U.S. Environmental Protection Agency Industrial Environmental Research PPA.fiflfl/7.TT-19O
Office of Research and Development Laboratory
Research Triangle Park. North Carolina 27711 NOVGITlber 1977
PARTICLE SIZE DEFINITIONS
FOR PARTICULATE DATA ANALYSIS
Interagency
Energy-Environment
Research and Development
Program Report
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EPA-600/7-77-129
November 1977
PARTICLE SIZE DEFINITIONS
FOR PARTICULATE DATA ANALYSIS
by
J.B. Galeski
Midwest Research Institute
425 Volker Boulevard
Kansas City, Missouri 64110
Contract No. 68-02-2609
Assignment No. 1
.Program Element No. EHE624
EPA Task Officer: Gary L Johnson
Industrial Environmental Research Laboratory
Office of Energy, Minerals, and Industry
Research Triangle Park, N.C. 27711
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
Office of Research and Development
Washington, D.C. 20460
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PREFACE
The work was performed in the Environmental and Materials Sciences Divi-
sion of Midwest Research Institute (MRI). Dr. J. B. Galeski, Senior Chemical
Engineer, Environmental Systems Section, served as the project leader, and
Mr. M. P. Schrag, Head, Environmental Systems Section, was the project manager,
ii
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CONTENTS
Summary „ ,
Introduction . 2
Particle Size Definitions 3
Stokes1 Diameter 3
Classical Aerodynamic Diameter 7
Aerodynamic Impaction Diameter 8
Particle Size Conversions. „ 9
Cascade Impactor Particle Size Data Reductions ..14
References 17
iii
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SUMMARY
This report presents the results of a measurement survey to identify all
equations required to represent particle size data according to each of three
particle diameter definitions--Stokes, classical aerodynamic, and aerodynamic
impaction (or Lovelace diameter). Although the particle diameter definitions
themselves are relatively simple, inconsistencies were found among various in-
vestigations in the use of particle size definitions, particularly in nomen-
clature. It is not always clear from the descriptions of various authors
which definition is intended. The present study presents a consistent set
of definitions and equations for use in interpreting particle size and impactor
data such as that found in the Fine Particle Emissions Information System
(FPEIS) data base. The equations may also be useful to readers of fine particle
sampling reports who may wish to convert the data from one definition to a
more convenient one.
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INTRODUCTION
Particulate sampling data are expressed in the literature in various ways;
this tendency being reflective, in part, of a broad spectrum of environmental
impacts. Physiological, meteorological, and other impacts generally are in-
fluenced differently by particle size and geometry. The impacts are determined
in many cases by analytical approximations which yield alternative character-
istic particle size definitions. Examples include Stokes' or settling diameter,
classical aerodynamic diameter, aerodynamic impaction diameter and numerous
other definitions, described by Raabe (1). For fine particulates, assuming spher-
ical particles, alternative definitions may yield differences of 30% or more
in the reported diameter. Furthermore, relationships between alternative size
definitions are not always well understood.
The objective of this study is to identify the equations required to
represent particle size data according to three diameter definitions--Stokes',
classical aerodynamic, and aerodynamic impaction. The primary purpose of this
study is to facilitate understanding and use of data contained in the FPEIS—
a computerized data base currently being developed by IERL-RTP to contain all
currently available fine particle source test measurements and control de-
vice (s) parameters, test details, particulate physical, biological, and chem-
ical properties, and particle size distribution data. By providing a uniform
compilation of fine particle information and data, the FPEIS can serve the
needs and interests of a broad spectrum of users. These users include plant
officials, control device manufacturers, measurement equipment/method de-
velopers, government officials responsible for the development of fine par-
ticulate control strategies, and other researchers.
The purpose of this document is to supplement existing FPEIS guideline
documents (2,3,4). Definitions of each particle size basis, mathematical
formulae, and techniques for interconversion of particle data are presented
in the following sections.
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PARTICLE SIZE DEFINITIONS
Particle size definitions considered here include:
(1) Stokes', or settling diameter;
(2) Classical aerodynamic diameter; and
(3 ) Aerodynamic impaction diameter (the latter also referred to
alternatively as the "Lovelace diameter" or "aerodynamic resistance dia-
meter" (1)).
It is recognized that a number of alternative diameter definitions
exist which are not presented here. The reader is referred to references
presented throughout this discussion for additional information on size
and measurement techniques pertinent to specific technology areas.
STOKES1 DIAMETER (1,5)
The aerodynamic separation of spherical particles is described by their
terminal settling speeds in any fluid and expressed as:
(1)
18
Where Vs = terminal velocity of a particle in free fall, m/sec
1 9
g = gravitational constant (9.80665 m/secz)
p = particle density, kg/nr
Ds = Stokes1 diameter, m
T] '— fluid viscosity, kg/m-sec
Re = Reynold's number, dimensionless
C(DS) = slip correction factor for spherical particles of diameter
DS, dimensionless.
-------
As indicated, Eq. (1) is valid for values of the Reynold's number less
than 0.5 (Stokes1 regime) (1).
The slip correction factor C(DS) (sometimes called the Cunningham cor-
rection) is an empirical factor which corrects Stokes1 law for discontinuities
when the mean free path (X) of the fluid medium is comparable to the particle
diameter. An approximation for the slip correction factor C(DS) for spherical
particles is given by:
C(Dg) - 1 + 2A (A.) (2)
with
A = ct + fte s (3)
The terms a, (3, and Y are empirical constants; currently accepted values
of these constants are presented in Table 1.
TABLE 1. CONSTANTS FOR USE IN CALCULATING SLIP CORRECTION FACTOR
(X ft Y
Fuchs (6)
Re if (7)
Gushing et al. (8)
1.246
1.26
1.23
0.42
0.45
0.41
0.87
1.08
0.88
Numerical constants presented in Table 1 are based on experimental data
and reflect some variation probably resulting from differences in experimen-
tal technique. The resultant variation in the slip correction factor is
relatively small (about 2 to 3% for particle diameters in the range 10~^ to
10~2 jum, decreasing to about 0.1% at Dg = 0.1 /zm) (1). Constants reported
by Reif (9) were based on experimental investigations by Langmuir, those
of Fuchs (6) were based on Millikan's classic oil drop experiments, while
the constants used by Gushing, et al. (10), are. averages based on data for
a number of different types of particulate. Recent theoretical studies have
shown that "constants" used in calculating the slip correction according to
Eqs. (2) and (3) are actually slightly variable, depending on the fluid medium
and the particle surface properties (11). Values of the slip correction ;
factor are presented in Figure 1 for various values of temperature, pressure,
and Stokes* diameter. The slip correction factor increases with temperature
and decreases with pressure, and this factor becomes increasingly significant
for very fine particles at low pressures. For coarser particles and/or for
higher pressures the Cunningham factor approaches unity and its variation
with temperature and pressure is insignificant.
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For a given fluid, the mean free path (X) is a function of temperature
(which determines the mobility of gas particles) , pressure (which determines
molecular concentration) , and gas composition (9) . Compositional dependence
may be expressed in terms of molecular diffusivity, thermal conductivity or
viscosity, the gas viscosity being most commonly used. An approximation for
the mean free path which is considered acceptable for particle size calcula-
tions is presented in Eq. (4) (10).
*=^o (TJ/TJO) (T/T0)1/2 (Po/P) (4)
where 1 is the gas viscosity at stated conditions, kg/m-sec
T?Q is the gas viscosity at reference conditions, kg/m-sec
T is the absolute temperature, °K
TQ is the reference temperature, 296.16° K (23.0°C)
P is the absolute pressure, kPa
PQ is the reference pressure, 101.3 kPa (1.0 atm)
A0 is the mean free path a.t reference standard conditions, ju,m
X is the mean free path at stated conditions , /u,m
The accepted mean free path of air at reference conditions of 23°C, 1 at-
mosphere is 0.0653 fjua (1).
The viscosity of gas mixtures (T)) used in Eqs. (1) and (4) may be estimated
from single component viscosity data using a procedure developed by Gushing,
Lacy , McCain and Smith (8) .
n r]
H- 1/x- x.
where is defined by the equation:
[1 -f
-------
1000
100
o
u
10
o!ooi
0.01
0.1 1.0
Stokes Diameter x Pressure, /tin-ATM
10.0
100.0
Figure 1. Variation of Cunningham Correction Factor in Air with Temperature and Pressure .(10)
-------
and rj. = viscosity of component i, kg/m-sec
x^ = mole fraction of component i
M. = molecular weight of component i
The viscosity of gases increases approximately as the 0.6 power of the
absolute temperature, and is also very weakly dependent on pressure. For air
at pressures less than 20 atm and at temperatures greater than 300°K, depen-
dence of viscosity on pressure is negligible. The temperature dependence of
single component viscosities for use in Eqs. (5) _and (6) can be found in stan-
dard references, for example CRC "Handbook of Chemistry and Physics" (12), or
equivalent sources.
Experimentation has shown that, for purely viscous flow at low Reynold's
numbers, the fluid resistance is described by Stokes' Law, even for particles
of nonspherical shape, if a numerical coefficient is introduced to account
for the particle shape (6). This correction is commonly referred to as the
"dynamic shape factor." For particle shapes which approximate regular poly-
hedra, the shape exerts less than a 10% influence on apparent (measured)
diameter, but for aggregates (6), and for rod-like geometries such as asbestos,
the particle shape may exert an influence of 30% or more on the measured diam-
eter (6,13) . Such geometries occur in rather limited instances and are not
considered in detail in this report. Where such geometries occur, and a
shape factor is used to describe the fluid resistance, the term "sedimenta-
tion diameter" should be used rather than Stokes1 diameter.
CLASSICAL AERODYNAMIC DIAMETER
The classical aerodynamic diameter is defined as the diameter of a unit
density sphere with the same settling velocity as the particle in question.
This definition is mathematically equivalent to that recommended by the Task
Group on Lung Dynamics for use in studies of aerosol deposition in respira-
tory compartments (14). The classical aerodynamic diameter differs from the
Stokes1 diameter only by virtue of differences in density, assumed equal to
unity, and the slip correction factor, which, by convention is calculated
for the aerodynamic equivalent diameter. From Eq. (1),
D.
Ae
gC(DAe)
(7)
where D = "classical" aerodynamic equivalent diameter, meters
Ae
FT?, V , g, C as previously defined (Eq. (1) .]
^ s
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AERODYNAMIC IMPACTION DIAMETER
The aerodynamic impaction diameter (also referred to as the aerodynamic
resistance diameter or the Lovelace aerodynamic diameter) is used by Cal-
ver (15), Mercer (16), and other investigators working with impactors.* The
aerodynamic impaction diameter is defined as the product of the Stokes1 di-
ameter times the square root of the product: particle density times slip
correction factor (5,15).
DAi = Ds\|
The significance of the aerodynamic impaction diameter is that the quan-
tity represented by Eq. (8) provides a unique measure of the performance of
impactors and other inertial classifiers (including sedimentation and elutri-
ation separators). The basis of this diameter definition is that it is not
possible, using inertial classifiers, to distinguish between two particles
having the same aerodynamic impaction diameter. From Eq. (8), it follows that
two particles having the same aerodynamic impaction diameter may have dif-
ferent Stokes1 diameters, provided that the product Dg[c(D )pj^'^ remains
constanto If particles having varying densities are present, the aerodynamic
impaction diameter should yield a more uniform measure of stage performance
than alternative size definitions, according to the theory of Ranz and Wong
(17). Note that this definition is dimensionally different from the preceeding
definitions, since the density factor is included in the diameter definition.
However, this definition is not used in the major portion of impactor
test data reported in the literature.
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PARTICLE SIZE CONVERSIONS
Equations required for interconversion among the three alternative di-
ameter definitions are presented in Table 2. The relationship between clas-
sical aerodynamic and Stokes' diameters is illustrated graphically in Figure
2 for assumed spherical particles of density 2.4 g/cm . The relationship
between aerodynamic impaction (Lovelace) diameter and Stokes1 diameter is
illustrated graphically in Figure 3 for assumed spherical particles having
densities ranging from 1.0 to 3.0 g/cm^. Note that the second aerodynamic
diameter definition (aerodynamic impaction or Lovelace diameter) is dimen-
sionally different from either previous definition since a density factor is
present. As is evident from Figures 2 and 3, the relationship between clas-
sical aerodynamic equivalent and Stokes1 diameter is qualitatively similar
to that" for the aerodynamic impaction, or Lovelace diameter, and Stokes1
diameter., For spherical particles, the aerodynamic diameter conventions
considered here are numerically nearly identical for particles greater than
about 1 jLtm; at 1.0 fJ.ro., and ambient conditions, the aerodynamic impaction or
Lovelace diameter is greater than the classically defined aerodynamic diameter
by only about 10% (1) . However, at 0.5 JLtm, the discrepancy under ambient
sampling conditions approaches 15% (1) , and increases at smaller particle
sizes.
In several cases, conversions between alternative diameter definitions
involve inherent computational difficulties, since it is not always possible
to express one diameter definition as an explicit function of another (see
Table 2). In such cases, either 'approximations or trial and error exact so-
lutions are required. An approximation given by Raabe (1) which can be used
to obtain explicit solutions for equations in Table 2 is to represent the
slip correction factor by the following approximate expression:
C(Ds) - 1 +2.52 (-A-) , Dg ^ 0.5 Jim (9)
s
Eq. (9) is reportedly valid for Stokes1 particle diameters greater than about
0.5 /am (1). An alternative simplification suggested here is to approximate
the slip correction factor for particles less than Dg =0.5 /im by the fol-
lowing approximate relationship :
C(Dg) 2-1 - py + 2(« + p) - > Dg < 0.5 jum (10)
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TABLE 2. EQUATIONS USED FOR PARTICLE SIZE CONVERSIONS—CLASSICAL AERODYNAMIC, STOKES1 DIAMETER,
AND AERODYNAMIC IMPACTION (LOVELACE) DIAMETER
a/
Conversion equation—'
Diameter definition Stokes'
(given) diameter (Dg)
Stokes 'diameter 1.0
Classical , — —
aerodynamic C(D \ 1/2
.1 • .... . i. .. fr\ ^ D = DA ., _ "®
diaiueLei (DAe) s Ae PC(DS)
Classical aerodynamic
equivalent diameter (D. )
"" "~1 1/2
DA = D pC(D ) '
Ae s H s'
C(DAe)
1.0
Aerodynamic impaction
(Lovelace diameter (DA>)
DAi = Ds[c(Ds)p]1/2
DAi - DAe[C^Ae)]1/2
Aerodynamic
impaction
(Lovelace)
diameter (
1/2
Js = uAi
C(Ds)p
DAe = DAi P 1
Ae Al |_C(DAe)_
1/2
1.0
* Notation: Dg = Stokes1 diameter, |j,m
DA = Classical aerodynamic equivalent diameter, |J
-------
100.0,
10.0
11)
2
u
i
1
I
o
u
'«
o
0.1
0.1
1.0 10.0
Stokes Diameter (/4m)
100.0
Figure 2. Relationship Between Stokes1 Diameter and Classical
Aerodynamic Diameter for a Spherical Particle,
p= 2.4 g/cm3 (8)
11
-------
10
err
i
S
u
I
E
o
O
o
I
§
r> -5
i
1.0
Stokes Diameter
Figure 3. Relationship Between Stokes' Diameter and Aerodynamic
Impaction Diameter for Spherical Particles, P= 1.0 •
3.0 g/cm3 (13)
12
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Eq. (10) is derived from a truncated McLaurin series approximation to Eqs. (2)
and (3), and is extremely accurate for particles less than about 0.1 /j,m. Eqs.
(9) and (10) have the same functional form so that a direct (approximate) so-
lution of equations in Table 2 can be accomplished using different parameters
for particles less than or greater than 0.5 /jun, Stokes1 diameter.
The preceding discussion has outlined methodology for conversion of al-
ternative particle diameter definitions from reduced data; the next section
will outline methodology and equations for data reduction from impactor test
data according to alternative particle diameter definitions.
13
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CASCADE IMPACTOR PARTICLE SIZE DATA REDUCTIONS
Separation of spherical particles in impactors can be approximated by
the following equation (1) :
L = V0PC(DS)DS2
(ID
where L is the stopping distance (6), meters
VQ is the axial component of particle velocity, m/sec
p, C(D ) , D , 7] as previously defined (Eq. 1).
According to the treatment of Ranz and Wong (17) , the preceding equa-
tion is written in dimensionless form and V0 is taken as the impactor stage
exit velocity.
^=-L_ = V0PC(DS)DS2
V d 18
where d. is the jet diameter, meters.
The impactor sizing equation, as developed by Cashing, et al. (8) , in-
cludes minor modifications of Eq. (12) to permit analysis of multiple jets per
stage, to include different calibration constants for each stage, and to
compensate for pressure losses through the impactor. Rearranging Eq. (12), and
making appropriate substitutions,
rjd...3 P, X.;1/2
D = k. k -l-i i—i.
s d ipC(Ds)PoQ
where k* is a dimensional constant
k is the calibration constant for the ith stage (dimensionless)
i
14
-------
X. is the number of jets at stage i
PQ is the pressure at the impactor orifice, kPa
P^ is the pressure at the exit of stage i, kPa
Q is the volumetric flow rate at the impactor orifice, nvVsec
7], di9 p, C(D ) as previously defined (Eqs. (1) and (12).
In order to determine the particle size distribution from impactor data,
the usual assumption made is that each stage can be characterized by a "cut-
off diameter"—the diameter at which particle collection efficiency for the
stage is 50%. It is further assumed that collection efficiency is zero for
particles having diameters less than the cut-off diameter. Thus, the fun-
damental impactor performance variable for a given test is the cut-off di-
ameter, also called the "cut-point." Either the Stokes1, classical aero-
dynamic equivalent, or aerodynamic impaction (Lovelace) diameter definitions
may be used (as well as other definitions (1)). Further details regarding
impactor size reduction techniques are available in Reference 8. Equations
relating the cut-off diameter to test data are presented in Table 3 for
alternative size definitions.
From Table 3, use of either the Stokes1 definition or the classical
aerodynamic equivalent diameter definition would require approximate or
iterative solutions for each stage cut-off diameter. According to the aero-
dynamic impaction (Lovelace) diameter convention, the slip correction fac-
tor is not used in calculating the cut-off diameters.
15
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TABLE 3. EQUATIONS USED FOR CALCULATING IMPACTOR CUT-OFF DIAMETER
(D5o> FOR ALTERNATIVE DIAMETER DEFINITIONS
Diameter convention
Stokes' (D-)
Classical aerodynamic
equivalent (D. )
Aerodynamic impaction
(Lovelace) diameter
Cut-off diameter (050)—'
1/2
kdki
kdki
PP0C(DS)Q
r*. P.x .
poCCDAe)Q_
1/2
1/2
a/ Notation: Den = cut-off diameter, urn
™"™ J VJ
kj = dimensional constant
r
= 10 ~T~" for dimensions specified below
kj = impactor calibration constant for ith stage, dimension-
less
TJ = gas viscosity, kg/m-sec
d^ = impactor jet diameter, cm
Pi = pressure at stage jet exit, kPa
P0 = pressure at orifice, kPa
Xi = number of jets per stage
Q = volumetric flow at orifice, m /sec
C(DS), C(D^e) = slip correction factors (dimensionless)
i = stage index (dimensionless)
b_/ According to the aerodynamic impaction diameter definition,
dimensionally (^m) (g/cm3 )1 ' (15).
is
16
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REFERENCES
1. Raabe, 0. G. Aerosol Aerodynamic Size Conventions for Inertial Sampler
Calibrations. JAPCA, 26(9):856, 1976.
2. Schrag, M. P., and A. K. Rao. Fine Particle Information System: Summary
Report (Summer 1976). U.S. Environmental Protection Agency, EPA-
600/2-76-174, Research Triangle Park, NC, June 1976.
3. Schrag, M. P., A. K. Rao, G. S. McMahon, and G. L. Johnson. Fine Par-
ticle Emissions Information System Reference Manual. U.S. Environ-
mental Protection Agency, EPA-600/2-76-173, Research Triangle Park,
NC, June 1976.
4. Schrag, M. P., A. K. Rao, G. S. McMahon, and G. L. Johnson. Fine Par-
ticle Information System User Guide. U.S. Environmental Protection
Agency, EPA-600/2-76-172, Research Triangle Park, NC, June 1976.
5. Raabe, 0. G. Generation and Characterization of Aerosols. In: Fine
Particle Technology, B. Y. H. Liu, ed. Academic Press, New York, 1976.
pp. 123-172.
6. Fuchs, N. A. The Mechanics of Aerosols. MacMillan, New York, 1964.
pp. 21-49.
7. Reif, E. A. Aerosols: Physical Properties, Instrumentation and Tech-
niques. In: Aviation Medicine Selected Reviews, C. S. White, W. R.
Lovelace II, and 0. G. Hirsch, eds., Pergamon Press, New York, 1958.
pp. 168-244.
8. Gushing, K. M., G. E. Lacy, J. D. McCain, and W. B. Smith. Particu-
late Sizing Techniques for Control Device Evaluation and Cascade Im-
Pactor Calibration. U.S. Environmental Protection Agency, Final
Report of'EPA Contract No. 68-02-0273 (to be published).
9. Hirshfelder, J. 0., C. F. Curtiss, and R. B. Bird. Molecular Theory of
Gases and Liquids. Wiley, New York, 1954.
17
-------
10. Rao, A. K., M. P. Schrag, and L. J. Shannon. Particulate Removal from
Gas Streams at High Temperature/High Pressure. U.S. Environmental
Protection Agency, EPA-600/2-75-020, Research Triangle Park, NC,
August, 1975.
11. Liu, B. Y. H. Particle Technology Laboratory, University of Minnesota,
Private Communication, September 16, 1977.
12. Handbook of Chemistry and Physics, R. C. Weast, ed. 57th edition, CRC
Press, Cleveland, 1976.
13. Gentry, J. W., Department of Chemical Engineering, University of Maryland,
Private Communication, April 19, 1977.
14. Deposition and Retention Models for Internal Dosimetry of the Human
Respiratory Tract. Task Group on Lung Dynamics, Health Physics,
12:173, 1966.
15. Calvert, S., et al. Scrubber Handbook. Ambient Purification Tech-
nology, Inc., July 1972.
16. Mercer, T. T., M. I. Tillery, and H. Y. Chow. Operating Characteristics
of Some Compressed Air Nebulizers. Amer. Indo Hyg. Assoc. J. 29:66,
1968.
17. Ranz, W. E., and J. B. Wong. Impaction of Dust and Smoke on Surface
and Body Collectors. Ann. Occup. Hyg. 6:1, 1963.
18
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TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
;. REPORT NO.
EPA-600/7-77-129
2.
3. RECIPIENT'S ACCESSION \O.
4. TITLE AND SUBTITLE
Particle Size Definitions for Particulate Data Analysis
5. REPORT DATE
November 1977
6. PERFORMING ORGANIZATION CODE
. AUTHOR(S)
8. PERFORMING ORGANIZATION REPORT NO.
J.B. Galeski
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Midwest Research Institute
425 Volker Boulevard
Kansas City, Missouri 64110
10. PROGRAM ELEMENT NO.
EHE624
11. CONTRACT/GRANT NO.
68-02-2609, Assignment 1
12. SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Task Final; 5-9/77
14. SPONSORING AGENCY CODE
EPA/600/13
is.SUPPLEMENTARY NOTES jERL-RTP task officer for this report is Gary L. Johnson, Mail
Drop 63, 919/541-2745.
16. ABSTRACT
The report gives results of a survey to identify all equations required to represent
particle size data according to each of three particle diameter definitions: Stokes,
classical aerodynamic, and aerodynamic impaction (or Lovelace diameter). Although
the particle diameter definitions themselves are relatively simple, inconsistencies
were found among various investigations in the use of particle size definitions,
particularly in nomenclature. It is not always clear from the descriptions of various
authors which definition is intended. The present study presents a consistent set of
definitions and equations for use in interpreting particle size and impactor data
such as that found in EPA's Fine Particle Emissions Information System (FPEIS)
data base. The equations may also be useful to readers of fine particle sampling
reports who may wish to convert the data from one definition to a more convenient one.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
Air Pollution
Dust
Analyzing
Particle Size
Definitions
Aerodynamics
Impact
Impactors
Stokes Law (Fluid
Mechanics)
b. IDENTIFIERS/OPEN ENDED TERMS
Air Pollution Control
Stationary Sources
Particulate
Lovelace Diameter
Classical Aerodynamics
c. COSATI Field/Group
13B
11G
14B
05B
20D
18. DISTRIBUTION STATEMENT
Unlimited
19. SECURITY CLASS (ThisReport)
Unclassified
21. NO. OF HAUL
22
20. SECURITY CLASS (flu's page/
22. PRICE
Unclassified
EPA Form 2220-1 (9-73)
19
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