Equation (6),  L. and L  must also
be related.   The equation  is                           °
L  = 1/2
 g
                                                                (9)

-------
Two other important scales 'can be defined from the functions f(r) and
g(r).  These scales are related to the shape of the  correlation functions
near r = 0,   It is possible to expand f(r)  in a Taylor series:
            f(r) -
21
                               r =o
                                    4!
                                                                 (10)
                                               r =o
For very small values of r, f(r) approaches a parabolic function of r.
It is possible to introduce a length X,. such that
     f(r)= 1 - f
                                                                 (ID
Where X  is called the microscale of turbulence   Ignoring the higher
order terms in Equation (10) and equating Equations (10) and (11), it
follows that                   i
l/Xf2 =   1/2
                                                                  12!
                                           '=O
A similar  scale, X  .,  is defined by
                  O
                                                                  131
                                          r =o
From Figure 2,  it can be seen that X.  is the intercept along the r
axis of a parabola "whose curvature af r = 0  is the same  as g(r).
X.. can be  interpreted  similarly.

It  is known that X is closely related to the velocity fluctuation fre-
quencies at which the most dissipation of turbulent energy  into  heat
takes place.   For this reason,  it is often called the dissipation scale.
The relation between  \. and X  is
                       f      e
       Xr  = X
                                                                 (14)
Energy Spectrum Functions in Isotropic Turbulence

It was previously qualitatively stated that  it was possible to view the
kinetic energy of turbulence as being distributed over a range of
frequencies   In 1938 Taylor [ 7]  showed that there is a relation
                                  16

-------
between the one-dimensional energy spectrum function — that is, one which
considers the velocity fluctuations  in one direction only —and the correla-
tion function f(r).

Ej (kj  ) is the one-dimensional energy spectrum function associated with
the wave number kj .     t

                              k, = £•£?-
                                    Ui

where Uj is the mean flow velocity and  n is the frequency.   The sum of
Ej (kj  ) over all wave numbers (or  frequencies) must equal the total
turbulent kinetic energy in the Xj direction, or the mean square fluctua
ting velocity:
                                  	
                             dkj  =uf   = u'2                     (16)
Taylor  showed that the longitudinal correlation function f(r) and one-
dimensional energy spectrum functions are Fourier cosine transforms
of each other,  i. e. ,
                             00       '

                f(r) =  -V J Ei (ki ) cos (ki r) dki               (1?)
                       u   o
                                00
                         7     f
                E'
                             O'
             00

(kj )  =|u'2 ff(r) cos (kj r) dr     .           (18)
There is also a three-dimensional energy spectrum function E(k, t),
defined such that:
     r*           3
     J E(k,t) dk =| u'2
                                                                (19)
The one-dimensional energy spectrum function is related to E(k, t) in
the following manner.
                            r"0       /    k  2 \
                E! (k! , t) =  J  EIjp-)  ( 1  - ^J-  ) dk    .           (20)
                          ki         \        /

Universal Equilibrium

It is known that the geometry of the physical system in which the flow
is taking place strongly affects the character of the low wave number
range of the turbulence  spectrum.  As has been noted, the integral
scale has often been related to a physical length involved,  e. g. , the
pipe diameter  in pipe flow.  An  equation can be derived [  2] relating
Ej (o, t) and L,.  However,  it is  found that at the higher wave numbers
                                 17

-------
under  certain conditions,  i. e. ,  high Reynolds number, the form of the
spectrum is independent of the conditions  in a particular turbulent
flow and. are universal in character.   This theory was first proposed
by A. N. Kolmogoroff in 1941  [ 8-10] and  is usually known as the
theory of universal equilibrium.   It states that athigh wave numbers,
the turbulence is  isotropic (no matter what the character of the over-
all turbulence may be) and that the spectrum in this universal equilib-
rium range will depend only on the rate of energy dissipation or
input,  £,  and on the kinematic viscosity, v.

Dimensional analysis reveals that a characteristic length and velocity
can be  defined in  terms of & and v.  They  are  respectively,

                                                                un


                           v=(ve)        .                      (22)
The length scale, T|,  is often called the Kolmogoroff microscale of
turbulence.  It should not be confused with \f and \g which were
discussed earlier and which are associated with G.I. Taylor.   i / T)
= k^ can  be taken as the wave number at which the  maximum of the
diss ipation spectrum,  k2  E(k, t), occurs.

A Reynolds number based on Equations (21) and (22) can be defined
and  its value is equal to unity.
                                  = i
                               V

This means that at the Kolmogoroff microscale, the inertial and
viscous forces are balanced.  A higher wave numbers viscous
forces become predominant.

In order for the equilibrium range to exist,  the energy input by
transfer must equal the energy dissipated by viscosity, or
                   3 Id u'2'
2ldt  .
                             = 2 v  J k2 E(k,t) dk   .             (23]
This will occur only if the wave numbers associated with the scale
Lf do not overlap with the wave numbers associated with the maximum
dissipation,  or r\ <« Lf.

In terms of Reynolds number, this condition  [ 2] is:

                                           L  •                   (24)
In the universal equilibrium range,  a dimens ionless function can be
found to relate E(k, t) to v and r\.   Dimensional analysis shows that

-------
                       E(k.t) = v2 TI E (kri)                       (25)
                                     e

or, substituting in Equations (21) and (22),


                     E(k,t) = v5/4 e1/4  E (kr|)    .               (26)
Thus,  spectra,  E(k, t), can be plotted in universal form by dividing by
v5'4  e1 '4 and plotting against kt|.  The same holds for the one -dimensional
energy spectrum [11],


                     E! (kt t) =v5/4  e1/4 E! ^ r$  .            (27)


An important corollary to the theory  of universal  equilibrium is that
for Reynolds numbers much higher than that given by Equation (24),
there is  a subrange of wave numbers for which the form of the  spec-
trum no  longer depends  on viscosity, but only on &.  In other words,
energy is transferred in at the lower end of the wave number range
and is transferred out at the higher end of  the range.  No production
or dissipation of energy takes place.   This is called the inertia!
subrange.

Hinze [ 2] concludes that the  requirement  for an inertial subrange to
occur is

                                               '               (28)
Gibson [11] derived the following criterion for the existence of an
inertial subrange:

                             u'Lf
                             - - > 3. 3 x 10s  .                (29)

It has been found that these criteria are essentially impossible to meet
with laboratory produced turbulence.   Experiments have been done  in
the ocean [ 12], however, with a Reynolds number, based on the channel
depth,  of  10 8-  It was found that an inertial subrange did exist and
extended over a wave number range of two orders of  magnitude.

This conclusion was  made by comparing measured spectra with the
form of spectra derived through dimensional analysis for the inertial
subrange.

                      E! (kj  , t) = A!  e2/3  kj " 5/3    .          (3Q)
                                  19

-------
A  similar equation exists for the three -dimension spectrum,


                       E(k,t) =A e2/3  k'5/3     .                (31)


It  is widely accepted that this is the form of spectrum in the inertial
subrange.

For values  of k > kT,  in the universal equilibrium range, the dependency
                  r±                                             _
on k is much greater,  A relation [ 13]  which agrees fairly well with
experiment is:

                                       k-7    .                 (32)
Hinze [ 2]  has noted certain errors in the derivation of Equation (32).
A  summary of the above spectra "forms  and the wave number ranges
is given in Figure 5 in the section on Review of Mixing Theory.
Decay of Isotropic  Turbulence

The mixing which occurs downstream from a grid is  in part governed
by the decay of the intensity of turbulence and the variation in the
scales of turbulence with increasing distance from grid.  For this
reason it is important to review the theoretical and experimental
work in this field.  As noted, isotropic turbulence  is easily produced
by passing a fluid through a grid of bars.   Development of the hot-
wire and hot-film anemometer have led to  a great deal of experimenta-
tion,  most of which has  been done in air.

As  the fluid passes through a grid with a center-to-center bar spacing,
M,  and a bar diameter,  d,  turbulent wakes are produced behind the
grid bars a,s a result of  vortex shedding.

This initial turbulence is highly anisotropic.   However,  these wakes
gradually coalesce and the  resulting turbulence is reasonably close to
isotropic.   The  distance downstream at which this  occurs  is approximately
20 M.

Between 20M and 100 M to  150 M downstream, the  initial period of
decay occurs.  In this period, inertial forces  are predominant in
determining the decay.   At distances greater than approximately
500 M downstream, the  Reynolds number of turbulence is  very  low,
and viscous forces predominate.  As has been noted, the Ka.rma.n-
Haworth equation is soluble in this case, and the decay of the intensity
of turbulence has been found to follow the solution,


                       u12 = const x t" 5'2                       (33)
                                20

-------
•where t is the time.

In the initial period of decay,  which is of greater interest, the most
well-known decay law is that proposed by Batchelor and Townsend [ 14]:
                             C
                              D
                     u,2
x-x
     o
                                    M
                                                                (34)
where c is a constant depending on grid geometry, Crj> is the drag per
unit area of the grid,  x is the distance downstream from the grid, and
x  is the distance from the grid of the apparent origin of the intensity
of turbulence.   For round-bar,  square-mesh grids,  C-p can be obtained
from [ 2].

                             _ (d/M) (2 - d/M)
                         ^D ~    (1  - d/M)4       '

Van der Hegge Zijnen [15]  has  reviewed the  experimental work of
several  experimental investigators,  including Batchelor and Townsend.
He found that no general law such as Equation (34) holds for all ex-
periments.   The rate of decay of u'  (i. e. , the exponent in an equation
of the form u'  = Kx~r) with distance varied from 1/2 as proposed by
Batchelor and Townsend to - 5/7, a value derived by Frenkiel [ 16].
Van der Hegge Zijnen found that it was possible to obtain a  reasonable
correlation between the data of five  different  investigations  by plotting,
MI '/Uj against (x-x )/d.  There is considerable  scatter which, makes
it  difficult to rely on the graph to predict actual values of u1 for applica-
tion under a particular set of circumstances.   The data are shov/n in
Figure 3.

It  should be noted that,  strictly  speaking,  it is inconsistent  to plot
results as shown in Figure 3. It implies that there should be no
dependence  of u1 on M/d.  This  ratio strongly influences the head loss
through the  grid which determines the turbulent kinetic energy produced.
Inspection of Figure  35  however, shows  no consistent dependence of
u1  on M/d.  The  conclusion which must be drawn  is that other factors
such as experimental error must have produced  differences in the
results which hide  the dependence on M/d.

Van  der  Hegge Zijnen also compared results of six separate investiga-
tions of the variation of the integral scale,  L., downstream from a
grid.  L./d  is plotted against  (x-x )/d.   M is  the other parameter
often reiated to the scale of turbulence.  Examination of Figure 4
shows no apparent  dependence an M/d.

-------
po
10. 0.



 8. 0
                 60
                 4. 0
                 2. 0
1. 0


0. 8




0. 6





0. 4
                                 10
                                  111
                                              ,v.

                                             A  a
                                                 A  *
                                                         V

                                                         *
                                                     • I
                                                     I •
                                       *
                                        i
                                      •
                                                           • •
A M/d = 2. 0



V M/d =2.7


• M/d =4

• M/d = 5

O M/d = 8. 0
                                             1      1    1    1
                                                               1    1
                                                                '•  BaB,
                                                                            ••   «•
                                                                                     •*•
                                                        I
                     10
               20
40     60   80  100


            (x - x )/d
                  o
                                          200
                                                                400    600  800  1000
                  FIGURE 3.  DECAY OF TURBULENCE AS MEASURED BY VARIOUS INVESTIGATORS

                                      (FROM VAN DER HEGGE ZIJNEN [ 15])

-------
10
8.0
6. 0

4. 0

2. 0
T3
M-l
J
1.0

0. 8
0.6
0.4
1 I 1 1 1 1 1 1 1
- « -
. •£*ft»*"** -
••• • • .? •• • *r*
'mf. • s**r
-•"."V"^4₯*|'V *
•• •** ^° s^* *
A . v D M/d = 1.5
A M/d = 2. 0
£ v V M/d = 2. 7
— D _
• M/d = 4
9 M/d = 5
0 M/d = 8. 0
1 1 1 1 1 1 1 1 1
20 40 60 80 100 200 400 600 800 1000 200
(x - xo)7d
FIGURE 4.  INTEGRAL SCALE OF TURBULENCE AS MEASURED
                BY VARIOUS INVESTIGATORS
            (FROM VAN DER HEGGE ZLJNEN [15])

-------
REVIEW OF MIXING THEORY
Criteria for Mixing

In a study of mixing  it is first necessary to define the terms involved.
Brodkey [ 4] defines mixing to mean a blending into one mass "a
complex of two or more ingredients .  .  „  which, however thoroughly
commingled,  are conceived as retaining a separate existence. "  This
definition, however, does not allow visualization of the mixing process.
Consider, for  example, the addition of a small amount of salt water to
a beaker  of fresh water.  If the water is stirred, the salt will become
spread throughout the beaker.  Soon the salt concentration at all
"points" throughout the beaker will be the same.  The mixing can then
be said to be complete.  By a "point"  is meant the  smallest volume
which is still very much larger than the dimensions of the molecules.
How small this volume  must be is  not easily defined,  Brodkey [4]
states that it must be submicroscopic, i. e. , smaller than that which
can be seen with the best microscope.   Gibson [ 11] states that it
must be smaller than that volume associated with microscale of scalar
fluctuations, a term which will be  defined later.  The term scalar
is used to denote  any tracer, contaminant, or chemical which is added
to and mixed with the fluid.  All correlations defined with a scalar
are also scalars whereas correlations defined  with velocities (a vector
or a first-order tensor) become higher-order tensors.  A scalar  is
a zero order tensor.

Before proceeding further,  it is  necessary to differentiate between
the terms mixing, diffusion,  and dispersion or  bulk diffusion.   Dif-
fusion should be more precisely termed molecular diffusion.  It is
due to the Brownian  motion of individual molecules.  Molecular
diffusion  is very  important  in the mixing process with which this pro-
ject is concerned.  The turbulence can act to create very small blobs
of scalar material, but even the  smallest scales of turbulence cannot
act to eliminate all variations in "point" concentration.   Molecular
diffusion must function  in conjunction with the turbulence to accomplish
complete mixing.   If turbulence •were not present, the mixing would
eventually be completed by diffusion.  However, the time required
would be quite long.  The random motions of turbulence break large
blobs of scalar material down into  the smallest blobs upon which
molecular diffusion can act with greater effectiveness.  A slightly
different  interpretation by  Corrsin [ 17]  is that the turbulence causes
an increase in the local, instantaneous concentration gradients which
allows molecular  diffusion to act more effectively.

The term dispersion is used to describe the spreading of a scalar  in
a flow field due to steady state spatial variations in the flow velocity.
The terms diffusion, bulk diffusion, or  Taylor  diffusion are often
used, but these are misleading because they tend to be confused with
molecular diffusion.   Consider for example, turbulent flow in a pipe.
If a tracer is released from a point source in the center  of the pipe
                                  24

-------
the turbulence will tend to spread the tracer across the cross-section.
Near the walls, the velocity will be lower which will cause the tracer
to disperse longitudinally to a greater extent than would be produced
by the turbulence alone in a uniform velocity field.   This  type of
phenomenon also  occurs in  laminar flow.  Molecular diffusion,  rather
than turbulence, causes the lateral spreading  in this case.

This project is concerned with the mixing which takes place down-
stream from a turbulence-producing grid.   Only  in the region very
close to the  grid bars will gradients of temporal  mean velocity  exist.
The scalar field will be inhomogeneous  in this region as there will
exist-gradients of  mean concentration.  The processes which occur
here are very  complex and  difficult to treat mathematically.  Con-
siderable experimental work has been done  on the turbulent wake
produced by a.  circular cylinder [ 18, 19].   Mixing and chemical
reactions in the wake of a cylinder have been studied for the case of
two-dimensional spreading  [ 20, 21],  Such results  might  be expected
to apply to a grid in the limit as  the spacing of the bars increases.
They clearly do not apply to the situation encountered in this  study
where the maximum M/d  ratio was 4, 0  and where the spreading Is
three -dimensional.,  Therefore,  as has  been done by previous investi-
gators [ 1 1, 22] , the problem of turbulence and transport  in the vicinity
of the  grid bars will be treated empirically  and,  consequently,  some-
what superficially. That  it is done in this manner does not mean that
the mixing which takes place in this region is unimportant.   In fact,
it will be found that most  of the decay of concentration fluctuations
occurs in this  region.

Further downstream, the tempcral mean value of the tracer concentra-
tion will become constant across the cross-section, even though the
rms concentration fluctuations at a given point will not be zero.  The
scalar field will become isotropic and will become  amenable  to theoret-
ical analysis.
Basic  Definitions in Mixing

It will be seen that the basic equations used in mixing will bear a close
resemblance to equations used to  describe turbulence,  An isotropic
scalar field is very similar to an  isotropic turbulent field,  with the
exception that  scalars  rather than vectors are involved.   It is possible
to view the mixing process as being analogous to the dissipation of
turbulent energy.  When large blobs of scalar material are added to a
fluid,  in terms of the scalar spectrum, these large blobs represent the
low wave number range.  The turbulence then acts to create smaller
blobs which correspond to higher  frequency,  or  higher wave number,
fluctuatrons.   Finally,  at the highest wave numbers, molecular dif-
fusion acts to spread out the smallest blobs in a manner analogous to
the  way viscosity damps out the highest frequency velocity fluctuations.
                                  25

-------
Consider an isctropic scalar field downstream from a grid.   No spatial
variations in temporal mean concentration exist.  At a particular point,
the instantaneous concentration can be taken equal to the sum of the
mean value plus a fluctuating value.

                               A = A + a   .                     (36)


This is similar to the expression for instantaneous velocity with the
exception that vector notation is no longer required.

As with velocity,  the rms value of the concentration fluctuations can
be defined:

                              a' =VlP.                       (37)


Dankwerts [  Z3]  defined the mean square concentration fluctuation
divided by the initial mean square concentration fluctuation to be the
intensity of segregation,  i. e. ,
                             s   a '2     .                       (38)
                                  o

This parameter, or its square root; will be used to indicate the
"goodness of mixing" obtained  in a given system.  When the scalar
is completely unmixed with the fluid to which it has been added,  I  = 1.
When the mixing is complete, and there are no deviations from the
mean concentration,  I  =0.  1 -~y I  is sometimes  defined as the
"degree of mixing'1 [ 24].

Dankwerts has defined another important parameter of mixing — the
scale of segregation.
                                 CO
                            L  = f  C(r) dr                      (39)
                               oj

where                         	
                         r*t  \   a(x) a(x-fr)
                         C(r) =	^72	     •                 (40)


C(r) is the Eulerian concentration correlation.  It is analogous  to the
Eulerian correlation function for velocity fluctuations.  Lg  may be
considered to be indicative of the size of the largest scalar blobs.

A scalar microscale,  X ,  can also be defined from the C(r) vs. r
curve.
                                  26

-------
  1   _ _ _!_
X 2     2
 s
                                   8r2
                                           r =o
Again,  this is analogous to the Taylor microscales,  \  and \ .
                                                     O

As with velocity spectra, considerable effort has gone  into determining
the shape of the  spectral curve in different wave number ranges.  This
investigation will be concerned with the case where the scalar material
is added to a liquid-   Under these conditions, the Schmidt number, NC^ ,
= v/D  the ratio of kinematic viscosity to molecular diffusivity is
much greater than unity.  Under  conditions of mixing in a gas,
v/D « 1 and the spectral "curve has a different shape.  The  reason for
the difference in shape is related to the fact that under conditions of
high and low Schmidt numbers, the wave  number at which molecular
diffusivity becomes important is  either much higher or much lower
than the Kolmogoroff wave number.   Thus, for  v/D« 1, molecular
diffusivity becomes effective in a wave number  range k < kj^ where vis-
cosity is not  important.  For v/D»  1, scalar transport due to con-
vection is  important at the higher wave numbers where viscosity has a
strong effect on the velocity spectra.
Considering turbulence in a liquid with a fully developed inertial sub-
range,  for -wave numbers k    « k « kt^ the form of the scalar
   6                       Oj, S          ^
spectra has been found to be

                     Es(k)  = B e/1/3  k"5/3                     (42)


where B is  a constant coefficient, and £s is the time rate of "dissipation"
of the mean square concentration fluctuation.

This  is called the inertial-convective  subrange because inertial forces
dominate  the velocity spectra  and convective  transport dominates the
scalar  spectra for corresponding wave numbers.   Batchelor [ 25] showed
that scalar  transport due to convection and transport  due to diffusion
become of the same order of magnitude at a wave number,
                            kB
                     1/4
                 T~I         .             (43)
                                    m
This is analogous to the Kolmogoroff wave number k^.  If D   « v,  it
follows from Equations (21) and (43) that kg » kj,.

For wave numbers k^ « k « kg, Batchelor determined that the
spectrum should take the form:
                      Eg(k) = A (£)  l  \ k"1      .              (44)

-------
 This is called the viscous-convective subrange,  because while con-
 vective transport is  still dominant, viscous diss ipation becomes
 important in the corresponding velocity spectrum.

 Figure 5  shows the form of the scalar spectra discussed above as well
 as that of the universal equilibrium range for turbulence.  It should be
 noted that the  shape  of the scalar  spectrum depends on that of the
 velocity spectra and if the Reynolds number is not high enough to pro-
 duce the  complete  universal spectrum shown in Figure 5, then the
 scalar  spectrum will also be altered.  As was noted previously,  a
 fully developed inertial subrange cannot be expected to be found in
 laboratory-produced turbulence.   Therefore, the resulting universal
 scalar  spectrum of Figure 5 cannot be expected to be  found either.
 However, this should not  prevent  these concepts from being used.  The
 Reynolds number necessary for universal equilibrium to occur can be
 easily obtained.  Several  investigators  [ 2, 11,26]  have  examined
 velocity spectra and found a universal form.  Usually, a line with a.
 -5/3 slope, corresponding to the inertial subrange, can be drawn
 tangent to the  experimentally-determined  spectrum curve.  Therefore,
 as a first approximation,  the characteristic spectra of Figure 5 can
 be used in the study  of laboratory-produced turbulence and the mixing
 resulting therefrom.


 Decay of  an Isotropic Scalar Field

 When an  isotropic  scalar  field is superimposed on a decaying  isotropic
 turbulent velocity field, it will decay in a  manner at least partially
 dependent upon the velocity field.  Only recently has this  rate of
 decay been studied experimentally or theoretically.

 Usually the rate of decay  of the intensity  of segregation in isotropic
 decaying  turbulence has been represented by an equation of the form:


                                                                (45)


                                                                (45a)
where a,  a\  are coefficients,  a is the decay rate.  Only two investiga-
tions [ 11,22,26,27] have been made concerning the  decay of an
isotropic  scalar field in water (high NSC case).   The resulting data
were shown to fit  such a  curve although the relationship of the
coefficients a and a to the physical parameters  involved remained
uncertain.

Hinze [ 2] derived a relation for scalar decay based  upon  the Karm-an-
Howarth correlation equation for a scalar field,  the assumption that
the form of the scalar correlation function maintains its shape  during decay,
                                 28

-------
   w
   o
   o
   o
   5
   w
   o
   o
                             ___„__   E(k)
                             .,_—_.-   E (k),  v/D
                                          s

                       INERTIAL-CONVECTIVE
                        SUBRANGE (-5/3)
                        rn
INERTIAL
SUBRANGE
  (-5/3)
                          \
\
VISCOUS -
CONVECTIVE SUB-
RANGE (-1)
  \
   \
    \
                                 \
           HIGHER WAVE
           NUMBER RANGE
                 (-7)
                                K
                     LOG (£/v3
                     LOG (e/vD 2 )* /4
                               rn
                                    LOG k
          FIGURE 5.  UNIVERSAL FORMS OF SCALAR AND
            VELOCITY  SPECTRA.  (FROM BRODKEY [ 4])
and Batchelor and Townsend's linear decay law for  isotropic turbu-
lence (Equation 34).  His equation is
                                 /    x-3/2
                                 /X-X \
                           T  _ r{ _,	o )
                           I  - O\ -~—:  /
                           S     -x lVl /
                                    (46)
Note that a value for C is not given in this derivation.

Gibson [ 11]  derived Equation (45) by dimensional analysis, assuming
that the rate of decay of a'2  was dependent only on U,  M, t, and aQ'2.

-------
Recently, Corrsin [ 17, 28] has attempted to derive relations for the
rate of decay of scalar fluctuations in decaying and nondecaying
isotropic turbulence for different values of Schmidt numbers.  The
case of interest here is high Schmidt number and decaying turbulence
[  17]-

The mass transfer equation for the case_ of a homogeneous scalar
field with a conservative tracer (i. e. ,  A = constant) is


                    -fj +u. |^  =D  V2 a    .                  (47)
                     3t     i 8x.    m
                              l


One can  convert this  equation to a more useful form [  2] by multiplying
by a,  averaging,  and putting u. inside the derivative.
                    dt
                                                               (48)
The scalar microscale is related to the derivative products in such a
way that
                                       D
                                  _
                            dt          m  \ 2     '
                                             s

A corresponding equation can be derived for the mean square velocity
fluctuations from the Navier-Stokes equation:

                           ui '2          Uj l2
                              ---2Qv-     •             (50)
Dividing (49) by (50), one obtains the relative decay equation:


                          u, '   da1   _ 1 i  f n/2
                          a'    duj '    5 N  \X
                                           s \  s

Equations for Xf and Xs in terms of the three-dimensional velocity and
scalar spectra can be developed
                                   CO

                                    k2 E(k) dk
                                 30

-------

                                   Es(k) dk

                                E  (k) dk
                                  s
 Corrsin's method was to use the characteristic spectral form shown
 in Figure 5 to obtain values for X£ and X-s.  These  in turn were sub-
 stituted into Equation (6i).  Corrsln did make one deviation from the
 spectra shown in Figure 5 in that he ignored the higher wave number
 range of the velocity spectrum and used a purely inertial spectrum.
 His  assumption was that the higher  wave number range would not
 contribute significantly to either integral in Equation (52).

 Corrsin's final equation, bypassing  the intermediate steps, Is
             da
                 i
                                            N
c
OC
                                          /3     c 3/ 2  log
                                                                (54)
All the terms in the equation have been defined previously.
It is instructive to examine the influence of the various parameters on
Equation (54).   The Schmidt number appears  in two places.   In the
numerator,  if NSC > 10, its effect becomes insignificant.  This is  the
s ituation with which this project shall be concerned.  In the denominator,
log NO   appears.  The rate of decay is  weakly dependent on Ngc, but
note that if Ngc = v/Dm -*•  co, log NSC  ~~*«> also, and the rate of decay
of a'goes to zero.  This means that  if the molecular diffusivity is
zero, mixing will not occur.  This effect of no molecular diffusivity
was noted earlier.

It is important for this project that the dependence on Ngc should be
weak.   The tracer used in  the mixing experiments necessarily has a
molecular diffusivity different from the  chemicals to be used in the
treatment processes.   In fact,  since the chemicals  will be undergoing
reactions during the mixing process, their diffusivity will probably
be undergoing changes as mixing occurs.  Very weak dependence of
the mixing rate on the molecular diffusivity means that results ob-
tained from the mixing experiments can be reasonably applied to the
treatment process experiments.

Since Equation (54) was developed on the assumption of an inertial
subrange,  it applies only to cases where Nj^e^ is large.   Under those
circumstances and if log NSC is not to° large, the second term in the
                                  31

-------
denominator of Equation (54) will be small and dependence on
will be weak.  At lower values of NRe. where,  strictly speaking,
Equation (54) does not apply,  it is possible that a dependence on N^e
may be discerned.

The other parameter in Equation (54)  is (L  /L ),  the  ratio of the scalar
and velocity integral scales.   There is a physical interpretation of the
manner in which this parameter affects  the rate of decay [ 22].   L£
itpresents  the largest scale  of turbulent motion.  L  represents
the largest  scale  of tracer blobs.  If L. is small with respect to Lg,
then the turbulent motion cannot be as effective in breaking up the
blobs of tracer.   If, however,  L£ is large with respect to Ls, the tur-
bulence can be much more effective in mixing and a more rapid decay
of tiie concentration fluctuations results.

It  L^ possible that by changing the physical characteristics of the grid
or the tracer injection system, (Lg/Lf)  can be made smaller and the
decay rate greater.  It was noted previously that Lf seems to be a
function of the grid bar  diameter,  d.   This means that an increase in
d, with other factors held constant,  should result in an increase in the
decay
It has been assumed by some [ 22, 29] that the scale of segregation is
a function of the number of tracer sources, LS decreasing when the
number of sources is  increased.  According to Equation (54), this would
cause an  increase  in the rate of scalar decay.   There seems to be no
rational reason for assuming that Lg is a function of the number of
sources.   The assumption seems to be based mostly on analogy -with
the dependence of Lf on d or, as  some investigators claim, M.

It is possible,  assuming that the  right-hand side of Equation (54) remains
constant during the period of decay, to integrate  Equation (54) and
obtain Equation (45).  The right-hand side becomes essentially the decay
rate, a, of Equation (45).  The coefficient,  a,  is  dependent on the
initial conditions at a  time,  to.  It  should be noted that the derivation de-
pends on the assumption that u1 = f(x/M).   If u1 =  f(x/d),  then d will
appear  in Equation (45).
Since Equation (54) was derived for high Np^e, ,  there is the implication
that it cannot be applied to laboratory experiments.  Strictly speaking,
this is true.  However,  it may be possible to qualitatively relate Equation
(54) to experimental  results obtained under the  conditions of low Reynolds
number.  In  particular; it may be possible to relate certain physical
characteristics of the experimental apparatus to Lg/Lf and, consequently,
the scalar decay rate.


Previous  Experimental Investigations

There have been two  previous investigations into the rate of decay of
concentration fluctuations of an  isotropic scalar field in isotropic
                                  32

-------
 decaying turbulence produced by a grid:  one by Gibson [ il, 26, 30]
 and the othe r by Keeler [ 22, 27} ,   Both used single electrode con-
 ductivity probes to  attempt to determine  "point" values of tracer
 concentrations.

 Gibson worked with a 6 in. x 6 in.  water  tunnel in which the flow was
 recycled.   For grids,  he used 3/16 in. and 1/8 in.  O. D. lucite tubes
 in a square mesh grid with the bar spacing chosen such that M/d was
 16/3.   The tubes were perforated by drilling 12 mil holes on the up-
 stream side halfway between the corners of the mesh.   The tracer was
 injected into the water stream through these holes.   For tracers,, he
 used NaCl solutions (v /D  = 700) and heated water  (v/D = 7).

 Gibson,  in his measurement of the rate of scalar  decay attempted to
 substantiate Hinze's equation,  Equation (46),   His curve had a  slope
 which was very close to  - 3/2 but later work by Keeler and the present
 study tend to  indicate that this  was merely a coincidence. Gibson also
 made measurements of scalar  spectra.  They  followed a universal form
 and fit the curves given in Figure 5 fairly well.

 Keeler's work was  done after Corrsin's relation,  Equation (54),  had been
 derived.  He used three grids with the same M/d  ratios but  different
 values of M.  This  was done in order to determine whether changing
 the scale of turbulence would affect the scalar  decay rate as predicted.
 Keeler indicated that  such a result was found although  inspection of his
 raw data seems to show that the difference is fairly small if not
 negligible.

 In order to insure homogeneity of the  scalar field downstream from the
 grid, Keeler used a "hairbrush" injection system which fed  the tracer
 into the water stream through many hypodermic needles connected to
 a manifold.  For a  4-Ln.  pipe,  156 needles  were used;  for a Z-in. pipe,
 37.  The  "hairbrush" injection device was placed  upstream from the
 grid and produced a scalar field which was  homogeneous at the grid.
 A drawback to this  method was that the injection system introduced
 turbulence which may have affected the turbulence field downstream
 from the grid.

 Keeler used two tracers,  NaNO3 (v/D  = 500) and  ZnSO4 (v/D   = 1000)
 in an attempt  to show the  effect of Ngc on scalar decay rate  as  predicted
 by Equation (54).  His results do indicate a slight difference in decay rate
 for the two tracers.  This appears to be a consequence of the low
 Reynolds number.   Corrsin [ 17] showed  that for  N^   = 100, this dif-
 ference in NSC should have essentially no   "feet on decay rate.   The fact
that a difference does occur may be significant in regard to  the present
work for the reason previously noted.

 Further  reference will be made to the results  of Keeler and Gibson as
they relate to the present work in Section VI.
                                  33

-------
REVIEW OF COAGULATION-FLOCCULATION THEORY

Although alum coagulation-flocculation has long been one of the most
widely used water treatment processes, the actual mechanism of
destabilization of clay particles is still  somewhat uncertain.   The pro-
cess is simple in execution.   Alurainum or ferric salts are added  more
or less rapidly to the turbid water and after slow stirring,  small
"floes" are formed which are removed by sedimentation and filtration.
The result is a clear water free of the colloidal clay particles which
are principally responsible for the turbidity.

Despite this  apparent simplicity,  uncertainty has arisen over  the years
concerning the mechanisms involved in  coagulation-flocculation.   In
part, this concern is due to the fact that the mechanisms seem to  vary
with pH, type and concentration of the material producing the  turbidity,
and the coagulating agent used,  Before  proceeding with a review of
these theories, it is necessary to make  a  distinction between coagula-
tion and flocculation,.  For the purposes of this investigation,  the term
coagulation will refer to the destabilization of the colloidal particles
through the addition of coagulant to the water.  Flocculation will refer
to the  collision and aggregation of the destabilized particles into rel
atively large alggregat.es known as floes  [ 31].  These definitions a.re
different from those given by LaMer [ 32] who defined coagulation as
processes which bring about the reduction of the repulsive potential of
the electrical double layer of the  colloidal particles and flocculation
as being the  bridging action of high molecular weight polyelectrolytes
which  brings about a loose three-dimensional floe structure.  LaMer's
definitions consider coagulation and fiocculation  as two different
mechanisms of colloid destabilization and aggregation.  The definitions
used in this  paper consider coagulation  as  the process of destabiliza-
tion of colloidal particles without  reference to the particular causative
mechanism.   The term flocculation is applied to the hydrodynamics of
aggregation  and floe formation.

The phenomena, which cause colloidal clay particles to remain suspended
in water are quite well known, from colloid chemistry and have long
been described in sanitary engineering texts  and papers [ 31—35]  and
need not be reiterated in detail  in this report.  It is sufficient to note
that much of the theory concerning the mechanism of coagulation centers
on the reduction of the zeta potential to  a level where the repulsive
forces are sufficiently low so that collision can  occur and the  Van der Waal
and other forces can be operative. The  colloidal particles can then
collide,, aggregate,, and form large settleable or filterable floes.


Coagulation  Theories

In 1949 Langelier and Ludwig [ 34] made a systematic study of various
clays suspended in water.  Their  main finding was a correlation between
the cation exchange capacity (CEC) of the  colloidal material and the
                                  34

-------
coagulant dose necessary to achieve a particular level of removal of
turbidity.  Although this study has been criticized [ 36,37] because of
lack of pH control,  it is  important for two reasons.  It demonstrated
that alkalinity is important in determining the coagulant  dose necessary
to achieve satisfactory clarification.   Also,  it was noted that in many
instances efficient clarification requires a  binder material of hydrolysis
products of aluminum or iron.  They concluded that the addition of
highly charged cations — Al+++ or Fe++ — reduced the zeta potential
of the colloidal particle to a level where aggregation could take place.
Then the hydrous oxide would act to bind the destabilized particles and
form large floes which could then be removed.

In 1965 Kim» Ludwig, and Bishop [ 36]  extended the work of Langelier
and Ludwig.  Coagulation jar  tests were made with the final  pH a
controlled parameter.   They found that  at low kaolinite concentrations
(< 100 mg/.£) there was an inverse relationship between the clay con-
centrations and the amount of alum necessary to produce clarification.
At high concentrations of kaolin, and with bentonite, they found a
direct relationship between clay concentrations and the coagulant dose.
This  implies that at different  kaolin concentrations,  different coagula-
tion mechanisms may be dominant.  At  low kaolin concentrations, they
found that the optimum pH for best coagulation was the same as the
isoelectric pH of the aluminum-hydroxo complex formed by the alum
and the alkalinity in the water.  That is, turbidity removal was greatest
— for a given kaolin concentration and alum dosage — at the pH of least
solubility of aluminum hydroxide.  At high concentrations of kaolin
and with bentonite they found tha't a slight positive charge on the
aluminum-hydroxo compounds which were formed resulted in best
turbidity removal.  They concluded that for suspensions  with high
particle concentrations,  a reduction in zeta potential to the point where
aggregation of destabilized particles may take place provided the most
efficient clarification.

Packham [ 38] reported  similar findings.  Conditions for the most
rapid coagulation of dilute concentrations of kaolin were  those leading
to the most rapid precipitation of aluminum hydrolysis products.  He
noted that the turbidity in samples of river water from Britain behaved
similarly to dilute kaolin suspension.   He also used bentonite and more
concentrated suspensions of kaolin and, as did Kim, Ludwig, and
Bishop, obtained results different from those obtained using  dilute
kaolin suspensions.

Many authors [ 37—41]  have pointed out that when alum is added to
water,- the Al"^++ ion undergoes  hydrolysis, the extent and character of
which depends on the pH and aluminum concentration.  Figure 6 shows
the concentrations of various  aluminum species at different pH values
in equilibrium with freshly precipitated Al(OH)3  ,  However,  it should
be recognized that equilibrium may not be reached quickly and that the
transition from A1+^+to A1(OH)3  occurs through successive  substitu-
tive reactions.  Stumm and Morgan [41] noted that the net charge on
                                  35

-------
                                    ARANGE OF
                                     ALUMINUM DOSES
                                     NORMALLY
                                     ENCOUNTERED IN
                                    IWATER TREAT-
                                        MENT
                                A113(OH)34
             A17(OH)I7
                                pH


FIGURE 6.  CONCENTRATION OF VARIOUS ALUMINUM SPECIES
  IN EQUILIBRIUM WITH FRESHLY PRECIPITATED A1(OH)3
                (FROM BLACK AND CHEN [ 39])
any aluminum-hydroxo compound is probably an average value, with
different charges being associated with different aluminum atoms or
groups of atoms.  Moreover, the forms present are probably not
restricted to those shown in Figure 6[ 38,41],  Polymers can be
formed by hydroxyl groups acting as a bridge between two or more
metal atoms.  These are termed "olation" reactions.
                                36

-------
Table 1  [ 38] shows the various types of reactions which are involved
in aluminum hydroxide precipitation.   Listed first are the ligand ex-
change reactions.   These reactions occur in sequence when Al(III) is
added to water.  Also listed are examples of olation reactions which
result in polynuclear polyhydroxo species.   The important point is
that at a particular pH and concentration of  aluminum in waters  not
just one, but many aluminum-hydroxo compounds  will be formed.
However,  one  species — insoluble aluminum hydroxide for example —
may predominates especially if sufficient time is  allowed.

Black and Chen [39] made  studies of coagulation  of clay by alum using
microelectrophoretic techniques to help determine the mechanism of
coagulation.  They noted that in most instances in water treatment,  the
aluminum ion concentration falls between 10~6 and id"4 M (see Figure
6).   For this range in aluminum ion concentration, the predominant
aluminum species in each of three pH ranges are  as follows:  Below
pH 4 the hydrated trivalent aluminum ion is  the most active species.
In the region between pH 4 and pH 6, one or more of the hydrolyzed
aluminum polynuclear cations,  such  as Al6(OH)j+^+ or A18(OH)^,4,
may predominate.  From pH 6 to pH 8, insoluble aluminum hydroxide
may be considered most important.

They concluded that different mechanisms were responsible for
coagulation  in  each of the three pH ranges.  Below pH 4 the trivalent
aluminum ion acts to reduce the zeta potential of the colloidal particles
and produce destabilization and agglomeration of particles.  In the
range where the multivalent polymeric aluminum-hydroxo species
exist; specific adsorption of these ions onto the surface of the clay
particle was concluded to be effective in producing destabilization by
reduction of zeta potential.   Between pH  6 and 8, physical enmesh-
ment (or sweep flocculation or sweep coagulation)  by aluminum hydroxide
or  mutual coagulation between positively charged  aluminum hydroxide
colloids and negatively charged clay  particles were concluded to be
the mechanisms involved.

The concept of specific adsorption of multivalent aluminum-hydroxo
compounds onto the clay particles leads to consideration of a  dif-
ferent concept of coagulation as discussed by LaMer [ 42],  Stumm
and Morgan [41],  Stumm and O'Melia [ 37], and Hahn and Stumm [  40].
This  may be termed the "chemical approach" as opposed to concern
with reduction of zeta  potential by electro-kinetic  attraction of counter-
ions.   Although this  division is convenient,  it can  be — as with all
simplifications —misleading.  For example, while chemical forces
may act to cause adsorption of positively charged  aluminum species,
the effect of this adsorption is the reduction of zeta potential,  allowing
coagulation to occur [  39«40].  Thus, both chemical and electrokinetic
phenomena are  involved.  Perhaps one of the best  examples of the
chemical approach to colloid destabilization is the coagulation of a
negatively charged clay colloid by a negatively charged long chain
polymer.  Since the two constituents  are  both negatively charged,
chemical forces must be acting in the process [ 42].
                                  37

-------
                                                   TABLE 1



                          TYPES OF REACTIONS INVOLVED IN HYDROLYSIS OF Al(III)

                                            (FROM PACKHAM [ 38])
00
           Llgand Exchange Reactions



                       1 a.  [  A1(H20)6]
               -H-+
                   + H2O
 A1(H20)5 OH]
              ++
                        b.  [ A1(H2O)5 OH]   + H2O



                        c.  [ A1(H20)4(OH)2]++H20



                       2    [ A1(H20)3(OH)3 ] +X=


                       3    [ A1(H2O)4(OH)2] + + X =
                                       A1(H20)3 (OH)3 ]  +H3 O"



                                       A1(H2O)4 X] +    + 2H2C



                                       A1(H20)4 X] +    +20H"
                                         (X Represents a Divalent Ion)
           Olation Reactions
                       4 a.  2[ A1(H2O)5OH]
                        b.  [  (H20)4A1(OH)2A1(H20)4]
                                                                          OH
                                                                          OH
                                                                 + 4


                                                                >   +2H2O
                                                     + 4
c.
                                           A1(H20)3OH]
                               A1(H20)5
[ (H2O)4A1(OH)2A1(H20)3 OH]




           OH  HJ°  OH


(H2O)4A1/^     Al        A1(H2O)4

         \   S \ \  s"
           OH  „' ^  OH
                                                                                                 + 5
                                                                                                 ^  +2H2 O

-------
 There  has been considerable disagreement among investigators over
 whether a "chemical" or "physical" approach should be taken in
 attempting to understand the  coagulation process.  It has now become
 apparent.- however, that both chemical and physical phenomena need
 to be considered.

 In 1967 Stumm and O'Melia [ 37]  published a paper in which they
 attempted to describe the mechanism of  coagulation at various pH's
 and colloid concentrations.  They drew upon the work of others as
 well as their own.  They concluded that at high surface concentrations
 (square meters of colloidal surface per liter),  coagulation takes place
 by adsorption of multinuclear hydrolysis products of Al(III).   At low
 concentrations of colloidal material —particularly kaolin concentrations
 less than 100 m.g/1— sweep flocculation,  or enmeshment by  insoluble
 aluminum hydroxide,  is responsible for  removal of colloidal material
 from suspension.   For sweep flocculation to occur,  the pH must be
 such that there  is  a tendency to precipitate insoluble  aluminum hydroxide.

 Figure 7 summarizes Stumm and O'Melia's conclusions. At low sur-
 face concentrations,  coagulation takes place through nonstoichiometric
 sweep  flocculation  (zone 4).   At higher surface concentrations, adsorp-
 tion of soluble  Al(III) hydrolysis products is responsible for  destabiliza-
 tion of the clay  particles (zone 2).  Stumm and O'Melia also  term this
 stoichiometric coagulation.

 It should be pointed out that mere physical enmeshment is not an
 adequate description of Stumm and O'Melia's sweep flocculation (zone
 4).  This would imply that the presence of the clay particles does not
 affect the hydrolysis  reactions of the Al(III),  i. e. ,  that the clay  is
 merely a passive component.  This is probably not entirely  correct.
 The studies of Kim, Ludwig,  and Bishop [ 36] and Packham  [  38] show
 that for low concentrations of kaolin at constant pH, the concentration
 of alum necessary to produce coagulation is inversely related to the
 kaolin  concentration.  (Furthermore, in  the present study,  it  has been
 found that addition of alum to clear water resulted in floe of  poorer
 quality being formed  much more slowly than when alum was  added  to
 the  same water containing 25 mg/^ of kaolin. )

 Stumm and O'Melia point out  two  possible reasons for the inverse
 relationship between  colloid  concentration and coagulant dose.  With
 colloidal particles providing  interfaces for localized  over-saturation,
 the  critical supersaturation necessary for rapid precipitation  could
 decrease with increasing clay concentration.  The alternative explana-
 tion considers mutual coagulation of the negatively charged colloids
 with small particles of aluminum hydroxide precipitates or aluminum
 hydroxo compounds.  It  can be postulated that at low  colloid  concentra-
 tions, an insufficient number of particles is present to provide the
 necessary contact opportunities in a reasonable time and the presence
 of Al(OH)3  particles  can produce efficient aggregation.  Thus, in-
"creasing the  clay particle concentration can reduce the necessary
 coagulant dosage.
                                  39

-------
    O
    i— i
    H
    W
    U
    £
    O
    U
    H
    O
    <
    O
    O
    O
    O
                                   REGION OF
                                 OAGULATION
NON-
STOICHIOMETRI
OR "SWEEP"
COAGULATION
                                     STOICHIOMETRIC
                                     COAGULATION
                                     ZONE i
                            100 mg/l
                            KAOLIN
                  LOG COLLOID CONCENTRATION

FIGURE 7.  EFFECT OF COLLOID CONCENTRATION ON COAGULANT
       REQUIRED FOR  DESTABILIZATION (AT CONSTANT pH)
                 (FROM STUMM AND O'MELIA [ 37] )
   In summary,  -while there is still confusion and disagreement over the
   exact mechanism of coagulation which may be effective under particular
   circumstances, some general statements may be made.  Neither the
   chemical or double layer models  can adequately describe the phenomena
   observed in the coagulation of various colloidal materials  at all con-
   centrations or pH values.
                                    40

-------
At low concentrations  of kaolin — less than 100 mg/i — and at pH values
near  7, it appears that rapid precipitation of uncharged insoluble
aluminum hydroxide is associated with efficient coagulation.  This
implies a  "sweep flocculation"  model.   At higher concentrations of
kaolin, and with other colloidal suspensions  such as silica and bentonite
at moderate concentrations,  some other mechanism is operative —
most likely the adsorption of multivalent polynuclear aluminum-hydroxo
compounds onto the surface of the colloid leading to reduction of the
negative charge and destabilization.
Review of Flocculation Kinetics

Smoluchowski [ 43,44]  first developed expressions for the frequency
of collisions of particles  suspended in a fluid.   Where the fluid  is at
rest, collisions can take  place  due to Brownian motion.  This is called
perikinetic flocculation.  The frequency of such collisions  is given by
Equation (55) :

                      I. .  = 4 TT  D. . R.. n. n.                      ,-.->
                        ij         ij  ij  i  j                      (55)

v/here I.,  is the number of contacts made per unit time  and unit
        n                                 r
volume; l>Lj is the combined diffusion coefficient,  D^ + D: ;  R^j is the
collision radius which equals the sum of the particle radii,  R^ + RiJ
and n^ and ni are  the number concentrations of particles of radius
R. and R..
  i       J
In addition to perikinetic  flocculation,  particles can collide as a
result of their motion with the fluid.  This is termed orthokinetic
flocculation and is perhaps  of greater importance in water treatment.
Smoluchow ski showed that for laminar flow, the collision frequency is
given by
                        J.. -    n. n. R.?                        (56)
                         ij   3    i  j  tj  dZ


where Jjj is the collision frequency due to laminar motion; dU/dZ  is
the laminar velocity gradient;  and ni, nj, and RJJ have the same
definition as in Equation (55).  This  equation is not useful because it
is restricted to laminar motion.   In  all instances of orthokinetic
flocculation used in water treatment, turbulent motion is  present.

In 1943 Camp and Stein   [ 45] used  Smoluchowski' s basic model to
develop a relationship giving the frequency of collision in turbulent
motion.  Using a theory of Stokes, they related the energy input to the
system and the resulting root-mean-square velocity gradient.
                             G  =-\                                (S7,
                                   41

-------
where G is the root-mean-square velocity gradient,  P is the power
input,  V is the volume,  and fi is the viscosity.

The resulting collision frequency  equation is


                           H.. =| n.  n. R3. G                   (58)
                             ij   3  i   J   1J

Several other equations [31, 46—50] have  been developed giving the
particle  collision frequency in turbulent flow.  Most bear a very close
resemblance to Equation (58), although various assumptions were made
in order to provide a more sophisticated treatment of the problem.
The above equation can be modified to give,  instead of the  frequency of
collisions, the rate of removal of the smallest, or primary, particles
from the system.   A simplified form is



                                                                <59)
where K . is an aggregation rate coefficient.  Argaman and Kaufman
[ 31,46] and Parker,  Kaufman, and Jenkins [ 51] have added another
term which represents the formation of primary particles  due to
surface erosion of larger particles.   In simplified form this  is
                                                                (60)
where KR is a breakup rate coefficient.  This equation is usually of
interest when applied to a CSTR.  For one compartment,  a materials
balance at steady state gives

                     Qn?  - Qn1  - K^1 GV r +KfiG2Vr =0      (61)



where Q is the flow rate, V  is the reactor volume,  n^  is the influent
concentration of primary particles, and n^  is the effluent concentration
of primary particles.  Rearrangement of the above equation and re-
placing V /Q by T,  the mean residence time, yields


                            n°    1 +K
                                    +KG2T
                                  42

-------
nj 'Hj  is termed the "performance parameter" and is often used in
plotting results of flocculation studies.  For convenience, the ratio
of the initial to final turbidity as measured by a light-scattering tur-
bidimeter is often taken to be equal to n° /n1 .
                               n        11
PREVIOUS WORK CONCERNING INITIAL MIXING
AND TREATMENT PROCESSES

There has been very little work published to indicate that rapid initial
mixing may be significant in water and wastewater treatment processes.
The reactions which occur when chemicals are added to the water
stream are often quite complex, as described earlier,  as well as
quite rapid.   Physical-chemical reactions  can occur between the added
chemical, the component of the water stream which is  the object of
treatment (e. g. ,  clay turbidity),  and other constituents of the water
stream (e. g. , alkalinity). Reactions between the chemical and these
other constituents may act in such a way as to reduce the effectiveness
of the treatment process. For example,  in alkaline waters poor
mixing may result in complete hydrolysis of the aluminum in only a
fraction of the stream being treated.

The relation between mixing and extent  of reaction has been of interest
in chemical engineering  studies*  Toor  [ 24] has studied the relation
between mixing and extent of reaction for a simple case, a very fast
reaction in-which two reactants, dissolved in separate streams of water,
of equal molecular diffusivity combine to form a product.

                             A + B -*C    .                      (63)

By the term very fast reaction,  it is meant that the rate  of reaction
is much faster than the rate of mixing.  Therefore the  extent of the
reaction is controlled by the extent of the mixing process.  For the
case where the  reactants are present in stoichiometric amounts,  it
is found that the fractional completion of reaction,  F,  is equal to the
fractional completion of  mixing, r\, i. e. ,

                           F = r, = 1  -^-     .                    (64)
For the case where one reactant is present in excess, for example,
3 times the stoichiometric amount, the expression is more com-
plicated.
                    F = 1 +(3-1  H+g
-i  fi+g a; (1  r,)  j
(65)
where
                  g(x) =ierc       j       .                   (66)
                                  43

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Equations (64) and (65) are shown in Figure 8 for various values of (3.
This graph  indicates that when one of the reactants is introduced in
excess,  the reaction will be completed,  L e. , the limiting reactant
will be completely utilized,  before mixing is completed.

Keeler [ 22] and Vassilatos and Toor [ 52] have  experimentally verified
Equations (64) and (65), and the concept  behind Equation  (64) had been
known and used previously [ 53].

In alum  coagulation-flocculation of a turbid water, the alkalinity of
the water may be considered to be a reactant present in excess of that
needed to react completely with the coagulant added to the stream.
Reaction of the alkalinity with the alum before the alum has  become
completely  mixed with the turbid water may act to detrimentally affect
process  performance.  Of course,  this process is much  more com-
plicated  than the simple case studied by  Toor.  First, the reactions
are very complex, their rate and extent  depending upon alkalinity
and pH.  Secondly, the rate of  reaction does not appear to be so fast
that it cannot be overcome by providing much faster  mixing.  This
second point is fundamental to the present study:  by providing more
rapid mixing,  crucial reactions which can occur  before the alum has
been dispersed evenly throughout the clay particles can be made to
occur  after this mixing has taken place.   Alternatively,  these reactions
may be prevented in favor of desirable physical-chemical reactions
between  the alum and the turbidity particles.

In a manner somewhat  analogous to the way in which increasing one
of the  reactants at a given degree of mixing will  increase the fractional
completion  of reaction  in Figure  8, increasing the alkalinity may allow
completion  of certain hydrolysis  reactions at a lesser degree of
mixing,  i. e. ,  at a time when greater segregation between the alum
and the turbidity exists.  Thus,  at high alkalinities,  it may be even
more important to attempt to insure that the rate of mixing is faster
than the  rate of the crucial reactions.

In a study concerned with water and wastewater treatment, Rudolfs and
Gehm  [ 54]  published a paper in 1936 describing  treatment of waste-
water with FeCl3 .   They found that slow mixing allowed  undesirable
hydrolysis reactions to occur which decreased the efficiency of the
process.

More recently, Selleck and coworkers [  55—57] reached a preliminary
conclusion that rapid initial mixing can be very important in waste-
water  chlorination efficiency.   They concluded that the combined
chlorine  residuals  formed in wastewater undergo rapid reactions in
the first  milliseconds of contact with the waste stream.   These changes
result  in a decrease  in the  bactericidal effectiveness of the chlorine.
If the mixing of the chlorine with the waste stream is rapid enough,
the more bactericidal compounds will come in contact with the bacteria,
and process performance will be improved.  (Studies of chlorination
and initial mixing are presented in Appendices A and B. )
                                 44

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                 0. 2
0.4        0. 6
                                 = 1  - a'/a1
                                          o
0. 8
1. 0
       FIGURE 8.  FRACTIONAL CONVERSION AS A FUNCTION OF
              ACCOMPLISHED MIXING (FROM TOOR [ 24] )
The increasing study and use of polyelectrolytes as coagulants and
coagulant aids may provide another area in which rapid initial mixing
may be important.  Riddick [ 58] notes that a long chain polymer may,
if mixing is not accomplished sufficiently rapidly,  react with other
similar polymers or itself and would be unavailable for reaction with
the colloidal material.
                                 45

-------
Recently, Vrale and Jorden [ 59] made studies of the relation between
rapid mixing and alum coagulation-flocculation, the same process with
which this study is concerned.  A high-speed backmixed  reactor (flash
mixer) and several i-in. I. D. tubular, plug flow reactors were used.
After the alum was mixed with the turbid water  (tap water with SiO2
colloid,  NaHCO3,  and CaCl2 added)  in the  initial mixing  device, jar
tests were made to determine if the  various  initial mixers caused
differences in performance.  They concluded that more rapid initial
mixing resulted in better turbidity removal and  that the high-speed
backmixed reactor, which is normally regarded as an adequate initial
mixing device and  which is often used in plant design, actually is much
poorer than a plug flow  system.

Similar results have been found by Wilson  [ 60]  in work done pre-
viously at the Sanitary Engineering Research Laboratory at the
University of California.  In these experiments, kaolin was used to
provide the colloidal turbidity.  With both jar tests and continuous
flow pilot plant flocculation  experiments it was found that the tubular
reactor initial mixers produced better results than did the backmixed
reactor, presumably because segregation between the alum and water
streams was eliminated more rapidly when the tubular reactors were
used.

In one sense, rather than being a duplication, the two investigations,
one by Vrale and Jorden and the other by Wilson,  complement each
other.   Vrale and Jorden used colloidal SiO2  to provide turbidity.
They found a stoichiometric relationship between the colloid con-
centration and the  coagulant dose necessary to produce coagulation
(at a constant pH).   In Stumm and O'Melia's terminology  [ 37], this
corresponds to an  adsorption-destabilization mechanism  of coagula-
tion.  Wilson used a dilute kaolin suspension. As noted previously,
this  seems to correspond to a sweep flocculation mechanism of
coagulation.  It has been shown,  therefore, that initial mixing seems
to be important regardless of the coagulation mechanism.  This  is
important with respect to application of such studies  to full-scale
water treatment facilities  where both types of colloidal material may
be present.  It is also important in that it may mean that the sweep
flocculation mechanism and the adsorption-destabilization mechanism.
are not so different as they might first appear.  As pointed out pre-
viously,  the term sweep flocculation is  somewhat inappropriate in that
the clay particles do not act as a passive component.  That initial
mixing is important with both mechanisms  seems  to indicate other
more basic similarities between them.
                                 46

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                            SECTION V

         MIXING STUDIES: APPARATUS AND METHODS
INTRODUCTION

The experiments  described in this and the following section were done
in order to determine what characteristics of the grid, the turbulent
flow field, and the scalar material affect the intensity of segregation at
points downstream from a biplane grid when a tracer  is introduced into
the flow through numerous orifices in the grid bars.   Closely related to
this is the question of what design parameters should  be used in the
construction of such grids for use in water and wastewater treatment
facilities.

This  second question can be divided into two parts.  First, what
parameters related to the grid affect the time  of mixing —the time  re-
quired to reach some arbitrarily-defined low value of the  intensity  of
segregation (for example, it could be defined as  the time required for
Is to  be  such that a1 /A = 10%)?  Second, what  is the relation between
the time of mixing and process performance, i. e., how rapid must the
mixing be  in order to produce a significant improvement in performance?
The latter question will be dealt with later when experiments  involving
alum coagulation-flocculation of turbid water will be discussed.

The work of Gibson and Keeler [  22, 27] was used as a starting point
for the present  studies [ 11.26,30],  In some instances, their con-
clusions have been substantiated  by these experiments; in other instances,
new conclusions have been drawn which conflict with previously held
theories.

The present  studies tested the theory of Corrsin [17, 28]  in that an
effort was  made to determine what  design parameters may determine
the scales  of turbulence and segregation which in turn should affect
the rate  of scalar decay in the system being studied.


EXPERIMENTAL APPARATUS
S_ingle_E_Iec_trode Conductivity Probe

The total resistance of a uniform piece of conducting material is
related to its  resistivity by the following  equation,

                             R =  PA                             (67)
                                  47

-------
where R is the total resistance, p is the specific resistivity in ohm-ft,
L is the length of the material, and A  is the cross-sectional area.,
In a standard conductivity cell, two electrodes of equal size are used.
They are separated by a distance L,, and the conducting solution between
the  probes has a constant cross-section,  A,  Equation (67) can be
written in terms of a cell constant,

                             R = PK   =-£                      (68)
                                   c   cr

where KC = L/A is the cell constant and cr = p    is the specific con-
ductivity of the  fluid.   Conductivity probes are usually calibrated in
terms of the cell constant.  Knowing the resistance measured by the
cell in a given fluid;  the conductivity can be calculated.

Consider a conductivity cell with two electrodes, A and B which vary
greatly in size.   Assume that the conducting solution occupies only the
space between the electrodes.  Equation (67) can be written in integral
form,
                                   B

                                                                (69)
The greatest contribution to the total resistance will come from the
parts of the system where A(Jt) is very small, i. e. ,  near the small
electrode.  Suppose now that p varies from point to point "within the
system.  If this variation is not so great that it dominates the effect of
the changing area, then R will tend to be a function  of the resistivity
near the small electrode.

With a probe of this type, a conducting tracer such  as NaCl solution is
used.  At low concentrations,  the  conductivity of the solution is pro-
portional to concentration.   A change in conductivity will be detected by
the probe and,  through the  associated electronic apparatus, a voltage
can be measured which is proportional to the concentration at a "point"
defined by the effective volume of  the probe.

This is the principle'upon which the single electrode conductivity probe
operates.  The  end of a small diameter wire  protruding from the tip of
a probe acts as the small electrode.  The ground of the system acts as
the other  electrode*  The single electrode probe was developed simul-
taneously by Gibson [  11, 30] and Keeler [ 22, 27]  and was an improve-
ment over the probe developed by  Lamb,  Manning,  and Wilhelm [  61 ].
Their probe consisted of a  large and small  electrode which allowed
current to leak to grounds in the system.   Using the system ground as
the large  electrode eliminated this problem.

It  is possible to develop some estimate of the volume over which this
type of probe effectively measures resistivity by considering a spherical
                                  48

-------
electrode of radius r_ immersed in an infinite body of electrolyte [11]
For this geometry, Equation (69) may be written
                                                                (71)
From Equation (68) the cell constant is

                                     1
                                                               (72)
If the effective cell volume is  taken to be that volume closest to the
sphere which contributes 90%  of R  ,  this volume can be easily found
from                            °°
                          °-9R« =         ^  dr               (73)
which leads to
                              0. 9 B = 10 r     .                 (74)
                                         o
Therefore,  the  effective probe radius can be considered to be approx-
imately 10 times the radius of the sphere.   This gives some indication
of how close to  a "point" the probe is measuring.

Keeler concluded that the  shape of the probe tip was very important
in determining the  spatial resolution of the probe because a blunt tip
disturbed the flow field in the vicinity of the tip.  He noted that when
Gibson replaced a 50-micron blunt probe by one 20 microns in diameter,
there was no apparent increase in the ability to resolve high frequency
components of the scalar spectrum.  Gibson also concluded that  the
blunt shape of the tip may have been the limiting factor in  spatial
resolution.

The  major contribution to  the rms concentration fluctuation is from the
lower wave number portion of the scalar spectrum.  Therefore,  when
rms values are  measured,  spatial resolution is not so important, and
larger,  more blunt probes can be tolerated,  which simplifies con-
struction problems.
                                 49

-------
The probe used in this  study had a tip 3 mils (75 microns) in diameter.
This is larger than those used by Gibson (10-51 (J.) and Keeler  (1—25 p.)
and is  the same size as the small electrode of the probe developed by
Lamb,  Manning,, and Wilhelm.  Attempts were made to build smaller
probes in order to compare the results  obtained from using  different
sized probes.  However,  difficulties were  encountered and no  reliable
results were obtained.  While no photographs of the probes actually
used by Gibson are available,  it is believed from his description of
their construction that  the probes used in the present study may have
been of superior shape.  He used a cast epoxy tip and attempted to
make the tip as sharp as  possible using needle  files and a  microscope.

Keeler's probes were designed specifically to avoid the problems which
a blunt tip might incur.  The  method of  construction was very tedious
and difficult [ 22}.   All of his probes were  small  enough so that the
rms fluctuations measured with them were only weakly dependent on
the probe diameter beyond a distance of 10 mesh  lengths from the
grid.

Noting that  the purpose of the present study was to  determine the
parameters which affect the rate of mixing downstream from a grid,
"true" values of rms concentration fluctuations were not essential in
the sense that what was sought was a comparison of the mixing obtained
from various  grids.  Nevertheless, the present work may be criticized
on the  grounds that smaller probes, with better tip shapes, might
have resulted in higher observed rms values.   All experiments of the
present study were made with probes of the same size so that the
results would be consistent.   Furthermore, based on the  results and
conclusions of Gibson and Keeler,  the rms values obtained should be
reasonably  close to  the "true" rms concentration fluctuations.   More-
over,  comparison of results with those  of Gibson (see Appendix C)
showed good agreement.
Probe Construction

A drawing of the single electrode conductivity probe used in the mixing
experiments is shown in Figure 9.  Photographs are shown in Figures
10 and 11.  It was constructed from 5/16-in. O. D.  thin-walled glass
tubing.  The tube was heated and drawn out to form a tapered tip,
having a hole  only slightly larger than the 3-mil platinum wire used
for the electrode.  It was found that tubing with reasonably thin walls
produced  the best tips.  A short section of 3-mil platinum wire was then
put through the tip and held in place at  both ends, and a casting resin
was poured into the large end of the tip.  The viscosity of this  resin
was such  that, before setting,  a small  ball of resin was formed out-
side the small end of the tip.  The platinum wire protruding from this
ball of resin was cut  off, and the ball of resin was carefully filed
down  to a sharp point with the platinum electrode protruding from the
end.  A binocular microscope was used to aid this process.
                                  50

-------
                                 Connector
                                 Epoxy Seal
                               Glass Tubing
Filed - down  Point
                                 Wire  Lead
                 Platinum Wire
                            Glass Tip
                                        Casting Resin

                                  Casting Resin
                                                  Epoxy Seal
                                               Glass Tip

                                             3 mil  Platinum  Wire
          FIGURE 9.  ILLUSTRATION OF CONDUCTIVITY PROBE
                                    51

-------

FIGURE 10.  SINGLE ELECTRODE
    CONDUCTIVITY PROBE
FIGURE 11.  PROBE IN PLACE IN
      TUBULAR REACTOR

-------
No doubt some errors due to probe interference with the flow field
did occur, but the difficulty of making probes in a manner similar
to Keeler and the insensitivity of rms values to probe shape and size
made more sophisticated probes unnecessary.

After the probe tip was constructed,  a wire lead was soldered to the
platinum wire and a glass tube with a 90° bend was cemented  to the
probe tip with epoxy resin.

After the probe was constructed, the platinum electrode was coated
with platinum black (finely divided platinum).  When current flows
across  the surface of the electrode* hydrogen and oxygen gases are
formed.  These gases add resistance to the system in addition to that
caused  by the solution resistivity.  A capacitive reactance is  also
produced.  An alternating current will allow some of the hydrogen and
oxygen  to recombine and reduce the additional impedance.  For this
reason, high frequency AC current is used in conductivity measure-
ments.   It has also been found that adding a coat of platinum black by
electrolysis  reduces the surface impedance.

For these experiments, the probes were platinized in a solution of
chloroplatinic acid and lead acetate according to the method proposed
by Standard  Methods [ 62]  with the exception that a Hewlitt-Packard
6215A DC power supply was used to supply the voltage.   This  allowed
control of the voltage to obtain best results.  Approximately 2 volts
with a platinizing time of 30 to 40 seconds was used,
Electronic Equipment

A Tektronix 3C66 carrier amplifier was used to transform the resistivity
(and hence concentration) near the tip of the probe into a voltage which
could then be analyzed for rms and mean values.   The 3C66 amplifier
is a plug-in unit for the Tektronix 560 series oscilloscopes.  A model
564B storage oscilloscope was used.

The oscilloscope permitted the trace (representing concentration vs.
time for the present work) to be "stored" on the oscilloscope screen
as the trace was normally on the screen for only a few milliseconds.
Storing a trace allows better visualization of the concentration-time
signal.   Although the storing apparatus was not used directly in this
work,  it proved to  be useful for demonstrating the use of the single
electrode conductivity probe.

A block diagram of the 3C66 carrier  amplifier is shown in Figure 12.
[  63].  It has the advantage of being a completely prepackaged  unit.
Although it was designed for use with strain gauges, it was used for the
present work without any modifications.  The 3C66 unit operates on
the principle of the AC bridge. A sketch of such a bridge is  shown in
Figure 13.  When the bridge is balanced, * = 0.  The condition for
this is,
                                  53

-------
TRANSDUCER
   INPUT
 dZ, ex dA
  AC
BRIDGE
AMPLI-
 FIER
 PHASE -
SENSITIVE
 DEMOD-
 ULATOR
                                       25-kc
                                      OSCIL-
                                      LATOR
                                                                                FILTER
                                                       dE
                                                  SIGNAL
                                                    OUT
                                           OUTPUT
                                           AMPLI-
                                            FIER
                                                                 OSCILLOSCOPE
                                                                      TRACE
                  FIGURE 12.
               BLOCK DIAGRAM FOR TEKTRONIX TYPE 3C66
                      CARRIER AMPLIFIER

-------
                              25 kc
               FIGURE 13.  AC BRIDGE CIRCUIT
                                                              (75)
where
           Z2, Z3 ,  Z4 are the impedance in each of the arms.  It is
found that the maximum sensitivity occurs when Zt = Z2 and Z3  = Z4,
Under these circumstances a change in Z: will be reflected by a
change in £ as follows:
                                55

-------
                           d|  _ 1  dZ,
                            E  'I  Z,                         (76)


where E is the voltage drop accross the branches from A to B.   This
relation holds as long as £ « E; otherwise the response becomes
nonlinear.

The probe was connected to the  AC bridge in a manner which required
the use of only one external arm.  A 120-ohm resistor was placed
parallel to the probe across arm No. 1 of the bridge as is shown in
Figure 14.  Under  such circumstances,  the conditions for balance
are Zl  = Z2  = Z3  = Z4,  and the resistance in each arm is approximately
1ZO ohms.  Ignoring the  reactive portion of the impedances across
arm No. i,  it is possible to determine the change in £ produced by a
change in R .
           P               R R'
                                 , R1 « R                    (77)
                     (R +R')R' - R R1      R|Z
                       P. _  P    -   K                  (7S)
              _  - _ . _       -
              dR         (R  +R1)2        (R  +R1)2
                P         P              P
                         R  +R1
                                dR  - TT;—,,-, ,4T-,—  dR
           ^
           T
Since R1 « R ,
             P
                (R +R')2  R  R1    p   (R +R')R      p   .      (79)
                                                              (80)
Ignoring the reactive impedance, Equation (80) can be substituted into
Equation (76)


                         ^-i ^-P    •
                                  P     V

The change in probe impedance is represented by dZ  in Equation
(76) and by dRp in Equation (81). In Equation (76), dZt  represents
the change in probe impedance while in Equation (81), it is represented
by dRp.  Using an arrangement which required only one external arm
made it necessary to sacrifice sensitivity, since R1 « R    For
measuring rms values with the probes used in this study there was no
problem in obtaining a sufficiently strong signal.  However, if attempts
                                56

-------
                        25 KC

                                   .1-
                                                    B
                                                         R' = 120
                                                    R  » R1
                                                     P
   FIGURE 14.  PROBE CONNECTED IN PARALLEL
               WITH 120-ohm RESISTOR
had been made to measure high frequency, low amplitude portions of the
spectra, it might have been necessary to use an arrangement utilizing
two external arms of the bridge.  The probe would be one arm, and a
variable capacitor and resistor,  representing Z2 in Figure 14 would
be the other arm.  A smaller probe might also require a similar
arrangement.  As
an increase in R  .
result.
R  - R   = p/4irr0, a decrease in ro would cause in
 From Equation (81) a decrease  in d£/E would
                                57

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 A calibration curve for such a probe is shown in Figure  15.  Above
 2000 ing/* NaCl the response of the system began to show a non-
 linearity due to  excessive unbalancing of the bridge.  The average
 concentration in the experiments was about 50 mg/i so this was not
 a problem.

 To obtain the rms value of the concentration fluctuations, a TSI model
 1060 rms voltmeter v/as used.  This instrument represents an improve-
 ment over the  rms voltmeters used Ln previous studies  in that it can
 average the fluctuations over a longer period of time; the time con-
 stant could be varied up to 100 seconds.

 The rms voltmeter used by both Gibson and Keeler had a time con-
 stant of only 2 seconds.  They reported that the output reading of the
 rms voltmeter fluctuated so  greatly that an analog averager had to
 be built to obtain steady readings.  An  important drawback to this
 method of obtaining rms values is that because of the small time con-
 stant, the contribution of low frequencies may be underestimated.
 These may constitute a considerable fraction of the total rms value.
 Thus, using an rms voltmeter with a greater time constant means
 more accurate results. For most of the rms made in the present
 study, a time constant of 10  or 30 seconds was used.  These time
 constants correspond to low  frequency cutoffs of approximately 0. 3
 and  1 cycle per second, respectively.

 In order to be certain that the scalar field was  homogeneous at the
 points of rms measurements, it was necessary to know the mean
 scalar concentration.   This information was also useful  in checking
 probe calibration and the tracer flow rate.  To make measurements
 of mean concentration,  a DC voltmeter with a low-pass DC filter was
 used.  The  time constant for this meter was 47 seconds.

 A disadvantage of using an averaging meter was the low  input impedance.
 When the rms voltmeter and the DC voltmeter were connected to the
 output of the 3C66  unit simultaneously,  the averaging meter tended to
 affect the reading of the rms voltmeter.  For this  reason,  it was
 necessary to switch off the averaging meter while  rms measurements
•were being made.

A schematic drawing of the electronic apparatus and probe is shown
 in Figure 1 6.
Flow Apparatus

Figure  17 shows a schematic illustration of the flow apparatus for the
mixing  experiments.  It consisted of a multiple-or ifice grid and
tracer injection system at the head of a 2-in.  I. D.  tubular reactor.
A nonrec irculating system was used to avoid the problem of tracer
buildup.
                                 58

-------
                       12
Ui
O
W
PH
O
O
w
O
                  10
                  O
                                                JL
                                         _L
I
                                       500        1000       1500       2000

                                            CONCENTRATION OF NaCl, mg/f.
JL
                                                                 2500
                               FIGURE 15.  TYPICAL CALIBRATION CURVE FOR SINGLE
                                          ELECTRODE CONDUCTIVITY PROBE
 I
3000

-------
Q
             TEKTRONIX
             564B STORAGE
             OSCILLOSCOPE
              3C66
              UNIT
         A = A +a
                        1
                               E = E +
                               £<=•< A
                                                    TSI MODEL 1060
                                                    rms VOLTMETER
E   <*   A
                                                    DC AVERAGING
                                                    VOLTMETER
        FIGURE 16.  ELECTRONIC EQUIPMENT FOR MIXING EXPERIMENTS

-------
          Constant Head Tank
 To
Waste
         Water  Supply
         from 3" City Line
               Nozzle  Meter
Honeycomb to  reduce
   pre-grid turbulence
Conductivity Probe
                           Injection Manifold
                           and Grid  Section
                                (Variable Length, Oto4 ft.)
                                                     Constructed from  2"I.D.  Plastic Pipe
                    FIGURE 17.  SCHEMATIC ILLUSTRATION OF EXPERIMENTAL SETUP  FOR
                                                  MIXING EXPERIMENTS

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 The raw water was taken directly from a 3-in.  East Bay Municipal
 Utilities District (EBMUD) line and fed to a constant head tank.   This
 tank was  important for two reasons.  It eliminated fluctuations in the
 flow rate, and it helped to eliminate air bubbles from, the water by
 allowing them to escape to the atmosphere.  Air bubbles can cause
 difficulties in that they represent a region of very high resistivity.
 Any of these passing close to the probe would be detected by the probe
 and would produce an error  in the amplifier output.

 From the  constant head tank, the water flowed through an I. S. A.
 nozzle flow meter and into the tubular reactor.   A 4-in.  section of
 aluminum "honey-comb" was placed upstream from the grid to help
 reduce the level of turbulence to avoid affecting the intensity of
 segregation downstream from the  grid.

 A drawing of  the injection manifold and grid section is shown in
 Figure  18. It was constructed of clear plastic.  The tracer flowed
 from a constant head tank through a  rotameter into the manifold,
 entered the grid bars through the wall of the 2-in.  pipe,  and was
 injected into the flow through the injection orifices drilled in the  grid
 bars.

 Downstream from the grid was a variable length tubular  reactor
 (0, 4, 8, 12, 1 6, 24, or 48 in. ) which was also constructed of transparent
 plastic.   Flanges with rubber gasket seals were used to connect the
 various sections together.

 Beyond the tubular reactor section was the probe section as shown
 in Figure  19-   This section was also used to divert part of the flow
 through the flocculator during the  coagulation experiments.  Two
 valves, one upstream and one downstream of  the reactor section,
 were used to  control the  flow through and the  pressure in the tubular
 reactor.
Multiple-Source Grids

The grids used for this  study were constructed from brass tubing,
1/4-in. or 1/8-in. O. D,  Metal was chosen in preference to plastic
because it was easier to drill holes in metal having the  same orifice
coefficient.   With plastic there is  a tendency for the edges of the
holes to become chipped.  Gibson  used plastic grid bars and found
that because it was impossible  to drill perfect holes,,  the tracer flow
from adjacent  sources varied greatly and artificially augmented the
concentration fluctuations downstream.  The orifices were 0, 021-in.
or 0, 0135-in.  In diameter, depending on the number of sources.  It
was desired that the tracer injection velocity  be  slightly greater than
the main stream velocity.  Brass  tubi.ng was chosen because it is
fairly resistant to corrosion.  The bars were held in place with
silicone rubber cement.
                                 62

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        SCALE:  6" = I1
                                  MANIFOLD
                                                            O-RING
                TRACER
                INJECTION
7////////f/TTTT/////
                                        I	I
               BOLT HOLES FOR
                MANIFOLD
     BOLT HOLES FOR
     CONNECTION TO
     UPSTREAM SECTION
                                                    BOLTS FOR CONNECTION
                                                    TO OTHER SECTIONS
FIGURE 18. CUTAWAY VIEW OF INJECTION MANIFOLD AND GRID SECTION

-------
SCALE:  6" = I1
                           O-RING
                              GASKET
        //////////////////
       V \
                                     BOLT HOLES FOR
                                     CONNECTION TO
                                     OTHER SECTIONS
 FIGURE 19.  CUTAWAY VIEW OF PROBE SECTION

-------
A photograph of one of the grids is shown in Figure 20.  For this grid,
d = 1/8 in. ,  M/d = 4, and the number of sources is  12.  Seven grids
were employed and their characteristics are listed in Table 2.  Figure
21 shows the injection manifold section.
                            TABLE 2

                    GRID CHARACTERISTICS
Grid
No.
1
2
3
4
5
6
8
M( in. )
0. 5
0, 5
0. 5
0. 5
0. 5
0,25
0. 5
d(in. )
0. 25
0. 25
0. 125
0. 125
0. 125
0. 125
0. 125
M/d
2
2
4
4
4
2
4
No. of
Sources
4
9
9
24
12
21
4
Source
Diam
(in.)
0. 021
0. 021
0. 021
0. 0135
0. 0135
0. 0135
0. 021
 EXPERIMENTAL PROCEDURE

 During each run, measurements of mean concentration and rms con-
 centration fluctuation were made with one grid, at a particular distance
 downstream from that grid.  Measurements were generally made at
 the centerline,  although the variation of mean and rms values across
 the cross-section was investigated.  The parameters which were
 varied during a run were the ratio of mainstream flow to tracer in-
 jection flow, QM/QT. and the mainstream velocity, VM-  This latter
 parameter determines the grid Reynolds number, Vj^d/v or
 Several runs were made in order to determine the decay of rms
 fluctuations with distance from the  grid.  Decay curves  for different
 grids  could in turn be compared in  an attempt to determine what
 parameters might be  appropriate for design.  Also, it was desirable
 to develop a rational model for predicting the scalar decay which
 can be expected from any given grid.

 Usually 20 liters of a 250-g/-? salt solution were prepared in advance
 for several runs.  On the day of the run, a portion of this was diluted
 to a SQ-g/Jt concentration in the tracer solution tank (see Figure 17).
 This tracer concentration was used for all runs. The tracer pump
                                  65

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      mmmm
      mmmm
   FIGURE 20. MULTIPLE-ORIFICE GRID
FIGURE 21. INJECTION MANIFOLD AND GRID SECTION
         66

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was started and the manifold was filled with tracer  solution.  Then the
mainstream flow was started by passing water through the large con-
stant head tank.  When there was flow through the tubular reactor,  it
was necessary to have a small tracer flow rate into the system in
order to prevent backflow of fresh water into the manifold.

Because the water taken from the city line was much colder than the
ambient temperature, it was necessary to let the water run for
approximately 30 minutes in order to obtain an equilibrium temperature.
This was important as changes in conductivity are related to temperature
as well as concentration variations.   The pressure  in the tubular
reactor was adjusted to be great  enough to prevent air bubble forma-
tion due to too low a pressure and low enough to allow the tracer to
flow  into the reactor.  Then the flow was  stopped and the conductivity
probe put in place.   The flow was started and adjusted to the desired
value.  The tracer flow was shut off and the AC bridge of the 3C66
unit was balanced.

The conductivity measured under these conditions was due  essentially
to dissolved minerals normally present in the water.  However, there
was also a slight leakage of tracer from the grid bars which could
not be prevented.   This meant  an error in the mean scalar concentra-
tion reading because the balance  condition of the bridge did not  cor-
respond to conditions of  zero tracer injection.  In order to eliminate
this error from the results, the tracer flow was shut  off and a relief
valve on the manifold was opened at the end of each run.  This caused
fresh water to flow from the reactor  into the grid bars and out of the
manifold through the relief valve.  No leakage of tracer into the
tubular reactor occurreds and  the amount of error previously incurred
due to such leakage could be determined.   The rms  value was not
affected by this error.

After the bridge was balanced,  the tracer injection flow rate was set
to a desired value.   The output of the 3C66 unit was connected to the
rms voltmeter and the rms voltage was read.  The output of the 3C66
unit was then connected to the averaging DC voltmeter,  and the mean
value of the signal was read.  When this was completed, the tracer
injection flow rate or the mainstream flow rate was changed and the
measurements repeated.

Drift of the bridge balance  condition was at times a  problem, and it
was often necessary to shut off the tracer flow during a run to insure
that the bridge was  still balanced and, if necessary, to rebalance it.

At the end of the run, the probe was  calibrated in a  beaker by adding
incremental  amounts of tracer  solution to tap water.  During the
first  few runs, a calibration was  made both before and after the run.
However, it  soon became apparent that the probe calibration was
fairly stable and that such checking was not necessary.  The fresh
water used for the probe calibration was taken from the tubular
reactor waste stream at  the end of the run to insure that the tempera-
ture was the same as that of the water used during the run.  After a
                                 67

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run the tracer supply apparatus was drained of tracer solution and
fresh water was pumped through it  in order to inhibit corrosion.
HEAD LOSS THROUGH GRIDS

If grid initial mixers are used in water and wastewater treatment
plants,  the head loss through the grid may be an important considera-
tion in design.  In many cases, allowable head loss may be limited
to a few inches.  Therefore,  loss of head measurements were made
for two grids having different  M/d ratios,  and these were  compared
with predicted values.

Baines and Peterson [ 64] have studied the head loss caused by flow
through grids.  They assumed that all the loss takes place downstream
from the grid, in the region where flow expansion takes place.  They
further assumed that the coefficient of contraction is 1. 0;  i. e, , that
the maximum fluid velocity as it passes through a grid is defined by
that part of the cross -sectional area which the grid bars do not cover.
Using principles of momentum and energy, they found that


                              hL       S2
                      KL =         =                          (8Z)
where S = A,    / AL .  ,.
            bars  total
It can be shown that the drag coefficient,

                                  KT
Therefore,


                            CD=~(fw    '                    (84)

It can also be shown that,  when square-mesh grids are used, this
relation is equivalent to Equation (35) used in the linear decay law for
turbulence given by Batchelor and Townsend [ 14].

In a note on the article by Baines and Peterson [ 64],  T. T. Siao noted
that as S -»O, C;p should become asymptotic to 1. 2, the value for
circular cylinders, instead of zero as Equation (84) predicts.  Thus,
Equation (82) is in error for low solidity grids (i. e, , high M/d).

The modification suggested by Siao is shown in Figure 22.  KL =
hL/(VM;/2g)  is plotted against M/d.  S is related to M/d for square-
mesh grids by
                                 68

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40

30


20
 10
5. 0
2. 0
1. 0
                             EXPERIMENTAL
                             RESULTS
0. 5
        FROM BAINES
        AND PETERSON [ 64]
0. 2
                        M/d

     FIGURE 22.  HEAD LOSS COEFFICIENTS FOR
                 SQUARE-MESH GRIDS
                      69

-------
                         S = 1  -
                                  (f)2
(85)
The head loss coefficients for two grids of the present studies
(M/d  = 4 and M/d = 2) are also  shown in Figure 22.   These coefficients
were  determined by measuring  the head a few inches upstream from
the grid and 4 ft downstream from the grid.  An estimate was made of
the head loss due to wall friction by using a friction factor correspond-
ing to a smooth pipe.  This estimated loss was subtracted from the
total  measured head loss to obtain a value  for the  head loss due to the
grid alone.  Measurements were made at  five velocities in equal  in-
crements from 1 to 5 fps, and at 0. 8 fps.   There was a tendency  to
have  higher values of KL for some of the measurements at 0, 8 and
1. 0 fps - 10% to 20% higher.  As will be suggested in Section VI,  this
could be a sign that a change in the character of the turbulent wake
occurs at such velocities.  This change, if it does occur,  also affects
the mixing provided by the grid,

For higher velocities, the values of KL were quite consistent.  It is
the average of these values which is plotted as  experimental results
in Figure 22.   For the low solidity grid (M/d = 4), the experimental
point  falls close to the line.  For the high  solidity grid (M/d = 2), the
experimental point falls substantially below the curve.  This  may be
due to the fact that there was a  slight space (d/2) between the horizontal
and vertical grid bars.  Thus, the contraction  of the flow was probably
not as great as assumed by Equation (82),  and  the head loss coefficient
was lower than predicted.  The head loss  which would be expected
from each grid at different velocities is given in Table 3.
                            TABLE 3

     HEAD LOSS THROUGH GRIDS AT VARIOUS VELOCITIES
VM< f?S
1. 0
2. 0
3, 0
4. 0
5. 0
hr (inches)
M/d=4
S^O, 45
0. 2
0. 8
1. 7
3, 0
4. 7
M/d-2
S=0. 75
0. 6
2, 5
5. 7
10. 0
15. 7
                                 70

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                             SECTION VI

            MIXING STUDIES: RESULTS AND ANALYSIS
RESULTS
In this section the mixing experiments which were performed are
described.  These experiments were intended  to meet objectives
1) and 2),  i. e. , to determine the parameters governing the degree of
mixing downstream from a grid initial mixer.   The experiments were
designed in such a manner that as much information as possible was
obtained from them.   After the various experiments are discussed,
a general model incorporating  the results of these studies  will be
developed.

Figure 23 shows a typical curve giving the rms concentration fluctua-
tions, at the pipe centerline, downstream from a particular grid (Grid
No.  1:  M = 1/2 in. ,  d = 1/4  in. , 4 tracer orifices  in the cross -section
of the 2-in. pipe). a'/aQ is plotted against x/d.   From a study of
previous experiments concerning turbulence,  in spite of the point
made in Section IV and M/d should affect the turbulence level,  and
the present mixing studies, it appears that d is a more appropriate
parameter to use in normalizing the distance from the grid.  The
decay curve of Figure 23 follows an equation of the  form,


                                                                  (86)
which is essentially the same as Equation (45a).  Two important points
can be made regarding this  graph.

The first point concerns the effect of mainstream velocity on the
mixing at downstream point.  The figure shows data for three main-
stream velocities, Vjyj = 1,  2, and 3 fps (some measurements were
made at  higher velocities during the first few runs).  These velocities
correspond to grid bar Reynolds numbers ranging from Vj^d/v  = 1.  7 x
103 to 5. 1 x 103 .  At a particular value of QM/^T'  tne ra-tio of main-
stream flow to tracer injection flow, there is no consistent difference
between  the values of a'/aoat different mainstream velocities.  That
a'/ai.  is not a function of mainstream velocity is consistent with the
work  of others [  11, 22}.

In some  of the runs,  there was a tendency to obtain abnormally high
values of a'/a1 at the lowest mainstream velocity of 1 fps.  This
                                  71

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     1. 00
     0. 80
     0. 60
     0. 40
     0. 30
o
o
- o
     0. 20
     0. 1!
     0. 10
     0. 08
    0. 06
                             D
                    D  QM/QT =   840
                    o  QM/QT = 1,050
                    •  QM/QT = 1.250
                        V   = 1,2,  and 3 fps
               M = 0. 50 In.
               \
             2 in.
  -H
                  na  \
                                                 \
                                                    \
                                                       \
   GRID NO. 1
  	I     1    I
 TRACER ORIFICES
   DLa.  = 0. 021 in.
d = 0. 25 in.
                                                             D
         20
30    40    50   60    80   100
                  x/d
                                                             200
        FIGURE 23.  DECAY OF CONCENTRATION FLUCTUATIONS
                      DOWNSTREAM FROM A GRID
                             72

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may be due to some change in character of the turbulent wake behind
the grid bars at this velocity.  Inspection of curves giving drag
coefficient and vortex shedding frequency vs. Reynolds number [  18, 65]
for circular cylinders showed no change in character at any Reynolds
number  near those at which the present experiments were done.  A
grid with a low M/d ratio is not,  however, a good approximation of
an infinitely long  circular cylinder.  Also, the measurements of head
loss through the grids showed that the head loss  coefficient KL = hL/
(V^,/2g) was substantially greater at a velocity of 1 fps than at higher
velocities.   This  is another indication that some change in the turbulent
wake did indeed sometimes occur at the lowest mainstream velocity.
One of Gibson's graphs  [11] showed a similar jump at a  low  velocity
although he did not comment on it.

The second point  regarding Figure  23  involves the value of a1  used to
normalize a'.  It  can be shown [ 22] that if a tracer of concentration
A-p and flow rate  QX enters a tubular reactor where the mainstream
flow rate is  QM>  the spatial root-mean-square concentration fluctua-
tion across the cross-section is,
                             ~AT~VQT/QM   .                 (87)
To  use a1  as the initial rms concentration fluctuation for an isotropic
scalar field, the assumption must be made that the tracer is  spread
out across the cross-section so that the mean concentration at all
points of the cross-section is the same while little decay of the con-
centration fluctuations has taken place.  It might then be expected
that measurements of time-averaged rms concentration fluctuations
near the grid would give results of the same order of magnitude as
the calculated value given by Equation (87).   However, this is not
what occurs.  Measurements approximately i in.  downstream from the
grid showed that the  rms values were from 1% to 4% of the calculated
value (there was considerable variation because of substantial dif-
ferences in mean concentration across the cross-section).

It appears that two different mixing phenomena  are occurring.  The
first involves mixing in the turbulent wake of the grid bars.   This
process is effective for only a few grid bar  diameters downstream,
but it is very important.  The vortices  shed by  the bars  act to spread
the tracer as it leaves the orifice.  This also acts to greatly  decrease
the concentration fluctuations at a "point. "  A short distance  from the
grid, the turbulent wakes from the individual grid bars will coalesce,
and isotropic decaying turbulence will develop.  The time-averaged
tracer concentration is fairly constant across the cross-section,  and
the decay of the rms  concentration fluctuations  follows Equation (86).

It should be noted that there may still be considerable segregation
beyond the "wake-mixing" zone.  For example,  if A, the average
                                 73

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concentration of the tracer following complete mixing with the main-
stream,  is 50 mg/S.,  a1  can be computed as approximately 1500 mg/f.
for_the present work.  If a1 = 15 mg/l at some point downstream,
a1 /A = 0. 30, which indicates an appreciable variation from the mean.
However, a1 /a1  = 0. 01,  a small number which gives the impression
of very little segregation.

Both Gibson and Keeler  observed similar phenomena, but their inter-
pretations were somewhat different.  Keeler used a "hairbrush"
injection system upstream from the grid in order to obtain a homoge-
neous scalar field at the grid.   In measurements very close  to the
grid,  he found that the rms values were approximately 10% of the
values given by  Equation (87).   He noted this and assumed that most
of the mixing took place between the injection system and the grid.
He did not,  however,  relate this reduction in  scalar fluctuations to the
spreading which occurred as the tracer left the  injection needles.

Gibson did not make any direct comment on the  fact that his  measured
rms values  were much lower than the. calculated values.  He was
concerned with the fact that at a given point downstream a1 was pro-
portional to QT/QM instead ofy/Qr/QM as would be  the case  if Equa-
tion (87) held.  He  developed a model to explain this phenomenon.
This model  also — almost inadvertently — gives  an explanation of why
the measured rms  values were so low.  Gibson's model •will be ex-
amined more closely later.

Some of the scatter in Figure 23 is  due to the  increase of a1 /a1  with
increases of Q^ at a fixed value of QM-  ^n most of  the experiments,
QM/QT did  not vary by more than a factor of  6 (for  Figure 23, this
factor is 1. 5) and was set so that the mainstream velocity •was of the
same order of magnitude as the  tracer  injection velocity.  Furthermore,
for the grids with an M/d ratio of 4, the scatter due to variations of
        was even greater.
Figure 24 shows a1 at a given x/d and QM plotted against QX for such
a grid.   There is almost a direct proportionality between a1 and Q>j-
This is the same phenomenon Gibson observed.  He concluded that
it was probably caused by the tracer injection orifices for his  ex-
periment facing upstream.  In most  of the present experiments, the
tracer injection orifices faced downstream.  It seems,  therefore,
that the phenomenon is due to the fact that Equation  (87) is  inappro-
priate for describing the initial rms  concentration fluctuation of the
isotropic scalar field.  It is,  however,  appropriate  for describing
the initial rms concentration fluctuation for the two  unmixed streams
before the wake -mixing zone and should be used for this.  The  effect
of QM/QT in determining the value of a1 downstream from  a grid will
be considered more closely later.  Nowy other experiments designed
to ascertain how other parameters may affect the mixing will be
discussed.
                                 74

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                                        T
          GRID NO. 5
          M/d = 4, M = 0.5 in. ,  d = 0. 25 in.
          12 ORIFICES
          VM - 3  fps
          AT =  50 g/l
          x/d = 196
g
"ttf
                 0. 5
i.O
1.5
2. 0
              FIGURE 24.  a1 vs. QT FOR GRID WITH
                              M/d = 4
2. 5
                               75

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Effect of Scale of Turbulence on Decay Rate

In Section IV, it was noted that the scalar decay rate,  a,  in Equations
(45) and (86) was closely related to the right-hand side of Corrsin's
equation,
2 +N -1
Sc
3 2/
3 {L,B*/*7IS*/Z log NSc
6(2> XL ' ' "V3' N "
             da'
             du1
               i
and is in fact equal to it if the right-hand side of Equation (54) is a
constant as decay proceeds.

L  and L,. are the two most important parameters in this equation as,
in any mixing system, they are the parameters which can presumably
be varied by changing the physical configuration of the system.  It was
noted in Section IV that L,. is  apparently a function of the grid bar
diameter,  d.Vj-

In order to  show the effect of the  scale of turbulence on the decay rate'';
experiments were carried out with two grids.   The number of tracer
orifices for both grids was  nine,  and the center-to-center spacing of
the bars,  M,  was 1/2 in.  The bar diameters  for the two grids,  ,.'
however,  were 1/4 and 1/8 in. , respectively.  The results are shown
in Figure 25. For the grid with the smaller value of d,  L /L- should
be greater, and the decay rate (slope of the scalar decay curve) should
be less.   This is what was observed.

Keeler also attempted to show qualitatively the effect of L /L- in
Equation (54).  He used two grids with the  same M/d ratios,  but with
one grid,  the values of M and d were twice that for the  other.  The
same hairbrush injector was  used for both grids.  Through a rather
ingenious method of plotting his results,  he showed a pronounced dif-
ference in scalar decay for the two grids.  More conventional plotting
of the data (as in Figure 25) shows that there was  actually very little
difference in the two values of a.   The reason for  the different results
of his experiments and those  of the present study is  not  clear.  Perhaps
in his study the value  of L  /L. was low enough so  that a. change in the
value did not affect the complete expression on the right-hand side of
Corrsin's equation.

In discussions of this  sort,  it should always be kept in mind that
Corrsin's equation strictly  applies only to those conditions  of high
unattainable in laboratory experiments.  The values of Nj^e>, for the
present study varied from 30 to 60.  Such values were termed "moderate
by Corrsin  [17].
11
                                  76

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bO
s
     60
     40
     20
    .10
                      9-ORIFICE GRIDS

                    M = 0. 50 in.
                    A  = 47. 5 mg/f.
                   a'   = i, 540 m.g/1

                   V,   =1,2, and 3 fps
                                     M
                                         GRID NO.  3
                                         M/d =4,  d = 0. 125 in.
X
                   X
                         X
                              8
                           X
                                LX
                        GRID NO.  2
                        M/d =2, d = 0. 25 in.
                                      X
                                        X
                                             \
                                               X
                                                 X
                                                     \   D
                                                       X
                                                        X
                                                                \
                                                                  x
                            I	i	I	I	L
        14     20
          40      60    80   100

                   x/d
200
400
            FIGURE 25.  EFFECT OF SCALE OF TURBULENCE
                         ON SCALAR DECAY RATE
                                    77

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Gibson estimated that u'Lf/v should be greater than 3. 3 x 10s  for an
inertial subrange to occur.  For the present work, this parameter is
estimated to be approximately 10s .


Effect of the Number of Tracer Orifices

As was noted in Section IV,  it has been assumed by  some investigators
[ 22, 29] that the scale of segregation,  Ls, is  a  function of the number
of tracer orifices with an  increase in the number of orifices pre-
sumably decreasing Ls.  Further, a decrease in Ls should cause an
increase in the scalar decay rate according to Equation (54).   To test
this,,  experiments were conducted with two grids,  identical except for
the number of orifices; one had 4 and the other had 9.  The scalar
decay curves for the two grids are shown in Figure  26.  For the 9-
orifice grid, the rate of decay was actually slightly  less, instead of
greater, as might be expected if the above assumption were true.
The conclusion which is drawn from this is that an increase in the
number of orifices does not  increase the scalar decay rate.  As noted
previously, there seems to be no rational basis for  such an assumption,
and these results seem to  refute it.

Figure 26 does seem to indicate that the  "wake-mixing"  is affected
by the number of tracer orifices.  At low values of x/d,  a1  is lower
for the 9-orifice grid,

Such a conclusion is further  substantiated by studies involving grids
with M/d ratios of 4.  Four  such grids were used with 4, 9,  12, and
24 tracer orifices.  It was assumed that the scalar decay rate of the
9- and 24-orifice grids applies to the other two  grids even though
measurements involving the  latter were only made at one x/d value
for each one.   Starting with Equation (86),
                           TT = ff(f)                            (86)
                           ao

one can solve for a'.
                           a -
                               (x/d)
                                                               (88)
Figure 27 shows a plot of a vs.  n,  the inverse of the number of
tracer orifices.  Except for the value at n = 4, there is a fairly strong
correlation between a and n 1 •  Extrapolation of the curves of
Figure 26 to  x/d - 1 also shows a direct proportionality between n
and a.   Therefore it will be concluded for the  purposes of this study
that in fact a is proportional to n"1.  Of course,  it will be evident from
a study pf the plotted data that a  slight shift of the line drawn through
the data points will change the value of a tremendously, perhaps by as
                                 78

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bo
a
"rt
    60
   40
    20
    10

     8
                        M = 0. 5 in. ,  d = 0. 25 in.
                        M/d = 2
                        A = 47. 5 mg/l
                a1 = 1,540 mg/i

                V= 1,2, and 3 fps
"xx
L    Bx
               x
                x
                  x
             X
               X
          O GRID NO.  2
            9 ORIFICES
           GRID NO. 1
         • 4 ORIFICES
                               I   I   I  I  !  I
       12
        20
40
60
80  100
200
                              :/d
      FIGURE 26.  EFFECT OF THE NUMBER OF ORIFICES
              ON SCALAR DECAY RATE, M/d = 2
                             79

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o
•v-t
 X
tf --,
m
O
                             n = 24,  x/d = 384

                             n = 12,  x/d = 384

                           Qn =  9,  x/d = 384
                             n -  4,  x/d - 192
                                   M/d
                                     d
                                     A   = 47. 5 mg/i
                                         = 1, 540 mg/i
                                   = 4,  M = 0. 5 in.
                                   = 0. 125 in
                                         = 1, 2,  and 3 fps
10 -
                  , 05
                       . 10
. 15
. 20
                     (NUMBER OF SOURCES)
                                             -l
                                            n
                                                  -l
25
     FIGURE 27.  INVERSE RELATIONSHIP BETWEEN NUMBER OF
               SOURCES AND a FOR GRIDS WITH M/d = 4
                                   80

-------
much as 50%.  This sensitivity must be kept in mind when workirg
with log-log plots of this sort.  Any value of a. obtained from such
extrapolation should be recognized to be of low accuracy.


Effect of Injection Sources JF/xcing Upstream

An effort was made to find ways of modifying the  injection system in
order to increase the scalar decay rate through a change in the  scale
of segregation.   An experiment was carried out in which a grid  was
turned around such that the tracer  injection orifices faced upstream.
The scalar decay curve for  this condition was  compared with one for
a grid with normal orientation (tracer injection downstream).   The
results are shown in Figure 28.

The values of a1 close to the grid are higher for the case in which the
orifices face upstream, apparently because the "wake-mixing" is not
so  effective in reducing the scalar fluctuations.  The rate of decay,
however,  is much greater.  Whether or not there is a  difference in
the scale of segregation is not known.  However,  it has been shown
that a difference in the scalar field will affect  the scalar decay rate
even though the turbulent flow field is essentially the same.

It was originally planned that measurements of Ls would be  made by
using one probe, making measurements of a Eulerian time correlations
relating this to the Eulerian space correlation discussed in Section
IV, and calculating the scale of segregation, Ls.   This was  to have
been done  by recording the data digitally on magnetic tape and utilizing
a CDC 6400 computer to make the calculations.  However, because  of
time limitations and a desire to proceed with experiments relating
process performance  (in alum coagulation,  wastewater coagulation,
and wastewater chlorination)  to goodness of mixing, the studies
involving measurement of Ls were not  carried out.   Such an experiment
would prove very interesting, particularly in relation to Figure 28,
as the scale of segregation has apparently not  been measured for any
system.

It is interesting to note that when the grid used for the  experiment
described  above was in the upstream injection orientation, the  system
was very similar to one used by Gibson:  upstream injection, d  = 1/8
in. , and orifices placed halfway between grid bar intersections.  M
was slightly different  for the two studies —5/8 in.  for  Gibson's  and
i/2 in.  for the present work.  A comparison of his  results and those
of this study is presented  in Appendix C.


Comparison of Geometrically Similar Grids

As  it may be difficult  to design grids with bars 1/4 or  1/8 in.  in
diameter for full-scale treatment plants,  it is important to attempt
to determine how scaling these grids in size affects the resulting
                                 81

-------
30
20
                           1    T
 10
                              24 - ORIFICE GRID
                           M     = 0. 5 in. d = 0. 125 in.

                           M/d  = 4

                           A     =47.5 mg/i

                                 = 1, 540 m.g/1
           O


           O
      TRACER INJECTED
        DOWNSTREAM
                TRACER INJECTED
                  UPSTREAM
                                 =1,2, and 3 fps
                                                    I
   20
40      60    80  100

               x/d
200
300  400
     FIGURE 28.  EFFECT OF CHANGING ORIENTATION
              OF TRACER INJECTION SYSTEM
                 ON SCALAR DECAY RATE
                             82

-------
scalar decay.  In order to make a study of the scaling  effect,  a grid
with M and d values one-half those of grid No., 1 was constructed with
21 orifices and designated as grid No.  6.  For perfect similarity it
should have had 42 - 16 orifices.  However, because of problems
with the  geometry of the configuration,  exact similarity could not be
obtained in this respect,

A comparison  of results obtained with the two grids is shown in Figure
29.  The results for  grid No.  6 were very poor,  giving a curve which
only with great imagination  could be considered a straight line on
log-log paper.   It would be very difficult to define a slope through
these points and impossible to  estimate a value of a. with any accuracy.
It is apparent,  however, that the smaller grid gives poorer results
than does the larger  grid.  Furthermore, attempting to compare
results from these two geometrically similar grids ignores two pre-
vious conclusions; the slope of the scalar decay curve  (for downstream
injection from the grid bars) is a function of the grid bar size,  and
the displacement  of the  scalar  decay curve,  or a, is a function of the
number  of sources.  For that reason,  perhaps it is appropriate to
compare the results  obtained using grid No. 6 with those obtained
using grid No.  4 (d = 1/8 in. ,  M = 1 /2  in. ,  24 orifices).   These two
grids are very similar with the exception that M/d = 4, 0 for grid
No.  4 and  20 for grid No. 6.  The comparison of results is  shown in
Figure 30.  The agreement  is quite  good, and while it  cannot be said
to confirm the  previous conclusions, it is at least compatible with
them.

It should be noted that Keeler  concluded,  through comparison of his
results with Gibson's, that the  M/d ratio  affects the displacement of
the scalar decay curve.   Such a conclusion  seems intuitively reasonable.
However,  because of differences in  the tracer injection systems for
the two studies and differences in their methods of calculating a' ,   it
seems that comparison  of results obtained in the two studies cannot
be made.  Keeler measured a' very close to the grid and empirically
determined that the initial_rms concentration fluctuation in the  isotropic
scalar field was equal to A,

Gibson,  in developing a model  to explain why a' was proportional to
QM/QT for his work, found that the initial rms concentration fluctu-
ation of the isotropic _scalar field was proportional to A,  and he there-
fore apparently used A to normalize a'.   Therefore,  the two curves
which Keeler compares  are  graphs of (a1/A)2 vs.  x/M, As the tracer
injection systems are different and the  values of QM/^T are different
(approximately 100 for Keeler  and 2000 for Gibson),  the fact that there
is a  difference in displacement between the two curves cannot be used
to prove  that M/d affects the value of a in Equations (86) or (45).


SUMMARY OF MIXING  STUDIES RESULTS

It would  be desirable to  relate the results produced by the various
grids and obtain an overall description of the mixing process which
                                  83

-------
oo
                   10
                so
                a
                                      00
                                 M = 0. 5 in.,
                                 d = 0. 25 in.
                                 4 ORIFICES
                           • •
                           M/d - 2

                           A = 47. 5 mg/t

                           a' = 1, 540 m.g/1

                           V  =1,2,  and 3  fps
                               \
                      •) GRID NO. 6
                         M = 0. 25 in. ,
                         d = 0. 125 in.
                         21 ORIFICES
                                                                        \
                                         \
                      20..
50
100
200
500
                                                          x/d
                             FIGURE 29-  RESULTS OBTAINED FROM GEOMETRICALLY
                                                   SIMILAR GRIDS
1000

-------
                  15
                  10
00
Ul
                              GRID NO.  6
                              M/d = 2,  M = 0. 25 in
                            *21 ORIFICES
                              GRID NO.  4
                            oM/d = 4,  M = 0. 50 in
                              24 ORIFICES
                                 20
50
d
A
a1
o
VM
= 0. 125 in.
= 47. 5 mg/i
~ 1, 540 mg/t
- 1, Z, and 3 fps
100
200
500
                                                      x
                                                       /d
                                     FIGURE 30.  EFFECT OF VARYING M

-------
occurs under the conditions found in this study.   To that end,  the con-
clusions reached in the previous sections are summarized below,

1.    The degree of mixing at a point downstream dees not  depend on
      the mainstream velocity.  The time necessary to reach a given
      degree of mixing is inversely proportional to the mainstream
      velocity.

Z_    a'  as calculated by Equation (87) is not a good indication of the
      initial rms concentration fluctuations  in the isotropic scalar
      field, A great deal of mixing occurs as the tracer  spreads upon
      leaving the orifice in the turbulent wake of the grid bar,

3.    At a  point downstream^  a' can be  said to be proportional to
      QM/QT rather thanV/Qj^/Q^ as suggested by Equation (87),
      This is the same as the  phenomenon observed by Gibson and
      is  closely related to the "wake-mixing" described above,

4.    Because  it determines the integral scale of turbulence, the
      grid  bar  size affects the rate of scalar decay as predicted by
      Corrsin, the rate increasing as the grid bar diameter increases,

5.    Within the limits of the present work, the number of tracer
      orifices does not seem to greatly  affect the scalar decay rate.
      It is  therefore concluded that the number of sources does not
      affect the scale of segregation.  Such parameters as method of
      tracer injection (upstream or downstream, for example) do
      seem to have a strong  effect on the scalar  decay rate when the
      turbulent flow field is essentially  unchanged.  The conclusion
      drawn is that Corrsin's  prediction concerning the effect of the
      scalar field,  as described by L ,  on the scalar decay rate, has
      been qualitatively shown.

6.    The number of sources as well as the method of injection seems
      to  affect  the "wake-mixing. "  To a reasonable degrees  the value
      of  a'  measured at a given distance downstream is inversely pro-
      portional to the number  of tracer  orifices  in a given cross-
      sectional area.

7.    Within the limits of these studies,  the M/d ratio seems to be
      important only in that more closely spaced bars can provide
      a greater number of tracer orifices per square inch,


Not all of the data substantiates each of these conclusions.  In some
cases it  has been necessary  to allow considerable latitude in i.ncorpora
ting specific results into the general model.  However^ such inter-
pretation is necessary  if any general conclusions are to be  drawn.
These conclusions have been drawn with the objective  of determining
the design  parameters for use with prototype grids.   In particular, it
appears  that "wake-mixing"  may be the most important consideration
                                 86

-------
in designing prototype grids.  From results of the process studies
described in Section VII, the time necessary for adverse chemical-
physical reactions to occur  seems to be sufficiently short such that
the degree of mixing taking  place in the first fraction of a. second
determines whether  process performance will be satisfactory.  It
may be that the portion of the scalar decay  in the isotropic scalar
and turbulence fields will be unimportant in this regard.


INTERPRETATION OF RESULTS:
MODEL DEVELOPMENT

A model which combines the above summary of results in a quantita-
tive and concise manner can be developed.   It  is a semi-empirical
model in that while the  straight-line, log -log form of the decay curve
and the dependence on the scales of turbulence and segregation have
been derived theoretically,  the actual values of the coefficients must
be determined from  experiment.  The general decay equation is
written,
                         le  ==«                             (86)
                              o
where a = fi (n  , Q-M/^T'  injection system),  a =f2(d,  injection
system),  and n  = the number of tracer orifices per square inch of
                           ™ 2
reactor cross -section,  in.

Let a' be the initial rms concentration fluctuation in the isotropic
scalar field


                           P-  =<*'~a                        <89>
                            i


where a{  = fa (injection system).

To derive an expression for a1 , assume that the tracer becomes
partially  mixed with a portion, of the mainstream flow  rate which
passes close to the  injection orifice.  This portion will be Q  and is
defined by,


              Qp=KpnsQM  '    QT<


where K,, = f4(injection  system).   Kp is essentially the cross -sectional
area with which the tracer is mixed.  This approach is similar to
Gibson's but is  different in that he arbitrarily set a value for  Kp.  He
also assumed that the tracer was  completely  mixed with the flow rate
Q  .  He called this  premixing.
 P
                                  87

-------
In this wake-mixing region, the average concentration of the tracer
mixed with this portion of the flow is,

                     A  -   T T  -   T  T                       (91)
                      p    Q    ~K n Q..
                      c      p      p s  M


It will be assumed — somewhat arbitrarily —that the rms concentration
fluctuation over the cross-section is,


                             a' =K  A                            (92)
                              i    w p


where K   = fs (injection system).  Substituting in Equation (91).
        w
                               K  A  Q
                          a' -  T.w  *  L        ,.                 (93)
                           i    K  n Q, ,
                                p  s  M

Eliminating aj from Equations (89) and (93),

                       ' a1 K  n  Q^,           -a
                        K  A_ QT
                          w   I  T
Combining coefficients,

                         a'n Q           -a
                          ATQT    -«  M'


This equation describes the rms concentration fluctuation,  a', which
can be expected at a normalized distance downstream,  x/d,  in terms of
the known parameters n  , QT^I  QT, and A ,  and the experimentally
determined scalar decay rate,  a,  and wake-mixing coefficient, a".
a is determined by the grid  bar diameter and the type of tracer in-
jection system (for  example, upstream injection or downstream
injection from the grid bars),  a/11 is determined by the type of tracer
injection  system used,  a11 has the units L~2  because it includes K ,
the cross-sectional area near each  source which defines the flow  "
rate involved in the wake-mixing, or premixing as Gibson terms it.

Since,

                                ATQT
                            A  =-^r-i        ,                   (96)
                                   88

-------
then Equation (95) can be modified to


                        a'n           -a
                        -=T- = «" (j)       .                    (97)
                          A         d

This can be transformed to a relation involving a1 ,  the initial rms
concentration fluctuation of the two unmixed streams, by use of
Equations (87) and (96).
                                            -a
                                          d'
= «" (f)      •              (98)
In order to illustrate that the results of this  study can be described
reasonably well by this model,  the data from seven different grids are
shown in Figure  31 a'ns/A  a" is plotted against x/d.  All the data
points represent injection from the downstream side of the grid bars.
ns varies from 1. 3 to 7. 6 orifices per square inch.   A varies  from 19
to 57 mg/L  To reduce the total number of points plotted,  only the
data for Vj^ = 2 fps are  shown.
There is, as might be expected, considerable scatter,  but it does
not seem excessive.  For the grids with d = 1/4 in. ,  taking  the tracer
source density into account actually increases the difference in results
between the 4-orifice and 9-orifice grids (see Figure 26 for comparison).
The wake -mixing,  as manifested by the value of a11 which fits the data
best,  does, however, seem to be described quite well by this model.
As  mentioned previously, it could well be that the wake-mixing is the
crucial step in the mixing process.

The value of a" which seems to fit these data is 5 in. ~2.  The decay
rate,  -a, is approximately -0.4 for the 1/8-in.  grid bars and  -0. 8
for the 1/4-in. bars.  The use  of this model to compare results of
the present study with those of  Gibson in the case of the tracer  being
injected  upstream  is given in Appendix C.  The agreement seems to
be quite  good.

The question which naturally arises  concerns the extrapolation of
these results to grids with larger bars.  The results of the alum
coagulation tests suggest that the grid bars in prototype mixers will
probably be held to 1/2 in. or less.  The decay rate for such a grid
will probably be  somewhat greater than the -0. 8 for the 1/4-in. bars
used in the present work. How much greater cannot be determined.
Presumably, though, the value  of a" which is controlled  by  the wake-
mixing would be the same. In Appendix D  are estimates  of the  scalar
decay curves for grids with larger bar diameters.
                                  89

-------
vO
o
                       1.0
                       0. 5
                       0. 1
                       0.05
                        . 01
                       0. 005
                                       d = 1/8 in.
                                       (a = 0.4)
GRID
NO.
  1
  2
  3
  4
  5
  6
  8
                                                      d - 1/4 in.
                                                      (a - 0. 8)
                                    \
                                                 10
                             50   100
500  1000
                                                         x/d
                      FIGURE 31.  GENERAL MIXING MODEL:  RESULTS FOR SEVEN GRIDS

-------
                           SECTION VII

         INITIAL MIXING AND ALUM COAGULATION -
                         FLOCCULATION
The purpose of the experiments described in this section  was to
demonstrate that rapid initial mixing is important in certain water
and wastewater treatment processes, specifically alum coagulati.on-
flocculation of a turbid water.  Another purpose  was to  show that
grid-type initial mixers,  the mixing characteristics of which were
described in Section VI, can be used to effect the rapid  mixing.  A.s
stated previously, very rapid mixing of the chemical •with the water
stream before certain reactions  can occur or be completed  might
result in improved  process performance.

Alum added to a turbid water with sufficient alkalinity undergoes very
complex, rapid, and  irreversible reactions.  This study and pre-
vious work have shown that if the Al(III) can come in contact with all
the turbidity particles before these reactions have proceeded too far,
then the alum can  be  more effective in performing its task of aiding
clarification.  It will be shown that the effect of  initial mixing is
dependent upon the alkalinity of the water.  If the alkalinity  is suf-
ficiently low, slow initial mixing will not  detrimentally  affect the
process performance.  However,  increasing the alkalinity results
in an increasing sensitivity to the adequacy of the initial mixing.

Because of the prohibitive cost and difficulty of performing  field
experiments, the work described herein involves pilot-plant studies.
This allowed close control of all parameters involved,  but from the
point of view of demonstrating  the applicability of this concept to
full-scale water and wastewater  treatment plants, there is one dif-
ficulty.  While it is not difficult to develop a device  producing very
rapid mixing in a 2-in. diameter pipe, it  is a more  difficult task to
design and  construct  a device producing mixing of equal rapidity in a
large pipe.

It  is possible,  through the use  of mixing theory and  experiments to
predict the  intensity of segregation (or degree  of mixing) at  a partic-
ular distance downstream from a given grid.  However, it is not
possible to  predict precisely at the present time  how rapid the  mixing
of the chemical stream with the water stream must  be in order  to
avoid poor  performance.  The  rates of the crucial reactions or
phenomena  are  not known.  Evidence will be presented which shows
that for alum coagulation-flocculation of a turbid water, the time of
mixing, the time required to reach some  low,  arbitrarily defined
value of the intensity of segregation, must be  very short if performance
is  to be improved.
                                  91

-------
This point is important because increasing the rapidity of initial
mixing only slightly, such as by improving the flash mixer, may not
lead to improved performance.  It is believed that a grid-type initial
mixing device will help overcome this problem.  The mixing pro-
vided by a grid  in a pipe  depends not on the diameter of the pipe but
on the physical  configuration of the grid:  the bar diameter, the bar
spacing,  and the number of tracer injection orifices per  square inch
of cross-sectional area.   Thus, if grids which are fairly fine with a
high injection orifice density can be  constructed  and placed in large
pipes, it may be possible to utilize rapid initial mixing to provide
an improvement in water treatment processes  or to decrease the
amount of  chemicals needed for the processes.
SEGREGATION JAR TESTS

In order to show the effect of prolonged segregation in the mixing of
alum with a turbid water,  a jar test which simulated the difference
between slow and rapid initial mixing was devised.  Two 500-m^
samples of turbid water were used.  In most instances the turbidity
consisted of a 25-mg/^ suspension of kaolin, although a 50-mg/J!
suspension of bentonite was used in a few experiments because of
the differences  in coagulation characteristics between the two types
of clays [ 36, 38],  An  "optimum" alum dose was determined for the
turbidity and alkalinity of  the sample by using jar tests.  Various
concentrations of alum were added to samples  of turbid water, and
the samples stirred in a jar test apparatus.  The  lowest alum dose
which resulted in the most rapid formation of visible floe was chosen
as optimum [ 33].

The experiment representing rapid initial mixing  was essentially an
ordinary jar test.  The previously selected alum dose was added
directly to one of the 500-m-f samples.  This was  vigorously stirred
with a glass stirring rod for a few seconds in order to effect complete
mixing,  Then the  sample was put in a jar test apparatus and stirred —
usually for 6 minutes at 70 rpm.  The floe formed -was allowed to
settle for 15 minutes,  A pipette was used to remove a sample of
supernatant from approximately one-half  inch below the surface of
the sample in order to  avoid entrapping floating floe particles in the
supernatant.  This supernatant was then analyzed for  residual tur-
 bidity using a light-scattering turbidimeter (the turbidimeter and
chemicals are described in the section on continuous flow coagulation-
flocculation experiments).

The experiment was  repeated with a second 500-rrJ sample  of turbid
water with the following modification.  This sample was divided  into
two portions, 100 ml and 400 m^ for example.  The alum was then
added to the 100-m-f portion and was vigorously stirred for 3 to 5
seconds.  Then  this 100 -mf. portion was added  to the remaining 400
ml   The two portions were thoroughly mixed with a stirring rod,
                                 92

-------
and the jar test was repeated.   This experiment represented poor
initial mixing, i. e. , prolonged segregation between the alum and a
portion of the turbid water.

Generally,  the jar test representing poor initial mixing resulted in a
higher residual turbidity than the jar test with rapid  initial mixing,
This difference in results  can be presented as the ratio of two aggre-
gation rate coefficients, KAm,  the  coefficient for the case of rapid
initial mixing, and KAS, the coefficient for the case  of prolonged.
segregation.  The values of rms velocity gradient, G,  and time of
flocculation,  T,  were  low  enough to allow deletion of the breakup
term in the equation describing the rate  of change of the concentration
of primary particles,
                                                                 (70)
This equation can be easily solved for a batch system.,


                       In (n, /nf ) =   K
In the  segregation jar tests, the values of G and  T were the same for
the experiments involving rapid and  slow initial mixing and can be
eliminated from the equation giving the ratio of the two aggregation
rate coefficients.


                       ln(ni   /n?)    KA
                       	—	  =^7-^-                     <99)
                          /     / o \     -tv .
                       In n,  /n  )      A
                            1 s    i        s

where n: m and nj   are the concentration of primary particles re-
maining for the case of good mixing  and poor mixing, respectively.
As noted in Section IV,  nx /nl   can be taken as the fraction of
turbidity remaining after treatment as measured by a light scattering
turbidimeter.
Effect of Bicarbonate Alkalinity on Jar Test R.esults

The water which is normally delivered to the  University of California
by the East Bay Municipal Utility District is  taken from the Mokelumne
River  in the Sierra Nevada Mountains.  The concentration of dissolved
matter in this water is unusually  low, the TDS concentration being
approximately 32 mg/1  The alkalinity,  as CaCO3, is 20 mg/1  It
was found that with a. 25-mg/l suspension of kaolin in this water,  no
effect  of initial mixing,  as measured by the segregation jar test,  was
                                  93

-------
apparent.  Even with segregation times  of up to 30  sec,  the results of
the jar test representing poor initial mixing produced results which
were as  good as those produced by the test representing rapid initial
mixing.

In order to determine whether  increasing the alkalinity might have an
effect on the jar test results,  sodium bicarbonate was  added to the
tap water before the kaolin.  The jar test described above was re-
peated at various alkalinities and alum doses.   The results are shown
in Figure 32 where KAm/Kj\  is plotted against alkalinity.  The
figure shows the results of initially adding the alum to 100 no? and
250 mf. of the 500-rrJ sample.   It can be seen that increasing the
alkalinity causes the effect of segregation to be increased.  Also,
initially  adding  the alum to a smaller portion of the total sample
causes the effect to be greater.   The range of alum doses  in Figure
32 is 23  to 40 mg/^,  depending on the alkalinity.  Not shown are the
results of  segregation jar tests  performed with a 50-nag/^ bentonite
suspension.  The data involving bentonite are  rather limited,  but  the
increase in the  effect of segregation with an increase in alkalinity
is also found there.  Vrale and Jorden [ 59]  discuss the  importance
of rapid  initial mixing in conjunction with silica suspensions which,
as noted in Section IV, have coagulation characteristics  similar to
bentonite suspensions.

It appears  that the alkalinity of the  water affects the process by
controlling the rate and extent of the hydrolysis  and polymerization
(or olation) reactions of Al(III).which occur in the presence of the clay
particles in the segregated portion of the sample.  This may be due,
in part at least,  to the buffer effect that alkalinity has on the pH as
alurn is added.  Stumm and O'Melia [37] have shown that the reaction
rates of  Fe(III)  and presumably  Al(III) are, strongly  affected by pH.
They found that the rate of removal of Fe    from the  system increases
100 times for every unit increase in pH.  It  is also  known that  the
polymerization  reactions are considerably slower than the initial
hydrolysis reactions [ 66], but how they vary with pH is unclear.   As
alum is added to a portion of the turbid water  sample,  the pH will be
depressed  to an extent depending upon the buffer capacity of the
water —the lower the alkalinity,  the greater the reduction in pH.
And as the pH is lowered, the rate  of removal of A1^^ from the
system decreases.  Thus, at low alkalinities,  the reactions which
can be detrimental to process performance might occur more slowly.

Figure 33 shows the final pH vs. the alkalinity for the optimum alum
dose  in the  segregation  jar tests.   The alum doses in mg/i are shown
next to the data points.  The final pH increases with increasing
alkalinity.   This adds to the effect  of buffer capacity discussed above
since, at higher alkalinities, not only will the  extent of depression
below the final pH in the segregated portion be less, but the final  pH
                                 94

-------
vO
U1
                3. 75

                3. 50

                3. 25

                3.00
2.
2,
2.
2.
i.
i.
i.
i.
0.
75

50

25

00

75

50

25

00

75
                                        ALUM INITIALLY
                                        ADDED TO 100 ml
                                        OF 500-rrL? SAMPLE
ALUM INITIALLY
ADDED TO 250 mi
OF 500-m£ SAMPLE
                            20     40      60       80      100     120

                                                 ALKALINITY, mg/1
                                                         140
          160
                                                                      180   200
                    FIGURE 32.  EFFECT OF SEGREGATION ON COAGULATION-FLOCCULATION:
                                                     JAR TESTS

-------
ffi
3
8. 0


7. 8


7. 6


7.4


7, 2


1. 0


6.8


6. 6


6.4


6. 2


6. 0
                    25 mg/4 KAOLIN
                    SUSPENSION
                                                             40
           35
30
                   23
                 23
  NUMBERS REPRESENT
  ALUM DOSES IN mg/4
         0    20    40    60    80    100   120   140   160   180  200

                      ALKALINITY,  mg/1 as CaCO3

          FIGURE 33.  RELATION OF PH AND ALKALINITY AT
                        "OPTIMUM" ALUM DOSAGES
  itself will be higher.  Thus, it is to be expected that at higher
  alkalinities,  the pH in the portion to which the alum is first added
  will be higher, and the rate of the hydrolysis and polymerizations
  reactions will be faster.

  Buffer capacity may affect the process in another way.  At low
  alkalinities the pH in the portion to which the alum is initially added
  may be driven low enough to prevent the formation of the  insoluble
                                    96

-------
hydroxide (see  Figure 1).  Not until the mixing is almost complete
will the Al(OH)3 s tend to be formed, and this may be the crucial
reaction which  it is necessary to avoid.  At higher alkalinities the
pH in the portion to which the alum is added will not be driven so low,
and Al(OH)3 g can form before mixing  is completed.  More rapid
mixing may overcome this.

It is possible that alkalinity has an even more direct effect upon the
hydrolysis  reactions.  Kim, Ludwig,  and. Bishop [ 36] found that the
isoelectric pH of the aluminum-hydroxo compounds was dependent
upon the alkalinity of the water and postulated that the bicarbonate
anion may have a stronger coordination tendency with the aluminum
ion than does a  hydroxide ion,  causing a decrease in isoelectric pH
with an increase in anion concentration.  It can be concluded from
this that the character of the reactions which occur are directly re-
lated to the alkalinity.

It should be noted that Kim,  Ludwig, and Bishop found that the iso-
electric pH decreased with increasing alkalinity.  In the present study,
the final pH at optimum alum dose increased with increasing alkalinity.
Although the optimum pH decreases with increasing alkalinity, the pH
range  for "good" coagulation becomes wider.  Thus,  "optimum per-
formance"  in the present sense does not necessarily correspond to
isoelectric pH.

It is also possible that the hydrolysis and polymerization reactions
•which occur when Al(III) is added to water  are so  rapid that their
degree of completion depends only on the degree  of mixing (see Figure
8).  It might then be postulated that the diffusion of the aluminum-
hydroxo compounds to the clay particles and the  resulting destabiliza-
tion may take a relatively long time (still less than one second).   Very
rapid mixing could allow the destabilization to occur in the presence
of more clay particles, and better performance  would result.  It is
unclear how varying the alkalinity  (or pH) would affect this.  It might
be that at lower alkalinities, a greater degree of mixing would be
necessary to reach a given degree of completion of the hydrolysis and
polymerization  reactions.  Thus,  more clay particles would be mixed
with the destabilizing compounds,  and initial mixing would not be as
crucial as at high alkalinities.

Adding the alum to a smaller portion of the turbid water sample  results
in an increased effect of segregation because the alum is segregated
from a greater  amount of the kaolin during the period that the crucial
reactions are taking place.  If  less kaolin ; ••< present during the
occurrence of these reactions, then the re^ dual turbidity after com-
pletion of the jar test will be greater.

It should be noted that there  is a slight, although reconcilable, conflict
between this result  and the conclusion regarding the effect of buffer
capacity on the  phenomena.   When the alum was initially added to
250 m.SL rather than 100 red of the turbid water  sample, the alum
                                  97

-------
concentration -was twice instead of five times the final dose in the total
500 rnl  Therefore, the pH was not driven as low,  and the reactions
could occur at a much faster rate, or,  alternatively,  Al(OH)3  could be
formed.   It might be expected, therefore, that adding alum to a larger
portion of the 500 m.1 would result in an increased effect of segrega-
tion.   That  such a result does not occur means either that buffer
capacity is  of little  importance in the alkalinity-segregation effect
relation or  that the  number of clay particles present during the crucial
hydrolysis and polymerization reactions  is more important.   The
latter  conclusion seems more likely.
CONTINUOUS FLOW COAGULATION-
FLOCCULATION EXPERIMENTS

In order to determine the effect of rapid initial mixing in a continuous
flow coagulation-flocculation system, two  of the multiple-orifice grids
used in the mixing studies described in Section V -were utilized as
initial mixing devices in conjunction with a tubular reactor.  Results
obtained using these devices were compared with results obtained
using a flash mixer — a  backmixed reactor utilizing a high-speed pro-
peller to mix the fluid streams.  The flash mixer provided mixing
which would be  considered sufficiently rapid by contemporary standards,
The purpose of  these experiments was to determine the advantage, if
any, in using a  multiple-source grid mixer at the head of a tubular
reactor.
EXPERIMENTAL APPARATUS

A diagram of the experimental arrangement utilizing the grid initial
mixers and,  alternatively, the flash rnixer is shown in Figure 34.
It is a modification of the apparatus used for the mixing studies.  At
a point 2 ft downstream from the grid a tube was used to divert part
of the flow into the multi-compartment flocculation chamber.   The
diversion tube was necessary  because the flocculator could accom-
modate only  a portion of the flow which the tubular reactor and grid
mixer were designed to handle.   A flow of ZO gpm was used in the
tubular reactor,  but only 0. 73 gpm was passed through the flocculator.
In order to minimize additional mixing caused by the diversion tube,
the  tube was centered in the tubular reactor.   The diameter of the
tube was such that the flow velocity in the tubular reactor was equal
to that in the  diversion tube.   There were no valves in the tube to
create turbulence.   Despite tK;se steps,  the tube connecting the
tubular reactor to the floccu; • cion chamber did,  of course,  provide
additional mixing of the alum with the turbid water.  It was believed,
however,  that the crucial period  would occur upstream from this
point in the region very close to  the grid, and the experimental
results seem to substantiate this.
                                  98

-------
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j 24-ORIFICE GRID
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-------
The flow from the tubular reactor to the flocculation chamber was
controlled by varying the pressure in the tubular reactor  section.
This was accomplished by adjusting two valves,  one downstream and
one upstream from the reactor section (Points A and B,  Figure 34).
The flow was measured directly at the  effluent end of the  flocculator.

To add the kaolin suspension and the bicarbonate alkalinity to the  raw
water,  a Sigmamotor model T65 positive displacement pump, powered
by a Bodine NSH 54 RL motor and a Minarlk SH-53 speed controller,
was used.  This type of pump can provide several streams of fluid
simultaneously.  The kaolin was added to the 2-in.  line at a point
approximately 10 ft upstream from the grid.  A  nozzle meter,  a
valve, and a 90° elbow between the two points insured that the kaolin
was completely mixed with the raw water at the  alum injection grid.
Sodium bicarbonate was added at a point several feet upstream from
the kaolin addition point.  Alum was supplied from the same  constant
head tank employed in the mixing experiments for the salt tracer.

When the alternative setup for using a flash mixer as the  initial
mixing device was used,  the  raw water was put through the small
constant head tank previously used for the salt tracer and alum
solutions.  A rotameter was used  to measure and control the flow.
The Sigmamotor pump described above was used to add the alum to
the flash mixer in addition to being used to add the kaolin and sodium
bicarbonate  to the raw water  line.  It  should not matter, from a
hydrodynamic standpoint,  that with the tubular reactor there was a
much greater flow in the initial mixing unit.  At  the point of diversion
in the  tubular reactor, the intensity of  segregation and the mean con-
centration of alum at all points of the cross-section were the same.
What was done was merely to divert a portion of this flow to the
flocculator.  The actual flow through the tubular reactor is not
relevant in the sense that a comparison of the efficiency of the two
types of initial mixing systems can be made.

The pilot-plant  flocculation chamber consisted of eight compartments,
each 8-3/4 in. x 8-3/4 in. with a water depth of  approximately 11 in.
For these experiments, only three compartments were used.  All
paddles were driven at the same speed by a Bodine  NSH 54 RL electric
motor and a  Minarik  SH-53  speed controller.

As noted in Section IV the energy per unit fluid mass and per unit
time dissipated in the system by the paddles is an important parameter
in flocculation kinetics. It,  together with fluid viscosity, determines
the rms velocity gradient, G.  Others  have discussed in some detail
the relation between G and the speed of rotation  of the paddles [ 31,51],
For the paddles used in this experiment,  this relation has been deter-
mined to be (67)

                         G  = 0. 15 N1'55                       (100)

where  N is the paddle speed in rpm and G is in sec " * ,
                                  100

-------
Initial Mixing Units

Two grid mixing devices in tubular reactors and one flash mixer
were used in these experiments.   The grids were two of those used
in the mixing studies described in Section V (Grids  4 and 8, Table  2).
The M/d ratio for both grids was 4, and the bar diameters were
1/8 in.  The only difference between them was that  one had 4 alum
injection orifices, and the other had 24.  This corresponds to orifice
densities of 1. 27 and 7. 60 in.  ~l ,  respectively.  From the mixing
studies, it  seemed that the  latter grid would provide better mixing
than the former because of  the relation between wake-mixing phenom-
enon and the tracer injection orifice density.

The velocity through the tubular reactor was  2 fps.  This value was
used in order to eliminate some of the problems which seemed to
occur at the lower velocities as described in Section VI.   For a 2-ft
tubular reactor, the residence time was 1 sec.   The tube connecting
the tubular  reactor to the flocculator was about 1 ft long and resulted
in a total residence time before the flow entered the flocculation
chamber of approximately 1. 5 sec.  The flash mixer was a 3-in.
diameter plastic tube  sealed at one end.  The turbid water entered
on one side at the bottom, and the alum solution entered on the other
side.  The propeller mixer rotated at  1600 rpm, and the water left
the flash mixer near the top.  The mean residence time was 23 sec.
Turbidimeter and Chemicals

A Hach laboratory turbidimeter, model I860, was used to determine
the relative number concentration of suspended particles in the
coagulation experiments by measuring the turbidity of  samples.   It
operated on the principle that light,  passing through a  substance,
before and after treatment, is reflected by particulate  matter su's-
pended  in the substance.  The turbidimeter was standardized with a
polyacrylic plastic rod  into which a  special turbidity material had
been cast.   Before each reading was taken, the turbidimeter was
checked with the standardized rod as the meter reading tended to
drift slightly.  It was  found in the course of doing the experiments
that there was a nonlinear  relation between the concentration of kaolin
suspended  in the water and the reading  of the turbidimeter.  Since
the parameter of interest was particle concentration (specifically,
relative particle concentration)  rather than turbidity per se,  it was
necessary  to relate the  two parameters by means of a  calibration
curve.

The turbidity producing  material used in these experiments was
kaolin N. F. colloidal, produced by Matheson,  Coleman, and Bell.
Bentonite and silica are two other types of colloids which could  have
been used.   As noted in Section  IV,  the coagulation mechanism
associated with these  types of suspensions appears to be somewhat
                                  101

-------
different from the  mechanism associated with dilute kaolin suspensioi
Packham [ 38] took samples from several streams in England and
found the suspension behaved similar to kaolimte.  Both bentonitic  an
kaolinitic type clays are found  in natural waters, but the proportion
is seldom reported.  While the differences between the two types
should be remembered,  indications  are,  from the segregation jar tes;
and the work of Vrale and Jorden [ 59], that the effect of rapid initial
mixing  seems  to be independent of the type of colloidal material used.

The alurn used was of technical grade.  A problem associated with
this was the fact that there was a considerable amount of insoluble
impurities present.  In order to deal with this problem, the alum was
dissolved in deionized water in a 20-liter bottle  at a concentration of
about 25 g/S. 24 hr  prior to a run.  This allowed  most of the insoluble
material to settle out overnight.  Then before the run was made,  the
supernatant was  transferred to another 20-1 bottle from which the alui
solution was fed  to the  system during the run.   Reagent grade powden
NaHCO3 , manufactured by Mallinckrodt Chemical Works, was used
to provide the  additional alkalinity during those runs where it was
needed.

The kaolin suspension to be fed to the system was usually  prepared
the day of the run.   The feed suspension concentration was usually
20 to 30 g/2 and was prepared with deionized water.   The suspension
was  stirred for several hours prior to  the run in order to  insure  that
the clay was broken up into the smallest particles possible.
Because the kaolin would not remain in suspension without stirring,
the propeller mixer was kept operating during the run.  Tests showed
that at all times  during the run, the kaolin feed concentration re-
mained the same,  demonstrating that the propeller mixer was effec-
tive  in maintaining uniform concentration throughout the bottle.  When
sodium bicarbonate was required to increase the alkalinity of the
water,  it also  was  prepared with distilled water at a concentration of
approximately 6  gli.  These concentrations apply to the use  of the
grid-type initial  mixers for which 20 gpm of water were passed
through the initial  mixing unit.   When the flash mixer was used, only
0. 73 gpm of water  was passed through  the initial mixing unit and  the
feed concentrations were approximately 1/20 the concentrations for
the tubular reactor.

It •was realized-that, while using the same feed concentrations for
both the grid and flash  mixers, especially for the alum, might be
desirable from the standpoint of consistency, there is no apparent
reason why such a  discrepancy might invalidate  the experiment.  The
concentration of  alum was quite high in both cases, and the pH was
low enough to insure that the predominant species in both cases was
probably the same.  It  should be noted  that changing the alurn feed
concentration will  change the value of a'  as discussed in Section
VI.  It will be  decreased in value with a decrease in the feed con-
centration.  By lowering the value of a' , a1 at a  given time will also
                                  102

-------
be decreased,  and the rate of mixing can be considered to be improved
by decreasing the alum feed concentration.  In this way, any error
caused by using the lower feed concentration for the  flash mixer can
be considered to be conservative because the rms concentration
fluctuations are lower than they would have been if the higher feed
concentrations had been used.  Even with this advantage, the flash
mixer provided the poorest results.
EXPERIMENTAL PROCEDURE

The raw water from the city line was fed to the appropriate constant
head tank.  The flow was adjusted to the desired value,  and if the
tubular reactor was being employed, the flow diverted from the
tubular reactor was adjusted to the desired value using the valves
upstream and downstream from the  reactor section.   As mentioned
previously, this adjustment was very sensitive.  When the flow was
adjusted to the desired value, the chemicals were fed into the system,
and the paddle speed was set to obtain the  desired value of G.   After
the flow from the  final compartment had reached steady state,  45
min —three times the mean residence time of  1 5 min — was allowed
for the  flocculation process to  reach steady state.  Then 100 rat.
samples were taken from each of the three flocculation compartments.
During  the first runs, three replicate  samples were  taken from each
compartment.   It  was soon found that the results were fairly con-
sistent,  and  subsequently,  only one  sample was  taken from each
compartment.   The floe in  the  samples was allowed to settle for 30
min-  and a pipette was used to remove a sample of supernatant for
analysis in the turbidimeter.  The supernatant was shaken vigorously
to disperse any floe remaining and the turbidity  measured using the
Hach turbidimeter.

The initial turbidity was measured by taking a sample from the out-
let of the final compartment to avoid floating material.  It was  found
that at low values of  G this method resulted in measured values of
turbidity which were too low, due to settling of large floes in the last
compartment.  Normally, the average value from several runs,  dis-
regarding the low values, was used to determine the initial turbidity.

After the run at the first value of G was completed,  the  paddle  speed
was changed in order to obtain another  value of G.  Then  30 min was
allowed — two times the mean res idence time — for the process to
reach steady state.   The sampling procedure was repeated, and
another value of G was then selected.  It was usually possible to
complete runs  with four different values of G  in  one day.
RESULTS

Continuous flow coagulation-flocculation experiments were carried
out at two alkalinities, that present in the tap water at  the time,
                                 103

-------
25-28 mg/f., and tap water with sodium bicarbonate added to bring
the alkalinity up to  70 mg/1   For the lower alkalinity the alum dose
was 23  rcig/i for the 25 mg/S. kaolin suspension. ,  For the -higher
alkalinity, the alum dose was 30 mg/1  As noted in the discussion of
the segregation jar tests,  it  is not possible to change the alkalinity of
the water and keep  all other  parameters constant.

Results of continuous flow experiments made at the two alkalinities
are  shown in Figures 35, 36, and 37.  nt  /n^, where m is the number
of compartments,  is plotted  against G,  the rms velocity  gradient  in
the flocculation chamber.  Figure  35 shows the results for one com-
partment with a mean residence time of 5 min; Figure  36,  two com-
partments and 10 min; and Figure  37,  three compartments and 15
min.  Also shown are results obtained with three different initial
mixing  devices —the 24-orifice grid,  the  4-orifice grid,  and the flash
mixer.   There was a pronounced tendency for the 24-orifice grid to
provide the best results  and  for the flash  mixer to  provide the poorest
results.  The dependency on initial mixing increases with compart -
mentalization and with alkalinity.

It would be instructive to consider the  values of both the  aggregation
and breakup rate coefficients for the data presented in  Figures 35—37.
However,  because  in the range  of high G values where breakup would
be important, the data are somewhat inconsistent,  only the values of
KA, the aggregation rate coefficient,  are presented here.  For an
m-compartment flocculator,  the resulting relation is
                            =d +K  GT  )                     (101)
                       n           Am


where Tm is the residence  time per compartment.  From these
equations, the value of K^ can be found from the low G part of the
performance curves in Figures 35—37.   These values are listed in
Table 4 for one, two, and three compartments  at  low and high alkalinity
using the flash mixer,  4-orifice grid, and the 24-orifice grid.  Also
shown are the average values of K^ for each initial mixer at each
alkalinity.
Figure 38 shows the average values of K^ normalized with respect
to KA for the flash mixer.   The effect  of alkalinity can be easily
discerned.

The dependence on alkalinity has been  discussed in relation to the
results of the segregation jar tests.  Segregation of the alum with
a portion of the clay particles under conditions promoting rapid
hydrolysis and polymer ization results  in a  higher residual turbidity
after completion of the flocculation process.   The alkalinity, through
its buffering capacity,  or by more direct action of the HCO3  ion,
influences the rate and extent of these  reactions.  Thus, with higher
alkalinity, it becomes more important to quickly reduce the intensity
of segregation in the mixing process.

                                  104

-------
Perhaps the formation of Insoluble aluminum, hydroxide is the crucial
reaction which results in poor coagulation.  It has been noted that the
best coagulation of low concentrations of kaolin occurs under con-
ditions of least solubility of Al(III).  It may be that the species res-
ponsible for the destabilization of the  clay particles are some of the
positively charged hydrolysis and polymerization products of Al(III)
which are adsorbed on the colloidal surface.  The insoluble hydroxide
would then form at the clay particle surfaces and act  as a binder
material  in the sense first proposed by Langelier and Ludwig [ 34].

Alternatively, it may be that some of  the charged hydrolysis and poly-
merization products formed early may be better coagulating agents
than those formed later.  Rapid mixing can bring these initial com-
pounds in contact with more of the  clay particles and  thus increase
their effectiveness.

Whatever the particular  species responsible for the critical "reaction"
of the alum and the clay,  very rapid mixing can result in avoiding the
premature formation of those species  with poorer coagulating ability
in cases of high alkalinity.  At lower alkalinities the problem of pre-
mature formation of critical species does not occur.

Figure 39 shows a comparison of results obtained when the flash
mixer was used and when the alum was added directly to the first
compartment of the flocculation chamber. The latter is a very poor
initial mixing device, especially at lower values of G. The measure-
ments were made at the  higher alkalinity, 70 mg/-?.  There was no
apparent difference in performance between the two systems.  The
conclusion drawn from this experiment is that a difference  in the time
of mixing •will not necessarily result in a difference in process per-
formance.  The time  of mixing must be short enough  to prevent the
critical physical-chemical reactions from occurring to any great degree
before the mixing is completed.  For  example,  from  Figure 1_9 it can be
found that for the 24-orifice grid it only took 0. 36 sec for a'/A = 10%
to be reached.  A similar situation occurred in the segregation jar
tests where the results  seemed to be more or less independent of the
time of segregation.   This will be especially important in field applica-
tions where the required short times of mixing will be more difficult
to obtain.

TeKippe and Ham [ 68]  recently reported on experiments  similar to the
one described above in which a flash mixer at the head of a flocculator
was used to mix the alum with the turbid water  in a pilot-scale study.
A  silica suspension was used to produce the turbidity. The value of
G  in the initial mixing unit was varied from 50 to  200  sec"1 , and the
value of Gt for the initial mixer was maintained at 48, 000.  Subsequent
to the  initial mixing step, the  mean residence time and the  rms velocity
gradient in the flocculator were 15 min and 50 sec"1 ,  respectively.
Samples of water were taken from the effluent end of  the flocculator
and allowed to settle for 5 and 30 min.  The  residual  turbidity in the
supernatant for a given  settling time was  taken as the measure of
                                 105

-------
  4. 0
  3. 0
o ~
   Z. 0
   1. 0
             Z4-ORIFICE
                 GRID
           1      I
                                      .4-ORIFICE GRID
0   ZO    40
                                                 I	I
60   80   100   1ZO  140

         G,  SEC"1

  a) ALKALINITY = Z8
                                                160  180  ZOO  ZZO
   4. 0
   3. 0
o -,
 rt
   \. 0
   1. 0
                           I      I
                  Z4-ORIFICE GRID
                       FLASH MIXER
                                                      I      i
                                       4-ORIFICE GRID
     I      l     l      I
                       I     1     i      l
                                                     180   ZOO  ZZO
0   ZO    40    60    80   100   1ZO  140   160
                        G, SEC"1

                b) ALKALINITY  = 70 mg/l

    FIGURE 35.  EFFECT OF INITIAL MIXING DEVICE ON
         FLOCCULATION PERFORMANCE: SINGLE
                COMPARTMENT,  T = 5  MIN.
                                106

-------
rj —(
 a
 7

 6

 5

 4

 3

 2

 1
o -,
 fl
11

10

 9

 8

 7

 6

 5

 4
       20
40
                                             1	1	—1	T~
                                                4-ORIFICE GRID
                                       24-ORIFICE GRID
                                  I
                                                              I
   0    20    40     60    80   100    120  140   160  180
                             G,  sec-1
                     a) ALKALINITY  = 28  mg/i
                                                             200  220
                                             24-ORIFICE GRID
                       _L
                        _L
                 _L
                                 _L
60
                        80
                                 100   120    140   160   180   200  220

                                 G,  sec 1

                        b)  ALKALINITY = 70 mg/f.
           FIGURE 36.   EFFECT OF INITIAL MIXING DEVICE ON
                  FLOCCULATION PERFORMANCE:  TWO
                       COMPARTMENTS,  T = 10 MIN.
                                  107

-------
o
00
    33

    31

    29

    27

    25

    23

    21

    19

"a" 17



    13

    11

     9

     7

     5

     3

     1
                                          4-ORIFICE
                                            GRID
                                                              o  «
                                                              a
                       20  40 60  80 100 120 140 160 180 200 220
                                    G,  sec-1

                          a) ALKALINITY = 28 mg/4
33

31

29

27

25

23

21

19

17

15

13

11

 9

 7

 5

 3

 i
                                                                                        24-ORIFICE
                                                                                          GRID
                                                       0  20  40 60 80  100 120 140 160 180 200 220
                                                                       G, sec
                                                                              -i
                                                              b) ALKALINITY = 70 mg/l
                        FIGURE 37.  EFFECT OF INITIAL MIXING DEVICE ON FLOCCULATION
                                      PERFORMANCE:  THREE COMPARTMENTS, T  =  15  MN.

-------
                         TABLE 4
         AGGREGATION RATE COEFFICIENTS FOR
            CONTINUOUS FLOW EXPERIMENTS
Alkalinity
mg /-fas
CaCO3
28 mg/t

70 mg/jf

No. of
Compart-
ments
1
2
3
Avg
1
2
3
Avg
Flash
Mixer
0. 0040
0. 0041
0. 0037
0. 0039
0. 0040
0. 0045
0. 0039
0. 0041
4-Orif ice
Grid
0. 0043
0. 0050
0. 0047
0. 0047
0. 0050
0. 0059
0. 0047
0. 0052
24-(3rif ice
Grid
0. 0054
0. 0059
0. 0057
0. 0057
0. 0061
0. 0073
0. 0071
0. 0068
   1. 8
   1. 6
   1. 2
   1. 0
   0.
               24-ORIFICE GRID
                       4-ORIFICE GRID
                       FLASH MIXER
                    -Q.
                  _L
_L
                  20         40

                   ALKALINITY, mg/t
                                        60
               -o-   -
                     80
FIGURE 38.  EFFECT OF SEGREGATION ON COAGULATION-
       FLOCCULATION: CONTINUOUS FLOW TESTS
                           109

-------
0 -
 q
     11
     10
             THREE
           COMPARTMENTS
             T - 15 min
     1	1	1	1	1      I
             NO INITIAL MIXING UNIT
       A O D
       A • •  FLASH MIXER
    TWO
    COMPART-
       MENTS
                             T = 10 min

                                ONE COMPARTMENT

                                  T = 5 min
                                                                  I
                   40
60
80
 100

G, sec
120
-l
140
160
180  ZOO  220
        FIGURE 39.   EFFECT OF INITIAL MIXING ON FLOCCULATION
           PERFORMANCE:  COMPARISON BETWEEN FLASH MIXER
            AND NO INITIAL MIXING UNIT, ALKALINITY = 70 mg/S.
    performance.  They reported that the various values of G produced
    no significant differences in results.  This is consistent with the
    conclusions drawn from the present study.

    In considering Figures 35—37,  it is necessary to consider that with the
    flash mixer being used as the initial mixing device (and with the alum
    being added to the first compartment) backmixing is occurring.  In
    Section IV it was noted that backmixing may be  inherently detrimental
                                    110

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to coagulation because of reaction of incoming Al(III) species with
products  of the completed reactions.  For example, Vrale and
Jorden [ 25] point out that Al(OH)3 g particles may act as  nuclei to
enhance the precipitation of Al    .  The present study produced no
conclusive evidence as to whether backmixing is inherently inferior
to plug -flow mixing for alum coagulation-flocculation.  While the
mixing provided by the flash mixer was quite  rapid, It is believed
that the time of mixing was probably lower than that provided by the
grid mixers.   No attempt was made to measure the concentration
fluctuations at the outlet of the flash mixer.  It was assumed that with
a mean residence time of 23 sec, t'he concentration fluctuations at the
outlet  were probably quite low.   That the flash mixer gave the poorest
results cannot be taken to mean that backmixing necessarily results
in poorer performance.  It may only mean that it is difficult to obtain
very rapid mixing with such a device.

In terms of a full-scale treatment plant, the argument becomes
Irrelevant.   While It Is  conceivable that fairly fine grids might be
constructed, it would be impossible to construct a  flash mixer which
would  provide  mixing times of a  fraction of a  second, and  it seems
that mixing times this low are necessary to effect an improvement  in
performance.


COAGULATION OF WASTEWATER

In order to ascertain whether the initial mixing  step is critical in alum
coagulation of wastewater, a series of segregation jar tests were
conducted at the Sanitary Engineering Research Laboratory of the
University of California.   As with the kaolin suspensions,  a 500-mi
sample of raw domestic  wastewater was divided into two portions,
100 rrJ and 400 rrJ.  The optimum alum dose (found from ordinary
jar tests) was  added to the 100-m^ portion and stirred vigorously for
a specified period of time (5 to 50 sec).  Then this portion was added
to the  remaining 400 -m^ portion.   The 500 -mi. sample was then
stirred In a jar test apparatus for 6 mln,  and  the resulting floe was
allowed to settle for 15  mln.  A sample of supernatant was taken and
analyzed for residual turbidity using a Rossum Model 600  turbldlmeter.

For comparison,  an ordinary jar test was made with the alum dose
being added to the total  500 -rrJ sample.  The  relation giving the ratio
of the  aggregation rate coefficients for the two experiments Is


                       KA     In

                           m
                       K.     In (nl  /n  )
                          s          s  i
                                         0-       .                (99)
                                  ill

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The results of these tests at various segregation times are  shown in
Figure 40.  It is significant that K^  /K^  continues to increase at
the higher segregation times (10 — 50 sec).  This  is in contrast to the
results from  the kaolin suspension studies in which there seemed to
be little change in performance when the segregation time was increased
beyond 3 to 5 sec,  the shortest segregation time practicable by the
test procedure.  The same conclusion was reached by comparing
performance  obtained from the flash mixer with that obtained by
adding the alum to the first compartment of the flocculator.   The
results with wastewater indicated that it is possible to obtain a very
significant improvement in performance (over  that of a poor initial
mixing device) without the extremely rapid initial mixing required
for improvement  in a kaolin-water system.  Consequently,  such fine
grid meshes would not be needed and the grid construction problem
would be simplified.

It is instructive to make a calculation concerning  the grid parameters
required to produc_e  a given level of performance.  It will be assumed
that a value of a '/A  = 10% is the level of mixing required.  This
assumption is strictly arbitrary.  From Figure 40 it will be assumed
that this level is to be attained in 10  sec.  From Appendix D the scalar
decay equation for 1/2-in.  grid bars is  estimated to be
                      a1 n
                                     ~1>13
                       =^  = 5.0(x/d)~1>1      .                   (102)
If the flow velocity is 2 fps,
                      x = vt = 20 ft  = 240 in.

equation 102 can now be solved for n
                                    s

            n  = 50  (480)"1'13  = 0. 0465 in. "2  = 6. 7 ft"2  .
             s


This means that 6. 7 orifices per^ square foot of  reactor cross-
section are required to give a1 /A  =  10% at x  = 20 ft when the main-
stream velocity is 2 fps.  A grid with the necessary parameters
would be relatively  easy to  construct.

A calculation similar to the one above was  not made for the kaolin
system because of the difficulty of estimating the segregation time
required to produce an improvement in performance.   This is in
addition to the problem of estimating what the level of mixing should
be at that time.

The  results of these tests can probably be assumed to hold if ferric
chloride is the coagulant.   Lee [ 69] has found that in lime coagulation
of wastewater the rapidity of the initial mixing has only a  slight
effect on performance.
                                 112

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5. 0
4.0
3.0
2. 0
1. 0
 I
 a T. = 196 JTU
 •  i
   ALUM DOSE = 160 mg/l

 O T. = 180 JTU

   ALUM DOSE = 100 mg/t

	I	I
              10
20         30        40

 SEGREGATION TIME, sec
                            50
60
      FIGURE 40.  SEGREGATION JAR TESTS FOR VARIOUS SEGREGATION
                TIMES -ALUM COAGULATION OF RAW SEWAGE

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                        SECTION VIII

                    ACKNOW LEDGMENTS
The research reported herein was supported in part by Research
Grant No.  17030 DLX from the  Environmental Protection Agency.
Ray Campbell provided invaluable assistance in designing and con-
structing the experimental apparatus.  Harvey  Collins and the
California  Department of Public Health aided in conducting the
chlorination experiments, and Fang Maw Lee assisted in performing
the wastewater coagulation experiments.   Useful  discussions con-
cerning water chemistry were held with R. Rhodes Trussell.   The
support of this project by the EPA Project Officer, Dr.  Sidney A.
Hannah,  is also acknowledged.
                                115

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                            SECTION IX

                           APPENDICES


                                                               Page No.

A,    Initial Mixing and Wastewater Chlorination .  ......    119

      Table  1:     Effect of Method of Applying  Chlorine
                   on Reduction of Coliform Organisms .  .  .    121

      Figure 1:    Schematic Drawing of Experimental
                   Apparatus for Pilot-Scale Chlorination
                   Study	    123

      Table  2:     Physical and Chemical Analyses of
                   Unchlorinated Effluent  ..........    125

      Table  3:     Effect of Initial Mixing on Disinfection
                   of a Primary Effluent in a Tubular
                   Reactor	    125

      Figure 2:    Performance of Various Non-Backmixed
                   Chlorination Units	    127


B.    Plant-Scale Study of the Effect of Initial Mixing in
      Wastewater Chlorination. .  .  .	    129

      Figure 1:    PVC Chlorination Grid	    133

      Figure 2:    Multiple-Or if ice Grid used as
                   Initial Mixing Device  ...........    134

      Figure 3:    Schematic Drawing of Rancho
                   Cordova Chlorination System  .......    136

      Table  1:     Analyses of  Unchlorinated Secondary
                   Effluent  .  . .	    137

      Table  2:     Operating Parameters and Bacterial
                   Survival Ratios   ..............    133

      Figure 4:    Coliform Survival Ratio in an Activated
                   Sludge Effluent ~ Effect  of Initial Mixing  .    139
                                  117

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                                                             Page No.

      Figure 5:    Fecal Coliform Survival Ratio in a
                   Chlorinated Activated Sludge Effluent —
                   Effect of Initial Mixing	.' .  .    140


C.    Comparison of Results With Those of Gibson	    143

      Table 1:      Parameters for Mixing  Experiments  .  .  .    145

      Figure 1:    Scalar Decay Downstream from a Grid:
                   Comparison of Results  From Present
                   Study with those from Gibson's Study  .  .  •    146

D.    Prediction of Mixing for Larger Grids	    147

      Figure 1:    Prediction  of Scalar Decay Curves from
                   Experimental  Data for d = 1/4  in	    149
                                 118

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                   APPENDIX A




INITIAL MIXING AND WASTEWATER CHLORINATION
                     119

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                          APPENDIX A

      INITIAL MIXING AND WASTEWATER CHLORINATION
Recent studies at the Sanitary Engineering Research Laboratory of
the University of California showed that rapid initial mixing may be
important in the wastewater chlorination process as well as in alum
coagulation-flocculation.  Selleck and Collins [ 55] and Selleck,
Collins, and White [  56]  have discussed the  reason which they believe
causes prolonged segregation of the chlorine from the bacteria to
result in poorer performance.  The bactericidal compounds are
formed by the  reaction of chlorine with nitrogenous and carbonaceous
matter to form chlorine  complexes.  The speed of these reactions
varies; some are quite fast while  others  are relatively slow.  Selleck
and Collins have concluded that the residuals initially  formed are
apparently much more bactericidal than the  compounds formed later.
They concluded that rapid initial  mixing allows these "hot" residuals
to come in contact with the bacteria and act  as  killing  agents.

Selleck and Collins also  concluded that backmixing may contribute
to poorer disinfection.  They noted that reactions may take place
between the more bactericidal residuals  initially formed upon entering
the reactor and the more complex residuals which form over a longer
time.   Thus,  these simple and more bactericidal compounds may be
"destroyed" before they  can act.

In one experiment described by Selleck,  Collins and White [ 56],
chlorination •was effected in two alternative _ways.   In one arrangement,
the chlorine was added directly to a CSTR (t = 37.  5 min) near the
paddle which rotated at 50  rpm.  Under the alternative arrangement,
the chlorine was added to a short  (t = 0. 12 min) tubular reactor placed
upstream from the CSTR.  The tubular reactor consisted of a  1/4-in.
PVC tee acting as a constriction  in a 3/4-in. line.  The chlorine was
added  through the stem of the tee.   Settled wastewater was the effluent
to be treated and an aqueous  solution of chlorine gas was the disinfec-
ting agent.

Table  1 summarizes the  data they obtained with these  two  systems.
Although the total mean residence time was  essentially the same,  the
kill obtained when the chlorine was  added at the head of the tubular
reactor was  much greater.  The  coliform survival ratio —the parameter
used to indicate bactericidal effectiveness — was about one order of
magnitude lower in this case.   However, -the coliform survival ratio
for the CSTR alone was approximately the same regardless of whether
the chlorine was added directly to the CSTR or to the tubular reactor.
The increase in kill was  due solely to the more rapid mixing which
occurred  in the tubular reactor.
                                 120

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                             TABLE 1

       EFFECT OF METHOD OF APPLYING CHLORINEjON
            REDUCTION OF COLIFORM ORGANISMS
              (From Sclleck, Collins, and White [ 56])
Run
No.
Chlorine Residual
mg/t
Coliform Survival
Ratio
A, _CHLORINE APPLIED IN TUBULAR REACTOR
(t = 0. 12 min) Ahead of CSTR (t = 37. 5 min)
1
2
3
3. 2
5. 1
8. 1
0. 00286
0. 00419
0. 00049
B. CHLORINE APPLIED DIRECTLY TO CSTR
1
2
3
4. 2
6. 1
8. 8
0. 0378
0. 052
0. 012
Another  result is that for each run,  the chlorine residual in the CSTR
was, slightly lower when the chlorine was applied to the tubular reactor.
It was concluded that the various reactions  involved were driven to a
greater degree of completion because of the more  rapid mixing.
PILOT-PLANT STUDY

Based on the evidence presented above that the  rapidity of the initial
mixing is an important parameter in wastewater chlorination, a pilot-
scale study was undertaken in cooperation with  the California State
Department of Public Health.  The purpose of the study was to determine
if any difference in performance could be effected by using two different
initial mixing devices in a tubular reactor,  one  which produced very
rapid mixing, and  one which produced relatively slow mixing.  If more
rapid mixing resulted in better performance, then it would indicate
the desirability of  carrying  out studies at a full-scale treatment plant.
                                  121

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Equipment

A  schematic diagram of the apparatus is shown in Figure  1.  The waste -
water was pumped from a large storage tank through the tubular  reactor,
a 2-in.  I. D. PVC pipe.  The distance from the point of chlorine injection
to the last of three sampling points was  38 ft.  There was  a section of
straight pipe approximately 8 ft long upstream from the point of chlorine
injection to help insure that the flow  and turbulence characteristics at
the initial mixing device were not affected by the bend.

Sketches of the two initial mixing  devices are also shown in Figure 1.
The first device was a 3/8-in.  I. D.  tube which introduced the chlorine
feed solution at a point in the center  of the  tubular reactor.  The  diameter
of the tube was such that the velocity of the chlorine solution entering  the
reactor was approximately the same as  the wastewater velocity,  reducing
the shear between the two streams.   Only the turbulence generated by
wall friction and the variation in temporal mean velocity across the pipe
cross-section,  also produced by the  wall friction, acted to mix the
chlorine with the waste stream.  Studies by Gibson [  1 l] ,  Keeler [  22],
and Lee [ 3  ] and the present mixing experiments have shown that this
produces relatively slow mixing in comparison with the other device.

The second  initial mixing device was a biplane grid of 1/4-in.  bars
spaced  1/2 in. center-to-center,  similar to those studied  in Section VI.
In order to obtain maximum benefit from the wake-mixing phenomenon,
thirteen 1/16-in. orifices were used as  chlorine injection  sources.
This was a much more efficient mixing device which, it was believed,
would produce greater bacterial kills.


Procedures

The experiments were run in the following  manner,   Effluent from the
primary waste treatment plant was collected over a period of several
hours in two large storage tanks.  Since the two tanks were being filled
simultaneously,  the composition of the sewage in each was the  same.
The wastewater  in the tanks was stirred slowly to prevent settling of
particulate matter in order to further assure constant wastewater com-
position during the course of the experiment-  The chlorine feed  line
(an aqueous  solution of chlorine gas was used) was connected to one of
the initial mixing devices.  When  the single source mixer  was used, the
section containing the grid and manifold was  removed.  Wastewater was
pumped through the tubular reactor  at a velocity of 2 fps (a flow rate of
20 gpm). The chlorine solution was  then fed into the reactor.

At each of three points — 10,  24, and 38 ft downstream — a sample was
taken and the total chlorine residual  determined amperometrically
according to the method suggested by Standard Methods [ 62],   Then
three replicate samples for determination of coliform concentrations
were taken at each point   They were dechlorinated as quickly as possible
with a sodium thiosulfate solution.   Samples  were also taken at a point
                                  122

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N)
OJ
                                     FROM PRIMARY TREATMENT
                    Q = ZO gpm

                    V =2.  fps
                     PUMP
                                         STORAGE TANK
                                            I. S. A. ORIFICE FLOW METER
                                            /
                                                       INITIAL MIXING
                                                          UNIT
                                                                   Z-in. I. D.
                                                                   P-VC PIPE
                                      1/Z"
                                      1/41
       SAMPLING POINTS


                        TO WASTE
!
I A I
L -c> +
p •" t> >•

-1 J


b


4
U( ^


^ <

	 1
b

                                                           1/16" Dia.
                                                                        / 7  /  / /  / /// /  /  /i /  /
                                                                                                           3/8M
                                                                 / /./  //////////////I
                                          MULTIPLE-ORIFICE
                                                 GRID
SINGLE SOURCE
                        FIGURE  1.  SCHEMATIC DRAWING OF EXPERIMENTAL APPARATUS FOR
                                             PILOT-SCALE CHLORINATION STUDY

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upstream from, the initial mixing unit to determine the initial coliform
concentration.  The task of determining the coliform concentrations
was performed by the California State Department of Public Health Ln
accordance with Standard Methods.

A sample of wastewater was analyzed at the Sanitary Engineering
Research Laboratory at the University of California to determine
ammonia nitrogen, organic nitrogen, total  suspended solids,  volatile
suspended solids, and COD concentrations.  The techniques were those
recommended by Standard Methods.  The results of  these analyses are
shown in Table 2.
Results

The results are shown in Table 3.  Two runs were made several
weeks apart.   During the first run difficulties were encountered which
make the results  somewhat unreliable, but they have  been included for
completeness.  The main problem centered on uncertainty regarding
the wastewater flow rates.  This is manifested by the fact that the
chlorine residuals were  somewhat lower when the grid was used as
the initial mixing device.   Still, a compar ison between the multiple-
Orifice grid and the s ingle-source chlorine injector can be made.   Using
the grid resulted  in coliform survival ratios about one order of magni-
tude lower.

During the second run the wastewater flow rate was controlled more
closely.   Use of the grid resulted in a coliform survival ratio approxi-
mately two orders of magnitude lower than did the single  source.   In
fact,  the  survival ratios  for the grid  were probably lower than those
shown because in the laboratory analysis the MPN's were biased
toward higher-than-likely values.

With the single source of chlorine, Table  3 shows that for the first
sampling point (contact time = 0. 08 min) the chlorine  solution was not
spread evenly over the cross-section of the tubular reactor at  that
point.  It should be noted that the chlorine contact time  will not be
the same for all the fluid particles.   It might be suspected that this
is the  reason for the difference in results  obtained with the two initial
mixing units.   However,  inspection of the  results shows that this  is
probably not true.  It can be assumed that the chlorine was completely
mixed with the wastewater by the second sampling point when the
single source was being used.  Thus,  at the third sampling point the
chlorine contact time for all the fluid particles was at least 7 sec.
The coliform survival ratio at this point was higher than for the grid
initial mixer at the first  sampling point (contact time  =  5  sec).
Therefore, the difference in contact times for  individual fluid particles
cannot be cited as the reason  for the  difference in results.

The conclusion drawn from this experiment is that prolonged segrega-
tion of the chlorine from the coliform organisms  allows the formation
                                  124

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                      TABLE 2

      PHYSICAL AND CHEMICAL ANALYSES OF
            UNCHLORINATED EFFLUENT
Run
No.
1
2
Volatile
Suspended
Solids
mg/£
46
33
Total
Suspended
Solids
mg/^
77
35
Ammonia
Nitrogen
mg/i
24. 6
15, 7
Organic
Nitrogen
mg/i
7. 6
3- 9
COD
mg/i
170
104
PH ,
7. 8

                     TABLE 3

EFFECT OF INITIAL MIXING ON DISINFECTION OF A
  PRIMARY EFFLUENT IN A TUBULAR REACTOR
Run
No,
(1)

Single Source

Multiple -Source
Grid

U)

Single Source

Multiple -Source
Grid
___
Contact
T ime
min

0. 08
0. 20
0. 32
0- 08
0. 20
0. 32

0. 08
0- 20
0- 32
0. 08
0, 20
Chlorine
Res idual
mg/i

5. 10
6. 30
6. 30
4. 85
4. 70
4. 80

5- 70
6. 25
6. 20
6. 20
6. 10
0. 32 6. 20
	 L —
Coliforrn
Survival
Ratio

0. 88
0. 41
0. 45
0. 159
0. 056
0. 026

0. 45
0. 37
0. 50
<0. 006
< 0. 008 •
£ 0, 006
                           125

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of less bactericidal chlorine residuals from the more bactericidal
residuals  initially formed.  Thus, more rapid initial mixing results
in better kills.   It is  important to note that very short  contact times
were involved in this experiment, from 5 to 19 sec.  This means that
if the above conclusion is true, the most bactericidal compounds must
exist for only a  very  short time — certainly less than 5 sec and pro-
bably much less.
 RAPID INITIAL MIXING AND LONG CONTACT TIMES

 Because the experiments described above  involved short contact times
 (<0. 3 min) and because an attempt to improve performance in a pro-
 totype treatment plant by effecting improved initial mixing failed (see
 Appendix B), an experiment utilizing the venturi type initial mixing
 device used in the work of Selleck and Collins and  longer contact times
 (up to 5. 2 min) was devised.  The initial mixing device was the 1/4-in.
 PVC tee described earlier.

 The tubular reactor  consisted of approximately 20 ft of 3/4-in.  PVC
 pipe and approximately 250 ft of 1/2-in.  rubber hose.  This provided
 a contact time of 2. 0 min.  Samples to determine coliform kill were
 taken at four points along the tubular reactor.   A small beaker was
 filled with chlorinated wastewater from the end of the tubular reactor
 in order to obtain  a sample with a longer contact time, 5. 2 min.  The
 residence time of  the tubu]?»T reactor, 2. 0 min, was much greater
 than the time necessary to fill the beaker,  0. 09 min.  This minimized
 backmixing during the filling of the beaker.  During the interval that the
 chlorinated wastewater was  in the beaker,  it was stirred continuously
 with a magnetic stirrer.

 The data were analyzed by the methods discussed earlier,  and the
 results are shown in Figure 2.  The coliform survival ratio, y/y ,  is
jplotted against  Rt  where R is the  total chlorine  residual in rag/f. and
 t is the contact time in minutes.   Also shown are results cited above
 for the 2-in.  tubular reactor and  those from the work of Selleck [ 57].

 For convenience,  two of the initial mixing  situations, the  75-gal batch
 reactor with the paddle mixer rotated at 50 rpm and  the 2-in. tubular
 reactor with the single chlorine injection tube,  have  been  designated
 as "poor. "  The other two initial  mixing situations, the i/4-in. tee
 in the 3/4-in. pipe and the 2-in.  tubular reactor with the  13-orifice
 grid, have been designated as "good.  "  This classification is strictly
 subjective.  While the times of mixing for  both  "poor" or  both "good"
 mixing situations is probably not  the  same, it is believed  that they
 are probably sufficiently similar  to allow the  above classification to
 be made.

 Figure 2 reveals that while rapid initial mixing provided improved
performance, i. e. , lower coliform survival ratios,  at low values of
 Rt, the "poor" and "good" initial  mixing produced the same results
                                  126

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1. 0
10
  -1
10
  -2
10
  -3
10
  -4
10
  -5
10
  -6
  D
  ——
  D
                                      "POOR" INITIAL
                                          MIXING
                                      "GOOD" INITIAL
                                          MIXING

            •POOR" INITIAL MIXING:
        O 75-gal BATCH REACTOR
           FROM [ 57]

        D 2-in.  TUBULAR REACTOR
           WITH SINGLE-SOURCE
           CHLORINE INJECTION TUBE
           "GOOD" INITIAL MIXING:
        v  13-ORIFICE GRID IN
           Z-in. PIPE
1/4-in.  CONTRACTION IN
3/4-in.  PIPE FROM [ 57]


i/4-in.  CONTRACTION IN
3/4-Ln PIPE
        I
                                                      00
I	O
     0. 1
   FIGURE 2.
       1.0           10           100         1000

          Rt, mg/t AND MINUTES

    PERFORMANCE OF VARIOUS NON-BACKMIXED
          CHLORINATION UNITS
                            127

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when t was increased with R maintained constant.   Thus,  in situations
where a long pipeline is used to provide contact time for disinfection
in wastewater treatment, any reasonably good initial mixing device
will probably produce the best obtainable results,  those of the batch
reactor  (see Appendix B).

The reason for the merging of the two curves at the higher values of
Rt is unclear.  It may be related to varying  resistance of the organisms
to disinfection.  The more resistant organisms, if not killed by the
highly bactericidal residuals which are initially formed  and which can
be utilized under cond_itions of rapid initial mixing, must be subjected
to the same  value  of Rt as would have been the case if the initial mixing
had been relatively slow.  Whatever the actual reason,  the answer
seems to lie in the mechanism of chlorine disinfection and the reactions
which chlorine undergoes in wastewater.

It may still be possible  to utilize the high initial  kill which rapid initial
mixing provides.  For example, existing plants  which have backmixed
reactors for chlorination could be improved by installing a chlorine
injection device in the pipe,  if one exists,  leading to the chlorine con-
tact unit.  As  noted, backmixing seems to be inherently detrimental
to chlorination efficiency.

Use of tubular reactors also provides a much better residence time
distribution  than a CSTR.  This  is particularly important in chlorina-
tion because the coliform kill is so strongly time dependent.  Use of
a backmixed reactor allows "short-circuiting" of fluid particles with
short chlorine contact times and thus a very high concentration of
coliform organisms.
                                   128

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                      APPENDIX B

PLANT-SCALE STUDY OF THE EFFECT OF INITIAL MIXING
             IN WASTEWATER CHLORINATION
                             129

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                          APPENDIX B

 PLANT-SCALE STUDY OF THE EFFECT OF INITIAL MIXING
                IN WASTEWATER CHLORINATION
INTRODUCTION

Because of the success  of the initial experiments involving  rapid
initial mixing and wastewater chlorination (see Table 3 of Appendix
A) and also because of the  recognized limitations of such small-scale
studies,  it was decided  that a full-scale investigation at a wastewater
treatment plant was called for.  Although it should be possible to
extrapolate the results of model mixing studies and estimate the degree
of mixing produced by larger grids, it is difficult to assess the com-
bined effects of mixing,  chlorine reactions  with impurities  present in
the waste,  and probable coliform kills.  With grids much larger than
those used in the pilot-scale investigations  (in terms of bar diameter
and spacing), a much longer time of mixing —time  required for the
concentration fluctuations to decay to  some arbritrarily defined low
value —would result.  Thus, the mixing might not occur fast enough
to allow  the most bactericidal chlorine residuals, which may be very
short-lived,  to act as killing agents.   The short contact times  involved
in the pilot-scale studies also limited their usefulness and prevented
their application to prototype systems.

Another  reason for full-scale plant tests was that if improved  initial
mixing were to result in improved performance, the evidence  indica-
ting that initial mixing is an important parameter would be  much more
compelling than if only pilot-scale studies had been made.  This would
be the  case even if the pilot-plant studies had no obvious  limitations
such as those discussed above.
CHARACTERISTICS OF THE RANCHO CORDOVA
WASTEWATER TREATMENT PLANT

The Rancho Cordova Wastewater Treatment Plant is located approxi-
mately  15 miles  east of Sacramento.   It is a secondary plant featuring
the Spirovortex activated sludge system.   The average flow through
the plant is approximately  t, 7 mgd (at the time of day that the tests
described herein were run, the flow was approximately 2. 4 mgd).

The Rancho Cordova facility was chosen for the project for several
reasons.  It was desired that the initial mixing system of the plant
be of good design by contemporary standards.   It is well known that
gross segregation of the chlorine from the waste  stream over  a period
                                  130

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of a minute or longer will give poor results.  An example of such gross
segregation would be where the chlorine was added to the waste stream
by placing the chlorine hose  into a large contact basin where the level
of turbulence was quite low.   Gross segregation can occur and poor
performance  will result.  Backmixing in the  initial mixing step is also
to be avoided.  Selleck and Collins [ 55] and  Selleck, Collins,  and
White [ 56] have noted that backmixing,  such as may occur in a typical
rapid or flash mixer, seems to have an  inherently detrimental effect
upon the wastewater chlorination process.  The alternative to backmixing
is a tubular reactor with characteristics as close to plug flow as pos-
sible.   Thus, to test the grid mixer it was  necessary to  find a  plant
where the chlorine was added to the waste  stream in a pipe leading from
the treatment plant, the pipe comprising the  tubular reactor.   Such an
arrangement  was desired for another reason.  Samples of chlorinated
wastewater must be taken to determine coliform kill and the correspond-
ing contact times should be  determined fairly accurately.  This is
possible in a  pipe, but not in most chlorine contact basins where short -
cLrcuiting occurs and dead space exists.

The Rancho Cordova plant met these criteria quite well.   From the
final clarifier,  the  effluent entered a large box structure by passing
over a weir.  From there it passed through an  800-ft,  27-in. diameter
pipe to  a pond.   The chlorine injection device was a 6-ft  long,  3-in.
PVC pipe placed in the bottom of the 27-in. pipe at the point where
the flow left the box.  The chlorine was  injected through  3/8-in.  holes,
spaced  1-1/4-in. apart along the top of the PVC pipe.  It was possible
to sample at the point wher'e the 27-in.  line entered the pond as it was
not submerged.  It was  also possible to  sample at a point 184 ft down-
stream from  the chlorinator.

There were three other criteria for the plant to be used.   These con-
cerned  installation of the grid.  First,  it was necessary  to be able
to tap into the existing chlorine piping system in order to deliver the
chlorine solution to the  grid.  This was fairly easily done at Rancho
Cordova.   Second,  it was necessary to be  able  to gain access to the
point where the grid was to be installed by  diverting the  flow around
this point or  stopping the flow.  At Rancho  Cordova the flow could be
stopped for about one hour which allowed rapid installation and re-
moval of the grid.   Finally,  it was necessary to have a physical con-
figuration such that placing the  grid in the pipe could be  easily
accomplished.  This was possible at Rancho  Cordova.

After permission was obtained from the County of Sacramento  to use
the Rancho Cordova plant, the grid was designed and built,  and the
tests were run.
DESIGN OF THE GRID

The grid used as the initial mixing device in this  experiment was
designed on the basis  of several criteria.  First, and most important,
                                   131

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it had to provide more rapid mixing of the chlorine  solution with the
waste stream than did the  system which was being used at the treat-
ment plant.  This required that the grid bars be as  small in outside
diameter as possible,  that the spacing of  the grid bars be small, and
that the number of points at which the chlorine was  injected into the
waste stream be as many as possible.

Other criteria, however, led to design features different from those
above.  Since at many plants,  excessive headloss through the grid
could not be tolerated — although at this plant,  a headloss of up to 2 ft
could have been allowed  —the grid bars could not  be spaced too closely.
Excessive headloss of the  chlorine solution flowing  inside the grid
bars could not be allowed as this would  lead to an unequal distribution
of chlorine flowing from each of the sources.   This  made larger
diameter grid  bars necessary.  In order to avoid  the possibility of
clogging very small orifices, larger orifices were preferable although
this meant fewer holes if a reasonably high injection velocity was to
be maintained,  A  high injection velocity was necessary to  decrease
the effect of chlorine  solution headloss inside the  grid bars and thus
insure uniform chlorine  distribution.  Finally, the grid had to be
reasonably strong  to withstand the force of the wastewater  flow.  This,
too, called for larger grid bars.  In order to have a grid meeting these
criteria it was necessary to  sacrifice mixing performance.

A drawing of the grid mixer  is shown  in Figure 1.   Photographs are
shown in Figure 2.  The grid was constructed from  3/4-in.  PVC
pipe and fittings.   The ratio  of the center-to-center bar spacing to
the bar diameter,  a parameter used in mixing  studies, was approxi-
mately  3. 5,  and the solidity,  the fraction  of the cross-sectional area
occupied by the grid,  was about 0. 48,   The main line  in the center of
the grid was a 2-in.  PVC pipe.  This  allowed the  chlorine solution
to be distributed evenly to  all parts of the grid without excessive
headloss.  The chlorine  injection  orifices, were  220 1/8-in.  diameter
holes on the downstream side of the grid.   These  did not point directly
downstream, but alternated up or down  at an angle of approximately
45°  from the horizontal.   It was believed that this arrangement would
improve mixing.  The value  of n  was 0. 39 in. ?
                                s

Based upon a chlorine solution flow rate of 20 gpm,  the velocity at
which the chlorine was injected into the wastewater  stream was 2. 4
fps.   The existing  chlorine diffuser injected the chlorine into the
waste stream at approximately 1 fps.

The  maximum velocity of the effluent  flowing through the grid was
approximately 2 fps   From  previous  studies,  the headloss through
such a grid at this  velocity was approximately  0. 8 in.  and the total
force on the grid was  16  Ib.  At a velocity of 1 fps,  the velocity when
the tests were  being made, the headloss and force were 0. 2 in. and
4 Ib,  respectively.
                                   132

-------
                                                       2-in. sch. 80
                                                       PVC PIPE
3/4-in.  sch.  40 SOCKET TYPE
TEES AND CAPS, JOINED  BY
3/4-Ln.  sch.  40 PVC PIPE (IN
SOME INSTANCES THE SOCKETS
OF THE TEES AND  CAPS WERE
PARTIALLY CUT OFF).
               EXISTING 3-in.
               PVC DIFFUSER
r27-in. DIAMETER
 R. S.  PIPE
                    FIGURE 1.  PVC CHLORINATION GRID
                                       133

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i

             A.  FRONT VIEW OF GRID


                                                .»• '
 B.  GRID IN PLACE IN 27-in. TUBULAR REACTOR


   FIGURE 2.  MULTIPLE-ORIFICE GRID USED AS
              INITIAL MIXING DEVICE
                        134

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The grid was connected to a frame constructed from i/2-in.  iron
pipe and fittings.  The frame was used to fix the grid in place inside
the 27-in. pipe.   Jacks mounted on the frame could be extended until
the grid and frame were firmly held in place.  The  adva'ntage in using
friction to keep the grid in place was that no permanent brackets had
to be installed in the plant,  and installation and removal of the grid
was quickly and  s imply accomplished.


EXPERIMENTAL PROCEDURE

A schematic drawing of the chlorination  system at the Rancho Cordova
Wastewater Treatment Plant is shown in Figure  3.  Two  runs, one
with the grid mixer and one with the  pipe diffuser, were made each
day for four consecutive days.  When the pipe diffuser was being
tested the grid was removed to insure that the grid would not interfere
or contribute in  any way to the turbulence characteristics of the existing
arrangement.

The runs were made in the following manner.  Each day the first run
was made with whichever device had been used last the day before.
This meant that  it was necessary to  stop the flow, de-water the box,
and remove or install the grid only once  each day.  When the flow from
the secondary clarifier reached a nearly constant rate, at approximately
1000 hours each day, the chlorine gas flow rate was set to obtain the
desired total chlorine  residual at the second sampling point.   Residuals
•were measured amperometrically according to the method given by
Standard Methods [ 62],   The residual was varied during the study
from approximately 1 to 6 mg/f..  When the desired residual was
obtained,  samples were taken to determine the fraction of coliforms
killed.   For each determination of coliform concentration,  four re-
plicate  samples  were collected.   Samples were  taken first in the box
upstream from the chlorine  injection device to determine the initial
coliform concentration,  then from sampling point Z, and  finally from
sampling point 1.  Samples for the determination of chlorine residuals
were taken.  The coliform samples were dechlorinated as quickly as
possible with 0, 5 m-0 of a 10% solution of sodium thiosulfate.   The
bacteriological analyses were performed by the Sanitation and Radiation
Laboratory, California State Department of Public Health in a mobile
laboratory located at the plant site.  All bacteriological determinations
were made on the basis of four dilutions, using  five tubes for  each
dilution, and following the procedure outlined in  Standard Methods.

After samples were taken with the first device,  the flow was stopped,
the box was de-watered with two gasoline powered pumps provided by
Sacramento County,  the  grid was installed or removed, and the flow
was  started again.  When the flow rate became constant,  the sampling
procedure was repeated  using the other initial mixing device.

Each day a 6-hr  composite sample of the unchlorinated secondary
effluent was collected.  This  sample was kept under refrigeration and
                                  135

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    \  \  \   \
                            r
                            •«•
    •:-'? ::-.'•.• •/-;••.'.:~-?.•>?••.?:•»'.•):'•'•'•*;.•
                                       WEIR CREST
                                        EXISTING
                                        DIFFUSER
                                                                 d = 27 in.
                                                                 A = 3. 98 ft2
                                                          SAMPLING
                                                          POINT i
FLOW  = 2. 2 to 2. 5 mgd = 3. 65 cfs

VELOCITY = 3. 65/3. 98 - 0. 92 fps

PIPE LENGTH = 184 ft to sampling point 1.     t[  =

PIPE LENGTH = 622 ft between points 1 and 2. T2  =
                                                                184
0. 92 x 60
   622
0. 92 x 60
                                                                       = 3. 3 min

                                                                       = 11.3 min
      rp  ,
                  t  = 14. 6 min
                                                                                              SAMPLING
                                                                                              POINT 2
FIGURE  3.  SCHEMATIC  DRAWING OF RANCHO CORDOVA CHLORINATION SYSTEM

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transported at the end of the day to the Sanitary Engineering Research
Laboratory at the Richmond Field Station of the University of California.
Determinations were made of the ammonia nitrogen, organic nitrogen,
COD, volatile suspended solids, and total suspended solids.  The
analytical procedures used were those recommended by Standard
Methods.
RESULTS

The physical and chemical analyses  of the unchlorinated secondary
effluent are shown in Table 1.  The coliform and fecal coliform sur-
vival ratios and the operating parameters are summarized in Table 2.
Each bacterial density shown (MPN per 100 mi) representes the log
mean of four replicate samples
                            TABLE 1

   ANALYSES OF UNCHLORINATED SECONDARY EFFLUENT
Run
1
2
3
4
NH3 -N
mg/i
12. 3
10. 8
13. 0
12. 5
Org-N
mg/i
3. 1
3. 8
2. 8
3. 0
SS
mg/4
9-0
4. 0
3. 0
6.0
vss
mg/i
8. 0
0. 0
0. 0
0. 0
COD
mg/i
54
51
57
46
Temp
°C
--
17. 0
18. 0
17. 5
PH
Unchlor.
--
7.4
7. 4
7. 4
Chlor.
--
7. 1
7. 0
7. 1
The results are plotted in Figures 4 and 5.  The coliform (Figure_4)
and fecal collform (Figure 5) survival ratios are plotted against Rt,  the
total chlorine residual in mg/i times the contact time in minutes.  These
figures show that the multiple-source grid did not improve process
performance as was expected.  Possible reasons for this  are discussed
in the next section.  A positive result of the experiment is the fact that
the  slope of the lines in Figures 4 and 5 can be taken as minus  3 on
log-log paper.   This  is the same decay rate that Selleck[  57] found
for  non-backmixed reactors using a primary effluent.
                                  137

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                          TABLE Z



OPERATING PARAMETERS AND BACTERIAL SURVIVAL RATIOS
Run



1





2






3




4



Initial
Mixing
Device


Grid


Diffuser


Grid


Diffuser


Grid


Diffuser


Grid


Diffuser

Calc.
Contact
Time

min
0
3. 2
13.9
0
3. 3
14. 5
0
3. 0
13. 3
0
2. 98
13
0
2.9
12. 5
0
3.0
12. 8
0
2. 8
12.8
0
3.0
13.3
Flow

mgd
2. 3
2. 3
2. 3
2. 2
2. 2
2. 2
2.4
2.4
2.4
2.45
2.45
2.45
2. 55
2. 55
2. 55
2. 5
2. 45
2. 5
2.6
2. 6
2. 5
2.4
2.4
2.4
Chlorine
Residual

mg/t
0
3.65
3. 55
0
4. 2
4.0
0
4. 7
4. 55
0
5.05
5.05
0
5. 55
5. 70
0
5. 90
5. 75
0
1. 60
1. 80
0
2.5
1.85
Coliform
Bacteria
MPN/100 mt
y &c y
0
1. 6 x IO6
<4. 7 x IO3
3. 0 x IO2
1. 1 x IO6
-
<4. 0 x IO2
7. 05 x IO5
7. 3 x IO2
1. 2 x IO2
1. 17 x IO6
2. 45 x IO3
1. 25 x IO2
1. 3 x IO6
1. 04 x IO3
1. 6 x IO2
2. 64 x IO6
1. 02 x IO3
4. 09 x IO2
2.01 x IO6
5. 28 x 10s
3. 34 x IO4
2. 6 x IO6
3. 41 x IO5
7. 7 x IO3
y/y0

1. 0
<2. 9 x IO"3
1.9 x IO"4
1.0
-
<3. 6 x IO"4
1. 0
1.04 x 10"3
1. 66 x 10"*
1. 0
2. 1 x IO"3
1. 07 x 10"4
1.0
8. 0 x 10"*
1. 23 x IO"4
1. 0
3. 9 x IO"4
1. 6 x IO"14
1. 0
2. 62 x 10"1
1. 66 x IO"2
1. 0
1. 33 x IO"1
2. 96 x 10"3
Fecal
Coliform
Bacteria
MPN/100 ml
n &c n
o
2. 5 x 10s
<2. 0 x IO3
<2. 0 x 10Z
<2. 38 x 10s
-
-
2. 64 x IO5
<2. 0 x IO2
<25
2. 86 x 10s
<2. 38 x 102
<25
4. 5 x 10s
20
<20
4. 5 x IO5
<32
<20
3. 06 x 10s
5. 67 x IO4
<4. 45 x IO2
8. 58 x IO5
3. 84 x IO4
<2. 0 x IO2
n /n
o

1.0
<8 x 10"3
<8 x IO"4
1.0
-
-
1.0
<7. 6 x 1Q-1
<9. 5 x IO"5
1.0
<8. 3 x IO"4

-------
        i, 0
                           2. 3
       10
         -i

  -I
  CO
  o
  O
  u
       10
         -2
       10
         -3
10
         -4
      10
         -5
      10
         -6
                              y/y  = [ VOTT9 Rt]
                LEGEND:
         O GRID

           DIFFUSER

          MLESS THAN OR EQUAL TO
          JTHE VALUE INDICATED


                              I
           0. 1
                i. 0          10
                      Rt,  mg/f-min
FIGURE 4.  COLIFORM SURVIVAL RATIO IN AN ACTIVATED SLUDGE
             EFFLUENT - EFFECT OF INITIAL MIXING
                                139

-------
 cn
 o
 o
 u
 w
                        1. 6
     1.0
     10
       -1
 o

 H   10-2
     10
       -3
10
       -4
     10
       -5
     10
       -6
                              o
                                   n/n  = [ VOT39 Rt]"3
                                      o
       LEGEND:


         O  GRID


         ^  DIFFUSER


         01 LESS THAN OR EQUAL TO


A           (THE VALUE INDICATED
                 I
I
         0. 1
                1. 0          10



                      Rf, mg/jf-min
           102
103
FIGURE 5.  FECAL COLIFORM SURVIVAL RATIO IN A CHLORINATED

            ACTIVATED SLUDGE EFFLUENT - EFFECT

                        OF INITIAL MIXING
                                140

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CONCLUSIONS

The results of this field experiment, coupled with.the previous and
subsequent pilot-scale experiments, have led to the conclusions
discussed in Appendix A.  Specifically,  while different rates of initial
mixing in a non-backmixed reactor may initially produce different
levels of disinfection,  at sufficiently long contact times — similar to
those found in practice —the results from the various times of initial
mixing are the same.

These experiments have shown,  however, that while the  colifdrm sur-
vival ratio in the effluent of a tubular reactor cannot,  in  practice,  be
improved as it had been hoped,  it has been found that  a tubular reactor
is superior to a  backmixed reactor for two reasons.   First, as noted
by Selleck, Collins,  and White [  56],  backmixlng apparently results
in a chlorine  residual with poorer  bactericidal effectiveness because
of reaction of the chlorine  entering the reactor with residuals pre-
viously formed.   Second, short-circuiting, or the presence In the
effluent from the reactor of fluid particles with a very short chlorine
contact time, can greatly affect  overall performance.  A tubular
reactor prevents this.
                                   141

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                   APPENDIX C




COMPARISON OF RESULTS WITH THOSE OF GIBSON
                           143

-------
                          APPENDIX C

  COMPARISON OF RESULTS WITH THOSE OF GIBSON [  11, 26]
Gibson used a  square-mesh biplane grid with 1/8-in. grid bars and
tracer orifices placed halfway between the grid bar  intersections on
the upstream side  of the bars.  This configuration is very similar to
that used for one run  of this study (see Figure 28, Section VI.)  The
grid bar diameters were essentially the same and upstream injection
was used in both instances.   The scaJLar decay rate should therefore
be the same.   The values of ns and A.were different for the two
experiments, but it should be possible to relate the  results through
use of the mixing model developed  in Section VI.  NaCl solution-was
used as the tracer in  both studies.   A more complete comparison of
the parameters of  the two experiments is  given in Table 1.

The results of the  two experiments are shown in Figure 1, with (a'ns)
/(Ao'1') plotted against x/d.  Within the accuracy of the measurements,
the points for both experiments  can be said to fall along the same line.
The value of a*11 and a for this line are 50-in.~E and 0. 86,  respectively.
In his  determination of the scalar decay rate,  Gibson obtained a
value of a = 0.  69-  If  Gibson's data points were considered separately,
a value of a-" much lower than the given value of 50 would result.
This,  as  noted previously, is the result of a-'1 being  very sensitive
to slight changes in the  slope  of the line drawn through the data
points.

The fact that the results of the two studies agree to a reasonable
extent is  important for two reasons.   First, it seems to indicate
that the probe  used in the present study was not  excessively large
and that a reasonable  approximation of the "true" rms values was
obtained.  It should be noted that the results of both studies may be
low; Gibson's because of an inability to measure low wave number
components of the  spectrum,  and those of the present work because
of the  large probe  diameteri.

Agreement between the two experiments also serves to further confirm
the usefulness  of the mixing model developed in Section VI.  It was
concluded that  for  a given grid bar diameter and tracer injection.
system,  the results should follow the  equation

                         a'M         , % -a
                             s    ' ,
                          ~A
                                  144

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                            TABLE 1

           PARAMETERS FOR MIXING EXPERIMENTS

M, in.
d, in.
M/d
Solidity
Tracer Source
Diameter, d , in.
Reactor Cross-
Section, in. 2
Tracer Source
Density, M , in. ~2
S J
A-p, mg/S.
A, m.g/1
Probe Diameter,
d , microns
o
Tracer Injection
System
Present Study
0. 500
0. 125
4. 0
0. 45
0. 0135
3. 14
7. 9
850, 1700, 2550
50, 000
47. 5
75
**
Gibson
0. 625
0. 117
5. 33
0. 34
0. 012
36. 0
5. 0
1,910
58,000
16. 6
.
«
            Not listed.  Probe size varied from 10 to 50 microns
         in Gibson's experiments.
         * *
            Tracer injected upstream through sources  in grid bars
         placed halfway between bar intersections.
where #''  and a are constants.   In Section VI the results of several
experiments  -were compared.   In all instances downstream injection
•was used.  Now,  reasonable agreement has  been found for two ex-
periments which were made in independent studies.
                                  145

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  0. 1

    . 08


    .06

    . 05

    . 04


    . 03



    . 02
K
•  . oi

  . 008

  . 006

  . 005

  . 004


  . 003


 0. 002
        20
                                   a" = 50 in.
                                   a  =  0. 86
                                             -2
                        a = 0. 69
                   FROM PRESENT WORK

                   FROM GIBSON [  11]
                         I	I
                                                       I
                                          J_
             30
40  50 60
80
  100
x/d
150
200   300  400  500
      FIGURE 1.  SCALAR DECAY DOWNSTREAM FROM A GRID:
          COMPARISON OF RESULTS FROM PRESENT STUDY
                WITH RESULTS FROM GIBSON'S STUDY
                                  146

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                APPENDIX D




PREDICTION OF MIXING FOR LARGER GRIDS
                       147

-------
                           APPENDIX D

          PREDICTION OF MIXING FOR LARGER GRIDS
Although a completely satisfactory method of predicting the time of
mixing which can be expected from larger grids has not been developed,
it is possible to use the results of the present mixing studies and
Corrsin's theory  to estimate what the scalar decay curve will be for
such grids.  Corrsin's equation is
        u
da1
du{
7 + M
NSc
0(3 2/3 ( Ls}2/3 , 53/2 log NSc
2 Lf 3 NRe
                                                                  54)
Assuming Batchelor;s turbulence decay law holds (u1 ax1),  the
right-hand side of the above equation is equal to a,  the  scalar decay
rate.  NSC - 700 for sodium chloride, and NRe,  = 45, the average
value for the present work.  Putting in these values,  Equation (54)
becomes
                                   Z
                     a =
                                    2/3
                                       + 0. 63
As mentioned in Section VI, L  depends on the method of tracer
injection (e. g. ,  either upstream or downstream) and Lf is proportional
to the grid bar diameter.   If it is assumed that L /L does not vary
as the mixing progresses,  it is  possible to obtain a value of  Ls/L-f for
an experimentally determined scalar decay curve.  With this known,
the value  of Ls/Lf for  larger grids can be estimated and a scalar
decay rate can be calculated.

The result of such calculations are shown in Figure  1.   The  experi-
mental  curves for d =  1 /4 in.  and d =  1/8 in.  were taken from Figure
31.  From the experimental curve for d = 1/4 in- , scalar decay
curves  were predicted for  d = 1/8,  1/2, and 1 in.

For d = 1/8 in.  the experimental value of a was  0. 4.  The predicted
value is 0. 54.   Because of the extensive scatter, a  line with a = 0. 54
would fit the data almost as well as the line which was used in Figure
31.  However, the as sumption that  a" is  constant places the predicted
curve somewhat lower than the experimental  curve.   A similar calcula-
tion using u'a x~ 5'7as proposed  by Frenkiel gave slightly poorer
agreement.
                                  148

-------
   1. 0
   0. i
K
   0. 01
                                          — —  PREDICTED FROM
                                               DATA FOR d =  1/4 in.
                                               EXPERIMENTAL
                                                  DATA
                                   I
             J	I
I
I
10    20     40  60  100   200

         x/d
                                                           400  600  1000
       FIGURE  i.  PREDICTION OF SCALAR DECAY CURVES FROM
                  EXPERIMENTAL DATA FOR d = 1/4 in.

-------
As no tests were done with grid bars i/Z or 1  in. In diameter, it is
impossible to know how accurate the predicted curves  are.  However,
this  graph may be used to estimate the time of mixing  to be expected
from prototype grids.
                                   150

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                            SECTION X

                            GLOSSARY


Symbol                      Definition

    A      "Point" tracer  concentration,  mg/&; coefficient in
            Equation  (31); coefficient in Equation (44); reactant in
            Equation  (63); cross-sectional area of conducting medium.,

    Aj      Coefficient in Equation (30)

    A      Mean component of "point" tracer concentration,  rag/I

    A      Average  concentration of tracer mixed with portion of flow
      P     during wake-mixing

    a       Fluctuating component  of "point" tracer concentration,
            scalar decay rate

    a'      rms concentration fluctuation, mg/f.

    a1      Initial rms concentration fluctuation, mg/-2


    a1      Initial rms concentration fluctuation of isotropic  scalar
      1      field, mg/.£

    B      Distance  from spherical probe which represents  volume
            within which  90%  of the total resistance exists, coefficient
            in Equation (42),  reactant in Equation (63)

    C      Coefficient in Equation (32), coefficient in Equation (46),
            Reaction  product  in Equation (63)

    Q
      D     Drag coefficient

    c       Coefficient in Equation (34)

    C(r)    Scalar correlation function


      i      Diffusion coefficient of i-fold particles


      ij     Combined diffusion coefficient of i-fold and j-fold particles


      m    Molecular diffusivity,  ft2/sec
                                    151

-------
Symbol                      Definition

  d          Grid bar diameter,  in.


  o        Probe diameter, microns

  E         Three-dimensional energy spectrum function, voltage

  E!        One-dlmens lonal energy spectrum function

  •p«
   e        Universal three-dimensional energy spectrum function

  •p-
   1 e       Universal one-dlmens lonal energy spectrum function

  T£
   s        Scalar spectrum function

  F         Fractional completion of reaction

  f(r)       Longitudinal correlation function

  G         rms velocity gradient,  sec"1

  g          Acceleration due to  gravity, ft/sec2

  g.(r)       Lateral correlation  function

  g(x)       Function defined by  Equation (66)

  jj
   Ij        Collision frequency  of l-fold and j-fold particles In
            turbulent flow


  L        Head  loss through grid,  In.


  ij        Collision frequency  of l-fold and j-fold particles due
            to Brownian motion


  s         Intensity of segregation


  ij        Collision frequency  of i-fold and j-fold particles due to
            laminar flow

  jr
   A        Aggregation rate coefficient

  •rs
   B        Breakup rate coefficient
                                  152

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Symbol



 K
   c




 KL



 K
 K
   w
 k*

 L
   g


 L
   s



 M



 MPN



 N



 NT
   Re,
 N
   Re
 N
   Sc
 n
 n.
               Definition




Conductivity cell constant




Head loss coefficient for grid




Cross -sectional area near each orifice with which the

tracer is mixed during wake-mixing




Coefficient  in Equation (92)



Wave number, ft'1



One -dimensional wave  number, ft
                                      1/4

Batchelor wave number (k—  = (e/vD 2)   )
                         rJ         m




Kolmogoroff wave number(k-r = (e /v3 )1'  4)


Distance between two electrodes

of a conductivity probe, in.




Longitudinal integral scale




Lateral integral scale




Scalar integral scale



Center-to-center spacing of grid bars, in.



Most probable number  of coliform organisms per 100 ml



Paddle rotation speed in flocculator, rpm
Microscale Reynolds number
Grid bar Reynolds  number
Schmidt number (Nc   = v/D  )
                   oc       m
                                               = u1 X  I v)
                                             = V  d/v)

Frequency of fluctuations,  sec



Number concentration of primary particles




Number concentration of i-fold particles
                                   153

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Symbol                       Definition


 n        Number concentration of primary part icles entering
          flocculator


 n        Number concentration of primary particles in m
  1       compartment of flocculator


 P        Power Input to flocculator


 Q        Flow through flocculator,  gpm


   M      Mainstream flow rate through tubular reactor, gpm


 Q        Flow with which tracer Is  mixed during wake-mixing


   T      Tracer Injection flow rate, gph


 R        Resistance, ohms;  chlorine residual,


 R        Resistance measured by a spherical electrode In an
   CO
          Infinite conducting medium,  ohms
 R        Resistance measured by probe, ohms


 R1       Resistance In parallel with probe,  ohms


 R^      R'R  /(R1 + R  ), ohms
  T         P       P

 R.       Radius of l-fold particles


 R..      Combined radius of i-fold and j-fold particles


  o       Radius of single electrode conductivity probe, microns

 —*•
 r        A vector


 S        Grid solidity,  I. e. , fraction of tubular reactor cross-
          section covered by grid bars, dlmenslonless


 T        Flocculatlon chamber  residence time,  min


 T
  m      Flocculation chamber .residence time per compartment,
          min


 t         Time


 t         Mean chlorine contact time, min
                                   154

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Symbol                       Definition

   [         Instantaneous velocity in i   direction in Cartesian
            coordinates, fps (i ='i,2,3)

 U.         Mean velocity in ith direction,  fps  (L = i, 2, 3)

 dU                              „!
            V elocity gradient,  sec
 X
 X.
 i         Fluctuating component of velocity in i   direction (i =  i,2,3)

u1, u!     rms velocity fluctuation  in isotropic turbulence, fps

V
  M       Mainstream velocity in tubular reactor, fps

V  V
  '  r      Reactor volume, ft *

v          Kolmogoroff characteristic velocity (v = (v &) 1'4 )

x          Distance downstream from grid, in.


 b         Apparent origin of rms velocity fluctuations, in.


 i         Cartesian component  of coordinate (i = i, 2, 3)

x          A vector

y          Most probable number of coliforrn organisms per 100 rrd
           after disinfection


^o         Most probable number of coliform organisms per 100 mi
           before disinfection

Z          Impedance, ohms

a          Coefficient  in Equations  (45a) and (86)

cx1         Coefficient  in Equation (45)

<*'          Coefficient  in Equation (89)

a"        Wake-mixing  coefficient  in general mixing model,
           Equation (97)

j3          Ratio of amount of reactant present to the stoichiometric
           amount
                                   155

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Symbol                      Definition

 £          Rate of energy dissipation

 £          Rate of scalar "dissipation"

 T|          Degree of mixing,  Kolmogoroff characteristic length
            scale


  f         Longitudinal microscale

  g         Lateral microscale

  s         Scalar microscale

 H-          Viscosity lb-sec/ft2

 v          Kinematic viscosity,  ft2/sec

 |          Voltage

 p          Resistivity, ohm-ft

 cr          Conductivity,  mhos /ft
                                   156

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                            SECTION XI

                          REFERENCES
 i.     Rich, L. G,  Unit Operations of Sanitary Engineering,
       New York:  John Wiley and Sons, 1961.

 2.     Hinze, J. O.   Turbulence.  New  York: McGraw-Hill, 1959.

 3.     Lee, John.   "Turbulent Motion and Mixing, " Ph. D. thesis
       in Chemical Eng. , Ohio State Univ. ,  1962,

 4.     Brodkey, R. S.   "Fluid Motion and Mixing, " Ch.  2 in Mbdng_ —
      .Theory and Practice.  Vol.  I, by V. W. Uhl and J. B.  Gray,
       New York and London: Academic Press, 1966.

 5.     Batchelor; G. K.  The Theory of Homogeneous Turbulence.
       New York:  Cambridge Univ. Press,  1953.

 6.     Taylor,  G.I.  "Statistical Theory of Turbulence, " Parts
       I-IV, Proc.  Roy. Soc. , A151:421,  1935.

                     "The Spectrum of Turbulence, " Proc. Roy.
       Soc. , A164:15,  1938.

 8.     Kolmogoroff,  A. N.  "The Local Structure of Turbulence in
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       Numbers, " C. R. Acad. Sci.  U. R. S. S. ,  30_, 301, 1941.

 9.     	.   "On Degeneration of Isotropic Turbulence in an
       Incompressible Viscous Liquid, " C. R.  Acad. Sci. U. R. 5. S. ,
       3j_:538,  1941.

10.     	.   "Dissipation of Energy in Locally Isotropic
       Turbulence, "  C. R.  Acad. Sci.  U. R. S. S.  ,  32:16, 1941.

11.     Gibson, C. H.   Scalar Mixing in Turbulent^FJ.OW,  Stanford
       Univ. Dept. of Chemical Eng. Report SChE-62-001,  1962.

12.     Grant, H. L. ,  R. W. Stewart, and A.  Molliet.  "Turbulence
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13.     Heisenberg, W.  "Zur  Statistischen Theorie der Turbulenz, "
       Z... Phys, ,  Hl:628, 1948.

14.     Batchelor, G. K. ,  and A. A.  Townsend.   "Decay of Isotropic
       Turbulence in the  Initial  Period, "  Proc.  Roy.  Soc. ,  A193:539,
       1948.
                                  157

-------
15.   Van der Hegge Zijnen,  B. G.  "Measurement of the Intensity,
      Xntregal Scale and Micro-scale of Turbulence Downstream of
      Three Grids in Air, " App.  Sci. Res. ,  7A:149,  1958.

16,   Frenkiel,  F. N.   "The Decay of Isotropic Turbulence, "
      J.  of App.  Mech. ,  _l_5_:31i,  1948.

      Corrsin, S.  "The  Isotropic Turbulent Mixer:  Part II.
      Arbitrary Schmidt  Number, " A. I.  Ch. E.  Jour. ,  _10.:870,  1964.

      Moore,  F. K.  (Ed. ) Princeton Series on High Speed Aero-
      dynamics^ and Jet Propulsion,  Vol.  IV-Theory  of Laminar
            , Princeton:  Princeton Univ. Press, 1964.

19-   Saidel, G. M. ,  and H. E.  Hoelscher.  "Chemical Reactions
      in the Turbulent Wake of a  Cylinder, " A. I. Ch.  E.  Jour. ,  11:
      1058,  1965.

20,   Kiser, K. M. , and  H. E. Hoelscher.  "Turbulence in the Wake
      of a Cylinder, " Ind. Eng. Chem. ,  49:970,  1959.

21.   Sparks, R. E. , and H. E. Hoelscher.  "Turbulence and Mass
      Transport in the Wake of a  Cylinder, " A. I. Ch. E.  Jour. ,  8; 103,
      1962.

22,   Keeler, R. N.  Mixing and Chemical Reactions  in Turbulent
      Flow Reactors,  Univ.  of California Lawrence Radiation Lab.
      Report UCRL-7852, 1964.

23,   Danckwerts, P. V.   "The Definition and Measurement  of Some
      Characteristics of  Mixtures, " Applied Scientific Research,  A,
      3_:279,  1953.

24.   Toor, H. L.  "Mass Transfer in Turbulent and  Nonturbulent
      Systems with Rapid Irreversible Reactions and Equal Diffusivities,
      A. I. Ch. E.  Jour. ,  8_:70, 1962.

25.   Batchelor,  G. K.  "Small-Scale Variation of Convected Quantities
      Like Temperature  in Turbulent Fluid — Part I,  General Dis-
      cussion and the Case of  Small Conductivity, " J. Fluid Mech. ,
      5_:il3,  1959.

26.   Gibson, C. H. , and W. H. Schwarz.   "The Universal Equilibrium
      Spectra of Turbulent Velocity and Scalar Fields, " _J_.	Fluid Mech. ,
      16:365,  1963.

27.   Keeler, R. N. , E. E  Petersen, and J. M. Prausnitz,   "Mixing
      and Chemical Reactions in  Turbulent Flow Reactors, " A. I.  Ch.
      E.  Jour., 11:221,  1965.                              ~
                                  158

-------
28.   Corrsln, S.   "Simple Theory of an Idealized Turbulent Mixer, "
      A. I.  Ch. E. Jour. ,  3^:329,  1957.

29.   Beek Jr. ,  John, and R. S.  Miller.  "Turbulent Transport In
      Chemical Reactors,  " Chemical Engineering Progress Symposium
      Series No.  25.  _5_5_:23,  1959.

30.   Gibson,  C. H. ,  and W. H. Schwarz.  "Detection of Conductivity-
      Fluctuations in a Turbulent Flow  Field, " J.  Fluid Mech. ,  JjS:
      357,  1963.                               ~

31.   Argaman,  Yerachmiel, and W. J.  Kaufman.  "Turbulence and
      Flocculation, "  Proc. ASCE, JSED,  9.6:223,  1970.

32.   LaMer,  V. K.  "Coagulation Symposium Introduction, " J._ Collgj.d
      Science, _1_9_:291,  1964.

33.   Fair, G. M. ,  and J.  C. Geyer.  Water Supply and Wastewater
      Disposal.  New York:  John Wiley and Sons, 1967.

34.   Langelier, W. F. , and H. F. Ludwig.  "Mechanisms of
      Flocculation in the Clarification of Turbid Waters, " JAWWA,
      4J_:i63,  1949.

35.   Rich, L. G.   Unit Proces ses of Sanitary Engineering, New York:
      John Wiley and Sons, 1963.

36.   Kirrij  Wonsuk, H. F.  Ludwig, and W. D.  Bishop.   "Cation
      Exchange Capacity and pH in the  Coagulation Process, "  JAWWA,
      5J7:327,  1965.

37.   Stumm,  W. , and  C.  R. O'Melia.  "Stoichiometry of Coagula-
      tion, " _JAWWA, _6£:514,  1968.

38.   Packham, R. F.   "The Coagulation Process —A  Review  of
      Some Recent Investigations, " Proc.  , Soc. for Water Treatment
      and Examination, j_2_:15, 1963.

39.   Black, A. P. and  Ching-Lin Chen.  "Electrokinetic Behavior
      of Aluminum Species in Dilute Dispersed Kaolinite Systems, "
      JAWWA, 5_9_:1173, 1967.

40.   Hahn,  H. H. ,  and Werner Stumm.  "Coagulation by Al(III);  The
      Role of Adsorption of Hydrolyzed Aluminum in the Kinetics of
      Coagulation, " Advances  in  Chemistry  Series, No. 79,
      "Adsorption From Aqueous Solution, " 91, 1968.

41.   Stumm,  W. , and  J. J.  Morgan.  "Chemical Aspects  of
      Coagulation, " JAWWA, 54_:971, 1962.
                                  159

-------
42,   LaMer; V. K.  "Coagulation Versus the Flocculation of Colloidal
      Dispersions by High Polymers (Polyelectrolytes), " Principles
      and__Applications of W_at;_c_r__Ch_emistry, S. D,  Faust and  J. V.  Hunter,
      (Eds, ) John Wiley and Sons, 1965.

43.   von Smoluchowski,  M.  "Drei Vortrage uber Diffusion,
      Brownsche  Molekular  Bewegung und Koagulation von Kolloidteilchen,
      Physik.  Z.  , r?:557, 1916.

44,	_.  "Versuch einer  Mathematischen Theorie der
      Koagulationskinetik Kolloid L'osungen, " Z. Phvsik.  Chem. ,
      9.2:155, 1918.

45.   Camp, T, R. ,  and P. C. Stein.   "Velocity Gradients and Internal
      Work in  Fluid  Motion,  " J.  Bos. Spc,  Civ.  Engrs. ,  30_:219,  1943.

46,   Argaman,  Yerachmiel, and W. J.  Kaufman.  Turbulence in
      Orthokmetic Flocculation,  SERL Report No.  68-5, Sanit. Eng.
      Research Lab. ,  Univ,  of Calif. , Berkeley,  1968.

47.   Harris,  H.  S. ,  W. J. Kaufman, and  R. B. Krone.   "Orthokinetic
      Flocculation in Water  Purification, " Proc. ASCE,  JSED, 9^:95,
      1966.

48.   Hudson,  H. E.  "Physical Aspects of Flocculation, " JAWWA,
      5_7:885, 1965.

49.   Levich, V.  G.  Physico-Chemical Hydrodynamics,  2nd Edition,
      New Jersey: Prentice-Hall, Inglewood  Cliffs,  New Jersey,  1962.

50.   Saffman,  P. G. ,  and J. S.  Turner.   "On the Collision of Drops
      in Turbulent Clouds, "  J. of Fluid Mechanics, J: 1 6, 1965.

51.   Parker,  D. S, , W. J. Kaufman, and D.  Jenkins.  Character -
      istics of Biological Floes  in Turbulent Regimes,  Sanit.  Eng.
      Research Lab. ,  SERL Report No.  70-5, Univ.  of Calif. ,
      Berkeley,  July 1970.

52.   Vassilatos, G. ,  and H, L.  Toor.   "Second Order Chemical
      Reactions in a  Non-Homogeneous  Turbulent Fluid, " A. I. Ch. E.
      Jour. , _ljL-666, 1965.

53.   Kramer,  I. H.  "Physical Factors in Chemical Reaction
      Engineering, "  Chem. Eng.  Sci. ,  8_:45,  1958.

54.   Rudolfs,  W. , and H. W. Gehm.  "Chemical Coagulation of
      Sewage.   V — Mixing of Chemicals and Coagulation, " Sewage
      Works Journ. . 1:547,  1936.

55.   Selleck,  R.  E. , and H. F.  Collins.   "Di sinfect ion in Wastewater
      Reuse, "  Paper presented  at the Second  Annual Univ. of Calif,
      Sanit.  Eng.  Research Lab.   Workshop, Tahoe City,  Calif. ,
      June 26,  1970

-------
 56.    Selleck,  R. E. ,  H. F.  Collins,  and G. White.   "Kinetics of
       Wastewater Chlor ination in Continuous Flow Processes, "
       Paper presented at the 5th International Water Pollution
       Research Conference,  San Francisco, July-August,  1970.

                      Talk given at the 5th International Water
       Pollution Research Conference,  San Francisco,  July-August,
       1970.

58.    Riddick,  T. M.  "Zeta  Potential and Polymers, " JAWWA,
       58.:719,  1966.                                    "

59.    Vrale, L. ,  and R.  M. Jorden.  "Rapid Mixing in Water
       Treatment,  " JAWWA,  _6_3_:52,  1971.

60.    Wilson, G.  Work  done at Sanit.  Eng.  Research Lab. ,
       Univ.  of California,  Berkeley, unpublished,  1969-

61.    Lamb, D. E. , F. S. Manning,  and R. H. Wilhelm.  "Measure-
       ment of Concentration  Fluctuations with an Electrical Con-
       ductivity  Probe, " A_Ii_2]i_^_Joiii- •  6_:682, I960,
62.   Standard Methods for the Examination of Water and Wastewater,
      12tn Ed. , APHA, AWWA,  WPCF, 1965.

63.   Instruction Manual for 3C66 Carrier Amplifier,  Tektronix,
      Inc. ,  1969-

64.   Baines,  W. D. ,  and E. G.  Peterson.   "An Investigation of a
      Flow Through Screens, " Trans.  ASME,  7_3_:467, 1951.

65.   Vennard, J. K.  Elementary Fluid Mechanics,  New York:
      John Wiley and Sons,  1963.                    /

66.   Hahn, H. H.  , and W. Stumm.   "Kinetics of Coagulation with
      Hydrolyzed Al(III)5  The Rate-Determining Step, " J.  of Colloid
      and Interface Science,  2_8:134, 1968,

67.   Kaufman, W. J.   Notes for CE 21 5A,  Univ.  of California,
      Berkeley,. 1969-

68.   TeKippe, R. J. ,  and R. K. Ham.   "Velocity-Gradient Paths in
      Coagulation, " JAWWA,  _63_:439, 1971.

69.   Lee,  F.  M.   The Optimization of C. .jemical Pr ec ipitation-
      Flocculation of Municipal Wastewater, Ph.D. Thesis, Univ.
      of Calif. , Berkeley, 1972.
                                    161
   . GOVERNMENT PRINTING OFFICE:1972  514-149/104 1-3

-------
   SELECTED WATER
   RESOURCES ABSTRACTS
   INPUT TRANSACTION FORM
                     /. Report No.
  4.  Title

     INITIAL MIXING IN COAGULATION PROCESSES
  7.  Author(s)

     Stenqulst, R. J. ,  Kaufman,  W. J.
  9.  Organization
     California Univers Lty,  Berkeley
     Sanitary Engineering Research Laboratory
                        3. Accession No.

                        W

                        5. Report Date March 1972
                        6.
                        8. Performing Organization
                          ^MRL 72-2
                       10. Project No.
                                         11.  Contract!Grant No.
                                         17030-DLX-(5)NC
                                         13.  Type of Report and
                                            Period Covered
  12.  Sponsoring Organization
  15.  Supplementary Notes
                     Environmental Protection Agency report
                     number EPA-R2-72-053, November 1972.
  16.  Abstract
     This investigation was undertaken with the objective of determining the importance
     of the initial mixing step in water and wastewater treatment processes and deter-
     mining whether increasing the rapidity of the initial mixing could improve process
     performance.  The principal process considered was alum coagulation-flocculation
     of a kaolin suspension in water.   The initial mixing device under consideration was
     a biplane,  square-mesh grid of bars placed  in a turbulent flow, tubular reactor;
     a 2-in.  pipe was used in the present studies.  Studies were made using a single
     electrode "point" conductivity probe and NaCl solution tracer to determine what
     parameters affect the mixing •which occurs  in the turbulent flow field downstream
     from a grid, and from these results a  general mixing model was developed.  The
     relation between initial mixing and process performance was  studied by using two
     of the grids from the mixing studies as initial mixing devices  in coagulation of a
     kaolin suspension.
  17a. Descriptors
     *Mixing,  *Turbulence, *Coagulation, *Water treatment,  Conductivity,
     Chlorination, Flocculation
  17b. Identifiers

     Initial mixing,  Conductivity Probes
  17c. COWRR Field & Group
  18. Availability
    05F,  05D
19. Security Class.
   (Report)

20. Security Class.
   (Page)
21. No. of
   Pages

22. Price
                                                      Send To:
                                                      WATER RESOURCES SCIENTIFIC INFORMATION CENTER
                                                      U.S. DEPARTMENT OF THE INTERIOR
                                                      WASHINGTON. D. C. 20240
  Abstractor
                                       Institution
WRSIC 102 (REV. JUNE 197l)
                                                                                 SPO 913.261

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