EPA-600/2-77-229
November 1977
Environmental Protection Technology Series
TIME-OF-FLIGHT AEROSOL BEAM SPECTROMETER
FOR PARTICLE SIZE MEASUREMENTS
Environmental Sciences Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, North Carolina 27711
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RESEARCH REPORTING SERIES
Ftesearch reports of the Office of Research and Development, U.S. Environmental
F'rotection Agency, have been grouped into nine series. These nine broad cate-
gories were established to facilitate further development and application of en-
vironmental technology. Elimination of traditional grouping was consciously
planned to foster technology transfer and a maximum interface in related fields.
The nine series are:
1. Environmental Health Effects Research
2. Environmental Protection Technology
3. Ecological Research
4. Environmental Monitoring
5. Socioeconomic Environmental Studies
6. Scientific and Technical Assessment Reports (STAR)
7. Interagency Energy-Environment Research and Development
8. "Special" Reports
9. Miscellaneous Reports
This report has been assigned to the ENVIRONMENTAL PROTECTION TECH-
NOLOGY series. This series describes research performed to develop and dem-
onstrate instrumentation, equipment, and methodology to repair or prevent en-
vironmental degradation from point and non-point sources of pollution. This work
provides the new or improved technology required for the control and treatment
ol pollution sources to meet environmental quality standards.
Thi<; document is available to the public through the National Technical Informa-
tion Service, Springfield, Virginia 22161.
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EPA-600/2-77-229
November 1977
TIME-OF-FLIGHT AEROSOL BEAM SPECTROMETER
FOR PARTICLE SIZE MEASUREMENTS
by
Barton Dahneke
Radiation Biology and Biophysics
University of Rochester
Rochester, New York 14642
R803065
Project Officer
Charles W. Lewis
Atmospheric Chemistry and Physics Division
Environmental Sciences Research Laboratory
Research Triangle Park, North Carolina 27711
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
OFFICE OF RESEARCH AND DEVELOPMENT
U.S. ENVIRONMENTAL PROTECTION AGENCY
RESEARCH TRIANGLE PARK, NORTH CAROLINA 27711
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DISCLAIMER
This report has been reviewed by the Environmental Sciences Research
Laboratory, U.S. Environmental Protection Agency, and approved for publication.
Approval does not signify that the contents necessarily reflect the views and
policies of the U.S. Environmental Protection Agency, nor does mention of trade
names or commercial products constitute endorsement or recommendation for use.
ii
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ABSTRACT
A time-of-flight aerosol beam spectrometer (TOFABS) is described. The
instrument has been designed and constructed to perform in situ real time
measurements of the aerodynamic size of individual aerosol particles in the
range 0.3 to 10 ym diameter. The measurement method consists of (1) allowing
a sample aerosol to undergo expansion through a nozzle into a vacuum chamber,
such that each particle acquires a terminal velocity depending on its aero-
dynamic size, then (2) measuring the terminal velocity by determining the time
taken for each particle to traverse a laser beam of fixed width. An experi-
mental calibration curve relating time-of-flight and aerodynamic size, based
on the use of polystyrene latex spheres, is shown to be in good agreement with
a theoretical calibration obtained from the gas - particle dynamics equations.
A comprehensive discussion of the properties and uses of aerosol beams is in-
cluded as an appendix.
This report was submitted in fulfillment of Grant No. R803065 by the
"University of Rochester under the sponsorship of the U.S. Environmental
Protection Agency. This report covers the period June 1, 1974 to February 28,
1977, and work was completed as of March 15, 1977.
iii
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CONTENTS
Abstract ill
Figures vi
Acknowledgements vii
1. Introduction 1
2. Conclusions and Recommendations 3
3. System Design 5
Vacuum system and sample inlet 5
Optical system 6
Electronic system 7
4. Calibration 10
Analytical calibration 10
Experimental calibration 12
5. Results 13
Appendix A
Aerosol Beams 35
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FIGURES
Number Page
1 Calculated TOF vs. particle size 14
2 Diagram of the vacuum-optical chamber 15
3 PM7 and logic electronic signals for 2.02 ym particles 16
4 Schematic diagram of the electronics system 17
5 Pre-amplifier (line driver) circuit 18
6 Measured TOF distribution for a polydisperse NaCl aerosol 19
7 Delay and buffer electronics 20
8 Peak detector and TOF pulse generator 21
9 TOT counter and buffer storage 22
10 Size calibration PROM, comparator and address encoder 23
11 Ti;ning diagram 24
12 Size sub-range counters 25
13 Starage address PROM 26
14 Data display control 27
15 Data output circuitry 28
16 Data output control circuitry 29
17 Interfacing chart 30
18 Calculated calibration curves 31
19 Calculated calibration curves 32
20 Comparison of calculated and measured calibration data 33
21 Pulse compressor circuit 34
v i
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ACKNOWLEDGMENTS
The expert electronics assistance of Danny McFee, Joe Allen and Jeff Link
is gratefully acknowledged. Their ability and energy in designing and per-
fecting the electronics circuitry was impressive. Partial support of this
work in the form of equipment, supplies and salary support was provided by
the University of Rochester Biomedical and Environmental Research Project which
is supported by the U.S. Energy Research and Development Administration, and
by a grant from the National Institute of Environmental Health Sciences.
This support is also gratefully acknowledged. The appendix section will
appear in Recent Developments in Aerosol Science, (D. Shaw, Ed.) John Wiley &
Sons, Inc. (in press) and is included by permission of the publisher.
vii
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SECTION 1
INTRODUCTION
In recent years the physical and chemical properties of airborne partic-
ulates has become a subject of keen interest because of the increase in air
pollution and the possible widespread effect on public health. However, the
problem of measuring the size distribution (not to mention the chemical nature)
of airborne particulates has proved quite difficult. 'Despite significant ad-
vances in measurement techniques and instruments obtained by the substantial
efforts in many laboratories, there is presently no single instrument avail-
able that can monitor the size distribution of an aerosol over the full "res-
pirable" size range, i.e., the particle size range between 0.01 and 5 ym diam-
eter.
Aerosol beams seem useful in the measurement of airborne particulates be-
cause the particles are isolated from their suspending gas which allows use of
sensitive detection and measurement techniques, such as mass spectrometry, and
because the terminal velocity obtained by the particles in the vacuum chamber
uniquely infers their "aerodynamic size", as described later in this report.
Because this report focuses on the description of a particular aerosol beam
instrument, we include as an appendix an article reviewing aerosol beams for
the reader with broader interest in this topic.
We proposed as the goal of this research to design and build a time-of-
flight aerosol beam spectrometer (TOFABS) capable of rapid on-line measurement
of the size distribution of atmospheric particles in the size range from ~ 0.5
to 10 ym diameter and to demonstrate the instrument by measuring example size
distributions of the atmospheric aerosol.
The instrument has been built and operated. It can measure particle
sizes in the range from 0.3 to 10 ym diameter. However, atmospheric aerosol
size distributions were not measured because of insufficient time to build one
final electronics item. This lack of time was due, in part, to unexpected
difficulty encountered in the development of the electronics components and
-------
in part to an unfortunate reduction in the project support due to an unantic-
ipated shift of Agency funds causing the project to be terminated six months
early. Evaluation of the instrument was therefore performed with laboratory
aerosols.
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SECTION 2
CONCLUSIONS AND RECOMMENDATIONS
1. The TOFABS technique provides a fast, on-line method for sizing airborne
particulates. When the particle density is known, the sizing is accurate.
For particles of unknown mass density, an inherent uncertainty in par-
ticle size exists which can be substantial. This sizing technique has
the advantage that particles are not removed from the beam but are avail-
able to subsequent measurement of, say, composition.
2. The measurement of particle TOF in a TOFABS would be more simply and
accurately accomplished by detecting the beam particles at two locations
of known separation rather than with a single detector as in the present
design. The advantage of the two detector method lies in the simpler
electronics required. For example, linear (analog) signal processing is
not required as in the present electronics system so that pulse compres-
sion is not needed. With two separated detectors the TOF could be mea-
sured using pure logic components regardless of whether the signal pulse
was amplifier chopped. Almost all of the electronics developed for the
present TOFABS system are directly usable in this type of system. An im-
portant advantage of the present instrument, namely small coincidence
error levels due to the short time required to measure the particle TOF,
can be retained in a dual detector system if two separate detectors are
used to provide start and stop signals to the TOF counters. Parallel
counters would allow counting of more than one particle simultaneously
passing between the detectors. In the event coincidence errors may be
significant due to faster particles overtaking slower ones between the
detectors, the addition of a third detector and suitable gating circuitry
could be used to eliminate coincidence errors altogether. However, this
third detector does not seem necessary unless long flight paths between
detectors are used and concentrated aerosols are being measured.
3. Even when operated in a "two location" mode, as indicated in 2., particle
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sizing in a TOFABS by optical methods cannot be strongly recommended
because
a. the laser light source, PMT and associated equipment are expensive,
b. this equipment is not well suited for field measurements because of
dts power requirements, cooling water requirements, fragility, and
the susceptibility of the optical components to contamination by
dust and other deposits, and
c. the huge variation in optical signal with particle size can present
difficult problems.
4. A novel method of particle detection more suitable for use in a TOFABS,
including use in field models, may be the charging of the aerosol beam
particles in a crossed electron beam with subsequent particle detection
by ele.ctron beam scattering as the charged particle passes through other
election beams. The feasibility of this method is investigated in the
Appendix. The electron beam method presents an added benefit, namely,
the possibility of electrostatically focusing the aerosol beam. This
method is being further investigated in our laboratory.
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SECTION 3
SYSTEM DESIGN
The basic operation of the TOFABS system comprises the expansion of a
sample aerosol through a nozzle into a vacuum chamber. Within the vacuum
chamber the aerosol beam particles pass through a focused laser beam. Each
particle thus generates a scattered light signal seen by a photomultiplier
tube (PMT) which converts the scattered light signal into an electronic sig-
nal. Because the velocity attained by each particle in its acceleration
through the nozzle-free jet expansion of the aerosol depends on the particle
aerodynamic size, the size may be inferred from a measurement of the particle's
time-of-flight (TOP) through the light beam. The intensity of the scattered
light signal is not used to infer particle size, as in optical type sizing
instruments.
Details of the system design and operation are given in the following
sections. As the system incorporates vacuum, optical and electronic components
the description is organized under these headings.
VACUUM SYSTEM AND SAMPLE INLET
The aerosol beam was generated by expansion of the aerosol sample through
a converging nozzle of 0.2 mm throat (exit plane) diameter having the geometry
shown as nozzle 1 of Fig. 1. The aerosol sampling rate was 100 cc/min en-
trained into the central core of a flow of clean, dry air through the nozzle.
The total flow through the nozzle was 342 cc/min. The aerosol sample being
confined to the central core of the expanding jet provided an aerosol beam
having substantially smaller solid angle. Thus, the beam particles passed
through the center of the laser beam giving uniform signals for similar par-
ticles.
The vacuum chamber is shown to scale in the diagram of Fig. 2. Of course
many details are omitted for the sake of clarity, such as the plug of the
bottom hole and the exhaust hole to the vacuum pumps located on the back sur-
face, right hand side, midway between top and bottom. The size scale of the
-------
diagram can be taken from the bottom hole which has a diameter of 2.54 cm.
The syistem was pumped by two Alcatel mechanical pumps type ZM2012 having
a combined pumping capacity of 600 liters/min. These pumps maintained a vac-
uum chamber pressure of 0.7 Torr as measured on a pair of Hastings Vacuum
Gauges, Models VT-4 and VT-6. Two gauges were continuously used to provide
a cross-check and to provide high resolution in complimentary ranges.
OPTICAL SYSTEM
The source of the focused laser beam was a Spectra-Physics Model 164-03
Argon laser tuned to 488.0 nm wavelength. Although the laser was capable of
producing more than 1 Watt of power at this wavelength, it was operated at an
output powe:: of 400 mW.
The laser beam was cleaned by passing it through a spatial filter
(Gaertner Scientific Corporation, Chicago) incorporating a 10X microscope ob-
jective, a 25 ym pinhole and a 20X microscope objective.
The laiser beam was then directed by means of two reflectors, which allowed
adjustment of the laser beam height and direction. The beam next passed
through an Iris diaphragm to stop scattered and reflected light from the lenses
and reflectors, except that which was nearly on axis.
The laser beam entered the vacuum chamber through a planoconvex cylin-
drical lens (Klinger Scientific, #318851) having 100 mm nominal focal length.
This lens served as a window to 'the vacuum chamber and focused the laser beam
in one dimension (the vertical). The plane surface was inclined 45° to the
laser beam to cause internal reflections to be separated from the primary beam
so they could be easily stopped. The intersection length for this lens is
normally 94.5 mm but because the lens was inclined to the light beam axis the
intersection distance was about 77 mm. This intersection distance caused the
laser beam to reach its one-dimensional focus at the aerosol beam axis, as
shown in Fi>. 2. The horizontal width of the laser beam at this point was
approximateLy 2 mm while its vertical thickness was about 100 urn.
Two sets of externally adjustable knife edge stops were located in the
vacuum chainDer between the cylindrical lens and the aerosol beam. These were
used to clean the beam of scattered and reflected noise generated in the cyl-
indrical lens and upbeam elements.
The laser beam light not scattered by aerosol beam particles passed
through a hole 4x5 mm cut into the spherical mirror of Fig. 2 and on into a
6
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light trap consisting of a bundle of needles located at the end of a threaded,
blackened tube of 25 cm length. This light trap was able to absorb the 400 mW
laser beam without detectable heating.
Light scattered by aerosol beam particles in the forward direction between
about 2° and 25° angle with the beam axis was collected by the spherical mirror
of Fig. 2 (Klinger Scientific, #340023) and focused onto the small plane de-
flector mirror also shown in Fig. 2. This latter mirror diverted the scatter-
ed light signals out the side of the vacuum chamber through a pair of biconvex
lenses (Klinger Scientific, #311138) which focused the scattered light signals
onto the cathode of the photomultiplier tube (ITT Model FW-130).
Since the light intensity' distribution was Gaussian across the focused
laser beam, the PMT output signals should be Gaussian in time as each particle
traversed the laser beam at constant velocity, provided the particle size was
small compared to the laser beam thickness. The upper oscilloscope trace of
Fig. 3 shows an example PMT signal which is indeed Gaussian.
To measure particle TOF across the beam, i.e., across a fraction of the
beam of fixed path length, it was necessary to turn on a counting system over
the duration for which the PMT signal exceeded a fixed fraction of the signal
peak. This process of "normalizing" the signal pulses was necessary because
variations in particle size, orientation and index of refraction can cause
changes in the pulse width, but not in the normalized pulse width.
Of course several equivalent electronics schemes can be used to accom-
plish this result. The electronics system we designed is described in the
next section.
ELECTRONIC SYSTEM
The PMT output signal is regarded as the input signal of the electronics
system shown schematically in Fig. 4. Not shown is a preamplifier circuit
(line driver) that boosts the power of the PMT output. This line driver cir-
cuit is shown in Fig. 5.
The basic operation of the electronics system is as follows. After am-
plification the signal reaches a peak detector whose output is divided by a
resistor chain to a constant fraction (namely 1/3) of the peak signal voltage.
This constant voltage level is provided as the reference level of the analog
comparator. The same amplified input signal, delayed 0.5 ysec, is the test
-------
Input of the analog comparator. The analog comparator output is therefore at
the low logic level except for the duration for which the delayed signal
exceeds 1/3 of its maximum amplitudes as shown by the lower trace of Fig. 3.
That is, the analog comparator output gives a high level logic signal for the
duration of the particle TOF across a fixed fraction of the laser beam thick-
ness. The TOF of each particle is therefore measured for the same path length.
The octput of the analog comparator triggers an AND gate, provided the
amplified PMT signal exceeds an adjustable noise level determined by the ref-
erence inpv.t of the lower analog comparator of Fig. 4. Thus, PMT or amplifier
noise is prevented from triggering the AND gate.
When the AND gate is triggered to the high logic level the particle TOF
through the laser beam is digitally counted on the binary counter driven by
the 64 MHz oscillator. Thus, the digital number accumulated in the binary
counter is incremented every 15.6 nsec. The resolution in particle TOF is
therefore better than 15.6 nsec.
When t:he particle passes out of the light beam the analog comparator out-
put drops t:o the low logic level causing the contents of the binary counter to
be transferred to a buffer storage (parallel load shift register), not shown
in Fig. 4. The circuit is then reset and ready to count the TOF of the next
particle while the further electronics continues to process the TOF data for
the last particle.
To determine the size sub-range of the particle from the measured TOF,
the digital TOF number in the buffer storage is compared by means of a binary
comparator to the various numbers (sub-range limits) stored in the size range
ROM. When the correct size sub-range is obtained, a single count is added to
the size range counter corresponding to that sub range.
The s:lze range counters are continually scanned and their contents dis-
played on an oscilloscope. Their contents can also be printed out with a
Teletype printer. An example oscilloscope display obtained from a poly-
disperse NaCl aerosol is shown in Fig. 6.
Complete details of the electronics system are shown in Figs. 7-17 on
which all components of the system are identified. The operation of the elec-
tronics is illustrated by the timing diagram of Fig. 11, where signals cor-
responding to the identified points throughout the circuitry are shown.
The e::fort we expended in the development of this electronics system
8
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was substantial. It comprised by far the majority of our effort.
In the meantime microprocessor systems have become commercially available
which can perform many of the functions of our electronics system. However,
the microprocessor systems of which we are aware are all far too slow to be
used in our system as presently constituted.
-------
SECTION 4
CALIBRATION
The calibration curve relating particle size and TOF is needed to obtain
the partic.'.e size distribution from the measured TOF data or to program the
size range ROM to give TOFABS output as the particle size distribution directly.
This curve was obtained in two ways, analytically and experimentally, described
in the following sections.
ANALYTICAL CALIBRATION
The motion of- a particle or droplet whose mass m may be changing due to
condensation or evaporation is described by the equation of motion
dv dm
and the energy equation
d(m c T) dm
where v is the particle velocity, v- the local velocity of the surrounding
fluid (calculated by ignoring the presence of the particle), t the time, f the
particle's friction coefficient, c the specific heat of the particle material,
T the particle temperature (assumed uniform), X the latent heat of condensation
or evaporation, and q the rate at which heat is being transmitted from the
particle to the fluid.
The particle's friction coefficient is
f = 6-rrya K/C [3]
s
where y i£i the fluid viscosity, a the particle radius, K the dynamic shape
factor and C the slip correction factor
S
C = 1 + Kn[1.234 + 0.414 exp(-0. 876/Kn) ] , [4]
S
Kn being l:he Knudsen number H/a where £ is the mean-free-path of the fluid
10
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molecules. For non-spherical particles the value of a must be adjusted in
this latter expression to give the proper correction C . For spherical par-
s
tides the factor K is approximated within a few percent by
K = 1 + 0.1062 Re0'8561, Re = 2a|vf - v | /V [5]
where v is the kinematic fluid viscosity. For non-spherical particles an ad-
ditional shape factor must be included in K.
The solution of [1] is
-/ta(t)dt f /Tada
vp(t) = e ° [vfQ + j ea~° a(T)vf (T)dT] [6]
o
where vf is the fluid (and particle) velocity at the nozzle entrance x = 0
and t = 0 and where
dm
a- (f + ^£)/mpV [7]
The particle location at time t is given by
x(t) = S\ dt. [8]
The following procedure is used to calculate the velocity of a particle
as it accelerates through a nozzle system into a vacuum chamber. First, the
steady state fluid velocity field vf (x) is calculated for the given nozzle
system. Second, for a specific particle size, shape and mass, [6] and [8] are
solved to obtain v vs. x. In practice, to prevent underflow and overflow
errors from occurring in the computer calculations, [6] and [8] are solved in
an iterative scheme, viz. ,
t+At t+At
-/adt r f /adt
vp(t+At) = e C |vp(t) + J ec a(t) vf (t) dt [9]
t+At
x(t+At) = x(t) + v dt [10]
t
11
-------
Furthermore, if At is sufficiently small so that a(t) does not change signif-
icantly over the interval between t and t+At, then
v (t+At) - vp(t) = [vf(t) - vp(t)](l - e"a(t)At). [11]
With sufficiently small At, [10] and [11] can be used with [2] to obtain the
v vs. x curve for a particle without incurring underflow - overflow problems.
Example results showing particle time-of-flight are shown in Fig. 1.
Further calculated results showing the influence of nozzle diameter and of
particle density are shown in Figs. 18 and 19.
EXPERIMENTS CALIBRATION
To ob'rain an experimental calibration curve, monodisperse latex aerosols
were generated and the PMT signals like that of the upper trace of Fig. 3 were
measured. For each particle size the width (TOF) of the Gaussian pulse at
1/3 the maximum pulse amplitude was measured. These measured data are shown
in Fig. 20.
The two measured values at 0.81 ym diameter were obtained for two batches
of Dow latex spheres, both identified as 0.81 ym nominal diameter. Our mea-
surements suggest that one batch had particle diameters slightly higher and
ithe other batch slightly lower than 0.81 ym.
\ Since the exact thickness of the laser beam was not known, the analytical
a\id experimental calibration curves could not be directly compared. However,
they were combined by assuming a light beam thickness of 72 ym, which gave the
\
best; agreement of the two curves. This value of the light beam thickness,
between paints where the intensity is 1/3 the maximum (axial) value, agrees
well with the estimated laser beam thickness of 100 ym between points where
2
the intensity is 1/e or 13.5% of the axial value. The curve shown in Fig. 20
is the analytical calibration curve for an assumed laser beam thickness
(flight path) of 72 ym. The good agreement of the calculated and measured
data suggests the validity of the calibration curve.
12
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SECTION 5
RESULTS
The TOFABS described in the preceding sections was used to measure var-
ious laboratory aerosols and the ambient atmospheric aerosol in the laboratory.
Some experience in its use was thereby obtained.
The TOFABS was found to work well in the measurement of monodisperse and
nearly monodisperse aerosols. To make these measurements the high voltage to
the PMT was adjusted so that the amplified PMT output signals lay in the range
between 0.1 and 10 volts. The lower limit corresponded approximately to the
noise level while signals above the upper limit were "chopped" by the input
amplifiers.
It was therefore not possible to measure the size distribution of moder-
ately or highly polydisperse aerosols unless various PMT voltages were used in
a sequence of measurements. The strong dependence of pulse height on particle
diameter allowed only a relatively narrow size sub-range to be measured at one
PMT voltage level.
We intended to solve this problem by the addition of a final electronics
element to the system, namely, a "pulse compressor" that would compress pulses
of a large range of amplitudes to pulses having a small variation in amplitude.
Pulse compression would not affect the particle TOF measurement provided com-
pression was obtained by linear amplification or attenuation of the pulse,
since the pulse was effectively normalized by the electronics system anyway.
A possible design of the pulse compressor is shown schematically in Fig.
21. Unfortunately, the Agency supporting this project experienced an unex-
pected shift of funds and had to discontinue support of this project before
this pulse compressor could be built. Measured data for highly polydisperse
aerosols including atmospheric aerosols were therefore not obtained.
13
-------
o
Lul
(/)
=*,
LL
O
h-
1.0
NOZZLE-I 2
DIMENSIONS IN MM
0.1
O.I
Dr
1.0
10.
Figure 1. Calculated particle TOF across a flight path of
100 ym beginning 2 mm from the nozzle exit vs.
particle diameter for beams of unit density
spheres. The aerosol beam was assumed generated
by expansion of an air aerosol at NTP through the
three nozzles specified.
14
-------
Figure 2. Diagram of the vacuum-optical chamber. The vertical
aerosol beam intercepts the horizontal laser beam at
its focus causing light to be scattered into the
spherical mirror.
15
-------
Figure 3. Upper trace: superimposed PMT signals generated by the
scattered light signals of 2.02 ym diameter latex spheres
traversing the focused laser beam. The horizontal scale
is 0.2 ysec per cm.
Lower trace: superimposed logic pulses of fixed amplitude
and width equal to the TOF of the 2.02 ym particles
"through" the laser beam. The logic pulse time scale is
delayed 0.5 ysec relative to the PMT signal.
16
-------
INPUT SIC
FtOM PMI
OISPIAY 01
fc-
PRINIOUT
Figure 4. Schematic diagram of the electronics system.
17
-------
-t-Sl/oltiO
FROM
P.M.T
PRE-AMP
OUTPUT
Figure 5. Pre-amplifier (line driver) circuit.
18
-------
Figure 6. Example display of a measured TOF distribution for a
polydisperse NaCl aerosol. The vertical axis represents
the number of particles (counts) per TOF sub-range while
the horizontal axis represents particle TOF. The maximum
corresponds to an aerodynamic diameter of 0.9 urn, that is,
a unit density sphere of this diameter will have the
same TOF.
L9
-------
DELAY LINE
&PIKOEL
TOJOO %7i*
.OV7 'oo f
JAWMT ^fe?I'
lOfl
J/
-------
2I-010J ?I-030D
ALL RESISTORS IN OHMS UNLESS UOTfO
ALL CAPACITD43 IN 4? CBRM. DISC UNLESS NOT ID
ALL if PIN i.e. , f Ve PIN 14 , GROUND PlM 7
A,tL SEJt7K,t\/cPIN »Oy+Vee P'H ^( -\/(» PIN 3
COMPONENT 3IOL OP P.C. OOAUD CROUND
NOTES:
(?) CAPACITOK IN p-f
@ POLVSTY RI M B
(j) TANTALUM
@) MONOL1
CARD E
PEA** OETCCTOR AND
TiMS Of PLIftMT PUttt (T.F.P.)
TCFFKEy G. LINK
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REV. A
Figure 8. Peak detector and TOF pulse generator. Output pulse D Is a
logic pulse of width equal to the particle TOF through the
laser beam.
-------
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All UESJITOftS ]N O.HMS V*rf V
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-------
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SHE HAWGt PROM, MAGNITUDE
COMPARATOR , AND IWUT
OKi ENCODER
JTIAU P177
TtFFKtf 6. LIMH
REV. F
Figure 10. Size range calibration PROM, magnitude comparator and storage input address encoder.
The PROM is coded through its various memory levels by clock #2 Q-6 MHz) and binary
counter A12 and A17. When the contents of a PROM memory level Cupper limit of a size
sub-range) equals or exceeds the particle TOF in the buffer storage, the magnitude
comparator output Q changes from high to low logic level, stopping the clock signal
and causing a single count to be added to the contents of the proper binary counter
(size sub-range channel).
-------
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Figur(i 11. Timing diagram showing the sequence of pulses at
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Cards 1-4.
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Figure 12. Size sub-range counters. Each card contains four 8-bit
counters or two 16-bit counters. Each size sub-range
channel can store either 0-255 counts or 0-65,535 counts.
The capacity of each size sub-range channel can be
selected as 8 or 16 binary bits. The storage capacity
is thirty one 8-bit channels, minus one channel for
each channel expanded to 16-bit capacity.
25
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Figure 13. Address PROM for identifying the output address of
the various size range channels. Since the output
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independent, a separate output address PROM is
used for data display and printout.
26
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27
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Figure 17. Interfacing chart for Cards 1-9. Connectors A and
B (22 pins each) represent external connections to
and outputs from the mother board which serves to
interface Cards 1-9. Thus, all connections except
those of A and B are internal within the mother board
and Cards 1-9 which plug into terminals on the
mother board.
30
-------
NOZZLE DIAMETER =0.1 mm
I I I I I I I I I
1 III
Figure 18. Calculated calibration curves for nozzle 2 of Fig. 1
with three nozzle diameters. Particle TOF was calculated
for a flight path of 100 ym beginning 2 mm from the
nozzle exit. An aerosol at NTP containing unit density
spheres was assumed expanded through the nozzle to
generate the beam.
31
-------
I I I I I I I
1.0
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= 2.0gm/cc
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I I I I I I I
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Figure 19. Calculated calibration curves for nozzle 2 of Fig. 1
for assumed expansion of air aerosols at NTP containing
spheres of three mass densities. The aerodynamic
diameter as it is usually defined is proportional to
mass density to the 1/2 power. The mass density
dependence calculated here is slightly stronger.
Particle TOF was calculated for a flight path of 100 ym
beginning 2 mm from the nozzle exit plane.
32
-------
1.0
I I TT
I I I I
-------
FRom p.m.T
O (XI PUT
t 4- t
REFERENCE VOU/IOE
PARflLLES
SWITCHES
SI ECT
Figure 21. Example pulse compressor circuit. The PMT current pulse,
delayed 0.5 ysec or longer, is attenuated by variable
amounts to maintain the amplifier input signal within a
limited range. This prevents amplifier chopping of large
amplitude pulses. The various resistor values are selected
to provide (a) the desired attenuation levels and (b) the
proper output impedance for the delay line. This pulse
compressor would also be useful in other systems such as in
measuring scattered light signals from aerosol particles.
Logic signals from the various analog comparators give the
order of magnitude of the signal while the compressed pulse
can easily be measured without amplifier distortion to give
the pulse magnitude within the order of magnitude range
(sequential coarse scale, fine scale measurement).
34
-------
APPENDIX A
Reprint of a Technical Article
Entitled "Aerosol Beams".
35
-------
AEROSOL BEAMS
Barton Dahneke
Radiation Biology and Biophysics
University of Rochester
Rochester, New York 14642
ABSTRACT
Because of their ability to focus large numbers of airborne particulates
into a narrow beam in which the particles are isolated in a vacuum environ-
ment, aerosol beams are useful for a variety of applications in the detection
and measurement of airborne particulates, in measuring particle-surface inter-
actions and in measuring the aerodynamic and other properties of particles.
Properties and applications of aerosol beams are described and critically dis-
cussed with particular interest in the use of aerosol beam techniques and de-
vices for measuring the size distribution and other properties of airborne
particulates!. One aerosol beam device for measuring the particle size dis-
tribution in described in detail.
To appear in Proceedings of the Symposium on Aerosol Science and
Technology, John Wiley & Sons, New York (in press).
36
-------
1. Introduction
An aerosol beam is generated when an aerosol expands through an orifice,
capillary or nozzle into an evacuated chamber. The gaseous portion of the
aerosol jet so formed is scattered by collisions with background gas molecules
and removed by pumping. The particles or droplets in the aerosol, because of
their relatively large momentum, are not scattered by the background gas but
form a high speed beam of the aerosol particles. The aerosol particles are
thus isolated from their suspending gas, except for the background gas in the
vacuum chamber, the density of which can be made very low by passing the beam
through multiple pumping chambers. The particles can therefore be detected,
counted, measured and collected with minimal interference from a suspending
gas. These features of aerosol beams make them uniquely attractive for cer-
tain measurement techniques.
Although aerosol beams have features in common with molecular beams,
these two types of beams also possess substantial differences. One example is
the pumping speed required in the two systems. Molecular beams are signif-
icantly dissipated over path lengths of the order of several mean-free-paths
of the background gas, due to collisions with these gas molecules. Molecular
beam systems are therefore generally operated under high vacuum requiring beam
skimming and several pumping chambers with relatively large vacuum pumps.
Aerosol beams, because of the large momentum of the beam particles, are not
rapidly dissipated in chambers of relatively high pressure. Some aerosol beam
systems operated at background chamber pressures between 0.1 and 1 Torr have
useful beam lengths of several cm. Such aerosol beam systems require vacuum
pumps of modest size so that portable systems are possible.
To determine whether an aerosol beam technique is suitable for a partic-
ular application, the various properties of aerosol beam systems must be under-
stood, preferably by means of accurate theories and specific experimental data
or, when these are not available, by use of qualitative results and approx-
imate information. The properties and certain applications of aerosol beams
have been investigated in various laboratories. The results of these inves-
tigations are summarized and critically discussed in the next section. Later
sections deal with the fundamental properties of aerosol beams, in particular
with the calculation of particle velocities obtained in a beam considering the
influence of nozzle shape and size, and with various applications of aerosol
37
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beams.
2. Summary of the Properties of Aerosol Beams
2.1 Particle velocities in an aerosol beam.
Particles and droplets in an aerosol beam obtain maximum velocities
in the vacuum chamber of the order of the sonic velocity of the suspending gas
(1-4). Thus, particles suspended in air obtain velocities of the order of 300
m/sec while particles in helium obtain velocities of the order of 600 m/sec.
The maximum particle velocity depends substantially on the particle size, mass
and shape. Particles of larger size (mass) obtain lower velocities. Because
of the importance of the velocity characteristics of aerosol beams, this sub-
ject will bs treated in a separate section.
Limited evidence (1) suggests variation in orientation of non-spherical
particles does not cause significant variation in maximum velocity. Identical
particles neutrally buoyant with respect to orientation seem to obtain a
unique maximum velocity due to time averaging of the influence of orientation
during the acceleration process. (This topic, however, needs further inves-
tigation.) Identical particles having a preferred orientation in the accel-
erating jet obtain a unique terminal velocity corresponding to that preferred
orientation,
2.2 Cross-section of an aerosol beam.
The cross-section of an aerosol beam always grows with downbeam dis-
placement in the vacuum chamber. The beam divergence is, of course, caused by
radial expansion of the aerosol jet as it enters the vacuum chamber. Since
smaller (lesss massive) particles follow the gas motion more readily than larger
ones, the solid angle of an aerosol beam increases substantially as the size
(mass) of the beam particles decreases. Effective techniques for reducing the
beam solid angle have been demonstrated. One method (5) accelerates the par-
ticles in a converging nozzle so that the particles at larger radial positions
obtain larger inward radial velocity components. Upon outward radial expan-
sion of the aerosol in the vacuum chamber, the inward radial velocity com-
ponents compensate the outward components to cause a substantial decrease in
the beam so],id angle, A second method (6) restricts the sample particles to
the central core of the gas jet and thus reduces beam solid angle by reducing
the radial £;as velocities seen by the particles in the expanding jet.
Collims.tion has been used to give extremely narrow beams. Disadvantages
38
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of this method include biasing of the size distribution in the beam sample and
plugging of the collimating hole if the aerosol sample contains a liquid
fraction. Los Angeles smog plugs collimating holes rather quickly. A collim-
ating hole in a heated plate would reduce the problem of plugging.
Because of the relationship of beam cross-section and velocity, the cross-
section of uncollimated aerosol beams will be discussed with beam velocity in
a separate section.
It seems possible to focus beams in one dimension by means of a gas cross-
jet intersecting the aerosol beam in the vacuum chamber. Deflection of beams
by asymmetric jet expansion has been demonstrated (6,7). In the similar case
of a cross-jet, particles nearer to the jet source obtain larger deflections
because the jet gas is more dense and better able to influence the particle
motion. An aerosol beam thus deflected should obtain a relatively narrow
focus. The "spot size" and focal length will depend on particle size. Two
cross-jets could provide two-dimensional focusing. Such a focusing process
has been independently proposed for molecular beams by Gspann and Vollman (8)
and for aerosol beams by the present author. However, the technique has not
yet been demonstrated for aerosols either experimentally or theoretically.
2.3 Size separation of particles in an aerosol beam.
Two techniques have been demonstrated for size separation of par-
ticles and droplets in an aerosol beam. In one (6), the aerosol beam is de-
flected by means of a cross-jet or by asymmetrical expansion of the aerosol
jet into the vacuum chamber. Since smaller particles are more readily deflec-
ted, the particle trajectory is diverted increasingly as particle size is de-
creased. Upon passing through the cross-jet or asymmetric expansion region
the various particle trajectories, corresponding to different particle sizes,
are linear. This technique has been patented (7).
In a second method (1,4,9), particle size is discriminated by measuring
particle velocity in the vacuum chamber. Since terminal particle velocity in
the vacuum chamber depends on particle aerodynamic size (which will be defined
in the next section), with smaller particles obtaining higher velocities, the
velocity measurement or, equivalently, the measured time of flight (TOP) re-
quired for the particle to traverse a fixed path length infers the particle's
size. This method of measuring particle size is also patented (7).
A technique commonly used in molecular beams can, of course, be used to
39
-------
separate particles of selected velocity range, i.e., of selected size range.
Velocity selectors used in molecular beam systems provide velocity resolutions
AV/2V between 5 and 25% and maximum transmission probabilities between 27 and
49% (10-29). These selectors pass some molecules at every velocity between
V - AV/2 and V + AV/2 with maximum transmission at V and zero transmission at
the two ext7-emes. Use of such a velocity selector with an aerosol beam should
provide a velocity selected beam containing up to 49% of the total particles
in the beam having terminal velocity V and lesser amounts at V ± 6V, where
0 < 6V < AV/2. Young (30,31) describes analytical inversion methods which
account for this variable transmission as well as other non-idealities of vel-
ocity selectors so that the velocity distribution of the beam can be accurately
obtained from intensity data for velocity selected beams. Thus, intensity
data for velocity selected aerosol beams can provide the velocity distribution
function of the beam particles, which infers their aerodynamic size distri-
bution. Since the particle number and mass distributions are frequently of
"intermediate" interest for calculating other distributions, velocity selected
beams have t:he advantage of allowing direct measurement of, say, the abundance
of a certain toxic chemical present in a selected aerodynamic size range of an
aerosol sample. Although all elements of the velocity selector technique have
been demonstrated in molecular beam research, they have not yet been success-
fully applied to an aerosol beam system.
Israel and Whang (32) captured aerosol beam samples on grease coated
slides to determine the deposit density distribution over the radial dimension.
They proposed using such data with experimental and analytical calibration
curves to ottain the size distribution of the beam particles from deposits on
a coated target. Because the deposit is cumulative rather than size sorted
as in (6), the analysis requires substantial microscopic counting.
The possibility of charging the beam particles and separating them in an
electrostatic or magnetic field is suggested by simple analogy with mass spec-
trometry. Eowever, unlike deflection of ions in mass spectrometry where one
or two charg;es is adequate and unit charge differences are easily distinguished,
aerosol beam particles require many charges to obtain adequate deflections and
techniques i'or obtaining uniform charges of this level have not yet been dem-
onstrated. The topic of charging of aerosol beam particles will be discussed
in a separate sub-section below.
40
-------
2.4 Detection and measurement of aerosol beam particles.
The most important current problem in aerosol beam technology is the
development of adequate techniques for detecting and measuring particles in the
beam smaller than ~0.1 ym. Detection and measurement techniques for particles
~0.1 ym and larger, such as light scattering techniques, have been demonstrated
(33), some of which can also be used in aerosol beam systems. Because aerosol
beam particles are isolated from their suspending gas, which frequently causes
the lower detection limit in light scattering techniques, it should be possible
to extend the detection and measurement limit to smaller particle sizes in an
aerosol beam instrument.
Note that in order to measure the aerodynamic size of a beam particle it is
sufficient in two techniques described above to simply detect the particle as it
either passes a location corresponding to a deflected trajectory or as it passes
two points of known separation. The problem of measuring particle aerodynamic
size thus reduces to the simpler problem of detecting the presence of the particle.
One method of detecting particles in an aerosol beam has been the use of
focused laser beams through which the aerosol beam is directed (1-4). The light
scattered by a particle passing through the beam is directed to a photomulti-
plier tube (PMT) which provides a current pulse in response to the scattered
light signal. One instrument (4) using this method can measure particles of
0.3 ym diameter and larger. With simple changes, their capability can be
extended to ~0.1 ym, but this limit is still inadequate. Moreover, the laser
system and associated electronics are large and expensive.
An alternative technique has been proposed by Schwartz and Andres (9),
wherein beam particles pass through a velocity selector before they are accum-
ulated on a peizo-electric crystal surface where their mass is measured by ob-
serving the change in the frequency of oscillation of the crystal. However,
this method may not be practical because unless the crystal surface is coated
to prevent particle bouncing, the particles are not retained on the crystal
surface. On the other hand, if the crystal is coated with, say, a layer of
grease sufficiently thick to capture particles, the mass loading may already
be so high that the crystal operates in the non-linear range so that frequency
changes cannot be used to monitor adsorbed mass changes.
Hollander and Schb'rmann (34) demonstrated a novel technique wherein aero-
sol beam particles were impacted on a thin plastic membrane which had been
41
-------
reflective aoated and was one of the mirrors in an interferometer. By obser-
vation of tie interference patterns (momentum changes) and independent measur-
ment of particle velocities they could measure particle mass directly, to a
-12
lower limit of 10 gm (1.3 y particle diameter for a unit density sphere).
The system was large, complex and expensive and only suited for laboratory
measurements.
The interferometer technique just described recalls an earlier technique
of Avy and .ienarie (35) described in one of the first papers on aerosol beams.
In their instrument Avy and Benarie directed an aerosol beam towards a sensi-
tive microphone. The instrument was able to detect particles above 30 ym
diameter. A refined instrument was described by Benarie and Quetier (36).
With it the authors could monitor the mass loadings of particles between 1 and
20 ym diameter.
Hepburn, et_ aL., (37,38) detected beams of highly charged glycerol drop-
lets by impacting them onto a phosphor screen or liquid crystal target. The
resulting luminescence of the phosphor screen revealed the beam geometry and
density distribution. Although this method removes the particles from the
beam when they strike the screen, this detection technique may be useful with
aerodynamic deflection in measuring the size distribution of the beam particles.
A technique for measuring the quantity of any of various atomic and mol-
ecular spec:Les present in individual beam particles or in accumulated samples
has been described by Myers and Fite (39) and by Davis (40). The technique
comprises inpaction of the beam particles onto a heated filament, usually
rhenium at about 1200°C, where the particles apparently stick and evaporate.
The evaporating atoms or molecules having sufficiently low ionization poten-
tial are ionized by the rhenium filament, because of its high work function.
The ions thus generated are focused into a quadrupole mass filter or magnetic
analyzer whereby the quantity of ions of a selected charge to mass ratio can
be monitored. Some of the compounds which Davis was able to observe using
this technique are listed in Table 1.
Because; of the difficulty in detecting small particles in aerosol beam
systems, it is sometimes desirable to grow the particles to a larger size by
condensation of a supersaturated vapor. The larger particles can be easily
detected by, say, scattered light signals. Although the initial size distri-
bution of the particles is not determined, this type of absolutely calibrated
42
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condensation nuclei counter (CNC) can detect each particle present which is
larger than the critical cutoff diameter (~20 A") and wettable by the conden-
sing vapor. (The importance of the latter condition seems to be poorly under-
stood.) Use of this CNC with additional devices that discriminate particle
size, such as an impactor, filter or diffusion battery, would allow inference
of the original size distribution of the aerosol sample. Further details of
this proposed system are discussed in (4).
2.5 Particle bouncing and sample collection.
Both experiments (41,42,43) and theory (44) have demonstrated that
micron size solid particles striking solid surfaces will bounce when the normal
component of their incident velocity exceeds ~1 m/sec. Viscous droplets are
captured on target surfaces placed in high velocity aerosol beams; however,
they burst upon impact so that parts may be lost from the target surface.
Solid particles are captured when the target surface is coated with a viscous
layer to dissipate the kinetic energy of the incident particle.
These results indicate that samples of aerosol beam particles should be
collected on grease coated targets or in special collectors within which the
particles will rebound many times without escaping. An exception appears to
be sampling on a heated filament. Evidently the particle tip is melted on
contact so that it provides its own viscous layer.
The grease coating on a collector surface must be supplemented or re-
placed periodically to prevent a solid overcoating on the grease surface.
This can readily occur in highly focused aerosol beams of solid particles.
Because solid particles moving at typical beam velocities may bounce on
uncoated solid surfaces many times before being captured, particles reflected
from, say, a velocity selector will reflect throughout the vacuum chamber.
Care must be taken to prevent "background particles" from reaching the detec-
tion system.
2.6 Alteration of particles in an aerosol beam.
Possible mechanisms by which sample particles may be altered in an
aerosol beam include evaporation, condensation, cooling in the adiabatically
expanding jet, freezing, breaking of frozen particles, breaking of droplets
and aggregates during acceleration and charging of particles in the acceler-
ating flow. The importance of the last four mechanisms in aerosol beam sys-
tems is not well understood. These topics need investigation. The first
43
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three, on the other hand, have been investigated.
In the course of measuring the free molecule drag on latex beam particles
passing through a deceleration chamber containing dilute air at controlled
pressure, one group of investigators (2,3) found the spheres had different
drag coefficients when the beam was accelerated in an air jet (air aerosol) or
in a helium jet (helium aerosol). The data and the associated analysis of
these authors suggest the difference is due to cooling of the latex spheres in
the adiabati.cally expanding jets, with substantially more cooling occurring in
the air jet. The authors estimated 2.02 ym latex spheres were cooled some
30°C in the air jet expansion but only a few degrees in the helium jet. The
difference seems to be due to condensation of gas molecules in the air jet
which draw their latent heat of evaporation from the warmer particles thus
causing significant cooling of the particles in the air jet. In the helium
jet no condensation was expected at the given expansion ratio so that these
particles were apparently not cooled by cluster evaporation.
The authors (2) went on to estimate the evaporation loss of a 1 ym water
droplet in an aerosol beam taking into consideration the cooling of the drop-
let in the air jet expansion process and the cooling of the droplet by evap-
oration. They estimated that the droplet diameter would decrease by less than
3% over intervals of ~1 msec, i.e., sufficient time for a particle flight of
40 cm in the vacuum chamber. Thus, evaporation of droplets does not appear
to cause substantial alteration of aerosol beam particles.
Another investigation (4) has shown that condensation in the jet does not
significantly alter beam particle size, even for high inlet vapor pressures,
because the rapidly accelerating particles spend too little time in the super-
saturated region of the jet to realize significant growth. This topic will be
discussed further in the next section.
In the case where a thin surface layer of liquid or adsorbed vapor is of
interest, then evaporation and condensation can have substantial effect in
altering par1:icles in the beam.
2.7 Electric charging of aerosol beam particles.
Because of its relation to the detection and measurement of particles
in an aerosol beam, this topic is of substantial interest. Unfortunately, its
importance has not been fully appreciated and relatively little work has been
done.
44
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Aerosol beams of charged particles can be obtained in several ways.
First, the particles can be generated in a manner that causes them to have a
high charge level (45) or the aerosol can simply be passed through a suitable
charging device (46) before it enters the aerosol beam system. Second, the
particles or droplets may be charged by breaking up in the air stream during
their acceleration in the jet, as mentioned earlier. Although this topic has
been investigated over many years in connection with meteorological studies
(47) (the generation of charge in thunderclouds) it is not yet well understood.
A third way of obtaining a beam of charged particles is by charging the
particles by means of a crossed electron beam in the vacuum chamber. This
technique takes advantage of the vacuum environment of the beam particles, as
the electron beam would be dissipated too quickly except at sufficiently low
gas density. Hall and Beeman (48) have demonstrated the charging of polysty-
rene latex beam particles in a sheet electron beam of 4 to 10 mA current with
electron energies of the order of 100 eV. The beam particles required between
5 and 10 ysec to traverse the electron beam during which time they experienced
an (overestimated) surface temperature increase of 17°C. Latex particles of
0.357 ym diameter obtained a calculated charge of 620 electronic charges while
0.557 ym particles obtained 965 charges.
A similar process, namely the charging of clusters in molecular beams,
has been discussed by Hagena (49). Bolder (50) reviews several techniques and
results of molecular beam investigations of ionization processes and inter-
actions of charged and neutral particles. Some of the techniques he describes
may be useful in aerosol beam systems.
Charging of beam particles is an important problem which deserves further
investigation. This topic is discussed further in the applications section.
2.8 Coincidence errors in particle counting.
In the counting or measurement of aerosols of high number concen-
trations, coincidence errors due to simultaneous occupation of an "observation
volume", such as a focused laser beam, by more than one particle can become
substantial. We show here that such problems are less serious in aerosol beam
systems.
Consider a system in which the aerosol particle flow rate is N.A.V ,
where N. is the particle number concentration, A. the flow cross-section and
V. the average particle velocity at location i. From conservation of particles
45
-------
N A V s N A V
222 VlV
Assuming negligible particle loss to the system walls, this expression must
apply regardless of whether the aerosol particles are suspended in a gas
medium or a vacuum.
The Ir.near density N.A. (particles/cm) provides a measure of the proba-
bility of a coincidence error occurring within the observation volume of fixed
thickness L. That is, for more particles per cm in the stream the probability
that more r.han one occupies the interval L at any time must increase. Because
the linear density
is smaller in an aerosol beaBi. where. V../V_ is small, coincidence errors in aero-
sol beam systems are always less than in other systems where V.. /V_ is larger.
Thus, for a given co-incidence error level, it is possible to count or
measure sample particles at higher number densities in an aerosol beam system
than in other systems.
3. Calculation of the Dynamical Properties of Aerosol Beams
The fvndamental properties of aerosol beams most pertinent to their eval-
uation as possible experimental or industrial systems are the velocity and
geometry characteristics of such beams. This section reviews methods for cal-
culating these properties of aerosol beams and presents example results. A
related problem of fundamental interest, namely, condensational growth of
particles in adiabatically expanding jetss is also considered.
The motion of an aerosol particle in a fluid stream is described by the
particle equation of motion
A
dv dm
where m is the particle mass (which may change with time due to evaporation
or condensation), v the particle velocity, t the time, f the particle
friction coefficient and vf the local fluid velocity. The ratio a = f/m is
given by
a = 9yK/2a2p C (2)
P s
where y is the local gas viscosity, a the particle radius (or equivalent
46
-------
sphere radius) , p the particle mass density, C the slip correction factor
P s
and K the dynamic shape factor that includes two factors « = 6a that correct
for non-negligible particle Reynolds number and for non-spherical particle
shape. Example corrections for non-spherical shape a, as well as the values
of C for such shapes, are described for several geometries by Dahneke (3,51,
S
52) . The factor 6 is given for spheres by the empirical expression
6 = 1 + 0.1062 Re0'8561 (3)
where
Re = 2apf |vp - vf|/y,
p.. being the local mass density of the fluid. This expression for 6 was ob-
tained by fitting the coefficient and exponent to experimental data for spheres
in continuum flow (53,54) to provide an adequate approximation when Re < 50,
which is the Re range encountered in aerosol beam generation.
For aerosol expansions through nozzles, orifices and capillaries of cir-
cular cross-section, the vector equation (1) is equivalently expressed in two
scalar equations for the axial (z) and radial (r) components of particle
motion. Thus,
dv
dm
m
1 * —
p dt
dv
•-- tf + dT]
dm
(VPZ - Vfz}
(la)
(lb)
If we define
dm
a'(t) =
then the solutions of these equations are
Vpz(t)
vfz<°>
/Vdv
(4a)
47
-------
-;VdV
.(t) = e
vfr(6)a'(6)de
(4b)
and
z(t) = z(o)
V (t)dt
pz
(5a)
r(t) = r(o)
v (t)dt.
prv
(5b)
These equations form the basis of numerical programs for tracing the motion of
particles in accelerating jet flows. When evaporation or condensation has
significant influence on particle motion or is otherwise of interest, an
energy equation coupled to the equation of motion may also need to be solved
simultaneous Ly.
When evaporation or condensation does not have significant influence on
particle motion, the a'(t) in equation (4) can be replaced by the a of
equation (2) , In this case it is sometimes convenient to delete the inter-
mediate parameter t from the calculation by use of the chain rule.
dv
v , = - a(v - v- )
pz dz pz fz
dv
— r
pr dr
- a(v - v,. )
pr fr
(6a)
v
(6b)
v
Although thes.e expressions are non-linear which tends to make their numerical
evaluation ur.stable, they are sometimes very convenient.
For exan.ple, when aerosol beams are decelerated in a motionless back-
ground gas, their dynamics is especially simple since vf = 0. For this case
axial motion of the beam particles is described by the simple expression
z
pz
a(v)dv
(7)
z =0
s
48
-------
where z is the upbeam distance from the particle's stopping location with a
s
similar expression applying for radial particle motion. For sufficiently
small z , (7) simplifies to
S
vpz = azs (7a)
where a is the constant given by expression (2). Dahneke and Friedlander (55)
and Dahneke (2,3) verified expressions (7) and (7a) for aerosol beams in a
motionless background gas and Dahneke (41) used this property of aerosol beams
to measure the capture of beam particles on target surfaces.
To calculate beam particle velocities, beam cross-sections and evaporation
or condensation obtained in an aerosol beam, the fluid flow field vf in
equation (1) must be known. The temperature, pressure and density fields of
the suspending gas are also required in these calculations. These present a
substantial problem. Fortunately, analytical, semi-empirical and empirical
expressions provide simple approximations of the gas jet centerline velocity
and state properties for nozzle flows. These simple approximations can be
used to estimate some of the properties of aerosol beams.
The fluid flow field in aerosol beam systems divides into four regions:
the nozzle orifice or capillary entrance region, the internal flow region with-
in the nozzle, the transonic flow region at the nozzle exit and the supersonic
free jet flow region. Beyond these regions the vacuum is.generally adequate
so that the motion of the beam particles is not significantly influenced by
the background gas except where high background pressures or long path lengths
occur.
Of the four flow regions, the entrance is usually not significant in
nozzle flows. It can be important in capillary flows, as discussed below.
But capillaries are not advised in aerosol beam systems because of particle
losses on the wall, especially in the entrance region. Thus, entrance region
flow is not generally important in aerosol beam dynamics and will be discussed
below only briefly in connection with capillary flows. Flow in the transonic
region near the nozzle exit is not understood. This flow region comprises one
of the classic unsolved problems of gas dynamics. Approximations of the center-
line flow must therefore be based on expressions for the nozzle and free-jet
regions.
The simplest model of compressible nozzle flow assumes one-dimensional,
49
-------
isentropic, frictionless flow of an ideal gas. This model provides simple
expressions for the gas velocity and all the properties of a gas in terms of
the stagnation condition of the gas and the local area ratio A/A*, where A*
is the nozzle throat area. These expressions are derived by Shapiro (56).
The Mach number M is defined by
M = vf//RT/M (8)
where v. is the local gas velocity, R the universal gas constant, T the local
absolute temperature of the gas and M the gas molecular weight. The Mach num-
ber and area ratio are related by
y+i
(9)
where y is the ratio of specific heats: y = c /c = 7/5 for air> 5.3 for
helium and ?/7 for CO-. The local state parameters of the gas are given by
TQ/T = 1 + (Y-l)M2/2 (lOa)
po/p = (1 + (Y-DM2/2)Y/(Y~1) (lOb)
po/p = (1 + (Y-DM2/2)1/(Y~1) (lOc)
where T , p and p are the stagnation state properties of the gas.
The moist severe of the above assumptions in the case of small nozzles is
the assumption of frictionless flow. This topic will be briefly discussed
below.
Free-jet flows have received considerable interest because of their use
in continuun source molecular beams. The properties of these jets are there-
fore known. This subject has been reviewed by Ashkenas and Sherman (57), by
French (58) and, more recently, by Anderson (59).
Ashkens.s and Sherman give an accurate fitting for the centerline Mach
number of a free-jet
M = AB - j (lti.)/(AB) + C/B3; B = {x/D - xo/D}Y~1 (11)
where D is the nozzle diameter and x the downstream distance from the nozzle
50
-------
exit plane. For air jets y = 1.40, A = 3.65, C = 0.20 and x /D = 0.40. These
authors also provide values for other gases. This expression applies for the
range
1.0 < x/D < 0.67 (p /P,)1/2,
o b
the upper limit being the location of the Mach disc or normal shock where the
overexpanded supersonic jet shocks to the background pressure. The ratio
p /p, is the ratio of stagnation to background pressure in the vacuum chamber.
The third term of the fitting formula is not included by Ashkenas and Sherman
on the basis of analytic considerations, as are the first two terms (by com-
parison to radial source flows). For the case of air and helium jets it does
extend the range of validity of the two term fitting formula, the two term
version being only valid above a lower limit of x/D = 6.
Since the gasdynamics solutions are not available for the transonic flow
region near the nozzle exit, flow in this region can be approximated by a
suitable expression that fits the boundary condition M = 1.0 at x = 0 and
matches expression (11) when x/D > 1. The result for the centerline Mach
number in the free jet within the range 0 < x/D < 6 is
5/7
M a i.o + A'X/D - B1(x/D) . (12)
When y = 1.40, A' = 1.55 and Bf = 0.042. The form of this expression is sug-
gested by the curves of French (58). Since the free jet flow is assumed to be
isentropic flow of a perfect gas, the centerline Mach number of expressions
(11) and (12) can be combined with expressions (8) and (10) to obtain the
centerline gas velocity and state properties.
The assumption of frictionless flow in the nozzle-jet system causes
errors in the calculated flows due to several types of viscous effects (57).
The most important of these in the small nozzle system used in aerosol beam
generation seems to be boundary layer formation. The boundary layer can pro-
duce a change in the effective nozzle diameter and a distortion of the flow
pattern in the transonic region near the nozzle exit. The effect is reduced
as the nozzle Reynolds number is increased, since boundary layer growth in
the nozzle is diminished. Ashkenas and Sherman (57) present experimental data
relating effective orifice size to nozzle throat Reynolds number for two
orifices and one long nozzle with length/diameter ~4. Their data suggest the
51
-------
influence of the boundary layer is not important for nozzle throat Reynolds
number exc€!eding a few hundred.
These centerline flow approximations for the nozzle, transonic and free-
jet flow reigions appear to be generally adequate for calculating aerosol beam
velocities, since it is good practice to confine the aerosol sample to the
central coie of the jet flow to obtain "focused" aerosol beams (6). Also,
for isentrcpic expansions of air at NTP9 the calculated nozzle throat Reynolds
numbers for throat diameters of 100, 200 and 500 ym are 1470, 2490 and 7340,
respectively, so that boundary layer formation should not substantially affect
the flow.
Figure 1 shows a comparison of measured particle velocities and those
calculated by use of the above approximation for the centerline gas flow (1).
The converging nozzle used to obtain these data had a diameter of 0.40 mm, a
length of 2.1 mm and was operated at a calculated nozzle throat Reynolds
number of 5370. The particles were confined to the central core of the nozzle
flow. A coLlimating orifice was located 2 mm downstream of the nozzle exit so
that a normal shock must have occurred just upstream of this location, but the
particles had essentially obtained their terminal velocity before reaching
this plane. Particle deceleration behind such a shock was calculated to be a
few percent for the smallest spheres used (0.81 ym diameter) and was less for
larger sizes?. The close agreement of the calculated and measured data
suggests th
-------
expansion of the aerosol at NTP through a capillary with square ends, a length
of 300 mm and diameter of 0.50 mm. The aerosol beam was collimated so that
the velocities correspond to centerline flow. This collimating effect tends
to occur naturally in long capillaries anyway, because the Bernoulli force
acting on the particles in the parabolic velocity field causes them to concen-
trate in the center of the capillary. The data have not been compared to cal-
culated velocities because no simple theory is available for choked capillary
flow (60). The largest particles obviously do not obtain velocity equilibrium
with the expanding helium jet at the capillary exit. Expressions (11) and
(12) for the centerline Mach number are probably inadequate in free-jet flows
originating from a capillary because the flow in the capillary is a boundary
layer flow.
Figures 4-6 show calculated particle TOF across a 100 ym path length
beginning 2.0 mm from the nozzle exit plane for spherical particles of unit
mass density. Nozzle 1 of Figure 4 is the nozzle for which the data of Figure
2 were measured and calculated, except for a constant diameter section of 0.1
mm length at the outlet end not present in nozzle 1. Comparison of the three
calculated curves show that nozzle geometry does not have substantial influ-
ence on particle terminal velocity.
Substantially larger differences in particle terminal velocity occur with
changes in nozzle diameter, as shown in Figure 5. This happens because the
nozzle and free-jet flow fields are scaled to the nozzle diameter. A larger
nozzle diameter means a slower rate of increase in gas velocity over (unsealed)
axial distance so that the accelerating particles can follow the gas motion
more closely. That is, particles in a larger diameter jet lag the gas veloc-
ity less than in a smaller jet. Particles in a smaller jet therefore have
larger TOF as shown in Figure 5.
This feature becomes important in certain applications of aerosol beams
such as in a time of flight aerosol beam spectrometer (TOFABS) (1,4). As il-
lustrated by the curves of Figure 5, to retain size resolving power down to
small particle sizes it is important to use a small diameter nozzle, which is
also helpful in reducing vacuum pumping requirements. The improvement thus
obtainable in small particle resolving power greatly exceeds the improvement
obtainable by shortening the nozzle or otherwise changing its geometry.
Although the above conclusion is believed to be generally valid, it
53
-------
should be noted that the calculated particle TOF values for the conical sec-
tion nozzles of Figures 4-6 may be less accurate than the calculated values
of Figures 1 and 2. Since the flow is actually converging rather than parallel
at the exit of these conical section nozzles, the effective value of nozzle
diameter D and apparent origin location x in expressions (11) and (12) may be
slightly different. No accurate beam velocity measurements have yet been re-
ported for conical section nozzles or any nozzles not having a constant diam-
eter length at the nozzle exit.
Figure 6 shows the influence of particle mass density on particle TOF for
nozzle 2 of Figure 4. Particles of unknown mass density can only be character-
ized in terns of their aerodynamic diameter, which is defined as the geometric
diameter of a sphere of reference mass density obtaining the same TOF. Since
atmospheric particles and droplets often have average mass densities near
3 3
1.8 gm/cm , a reference density of 1.8 gm/cm would be useful for defining the
aerodynamic diameter of atmospheric particles as this would give an aerodynamic
diameter corresponding closely to the particles' geometric diameter.
Dahnekc. and Padliya (4) used the simple centerline flow theory, expres-
sions (8) through (12), together with an interpolation formula for the conden-
sational growth of small particles in an adiabatically expanding jet. Their
interest in this problem was in the possible use of condensational growth to
aid in the detection of very small particles. They therefore considered jet
expansions containing various vapors added to the aerosol sample at their sat-
uration pressure for this purpose. Although some questionable assumptions
were made ir. the calculations, such as assuming temperature equilibrium be-
tween the pg.rticle (droplet) and expanding gas throughout the nozzle flow,
these assumptions were conservative in the sense that they would cause an
overestimate, of condensational growth. Thus, actual growth would be less than
their calculated results shown in Table 3. The calculations reveal that in-
crease in pe.rticle size is not significant in the jet because the particles
spend insufficient time in the growth region between the critical super-
saturations for the onset of heterogeneous nucleation and homogeneous nucle-
ation. Dahreke and Padliya concluded that to obtain sufficient growth to aid
particle detection, the particles must be allowed to grow in a growth chamber
upstream of the jet in which the vapor supersaturation is controlled by, say,
a relatively small pre-expansion of the gas-vapor-sample mixture.
54
-------
Of course, the centerline gas velocity and properties cannot be used to
calculate aerosol beam expansions in the vacuum chamber. The calculations of
Israel and Whang (32) and the measured data of various investigators (5,6,32)
remain the only information available. Some aerosol beam diameters measured
by the present author are shown in Figure 7.
Israel and Whang (32) analyzed the dynamics of aerosol beams generated by
aerosol expansion through a capillary and converging nozzle and compared their
results to experimental data. They considered three flow regions: flow near
the capillary or nozzle inlet, flow within the capillary or nozzle and free
jet expansion flow near the capillary exit. In each case they made idealized
assumptions to simplify the calculations. However, their calculated results
reveal interesting details of the beam dynamics which were supported by their
measured data.
For expansion flows through a capillary, they found that the beam geometry
in the vacuum chamber was substantially influenced by the entrance region flow.
They predicted and observed annular deposits reminiscent of the "halo deposits"
sometimes observed in impactor samples. Such deposits were also reported for
capillary expansions in one figure of Israel and Friedlander (5). Israel and
Whang's analysis indicates this effect in aerosol beams (and probably in im-
pactors) is due to the particle distribution in the flow field obtained in the
inlet flow region of the capillary and to the beam expansion caused by the
radial expansion of the jet in the vacuum chamber. In their converging nozzle
design this effect was not significant.
To analyze the beam dynamics for the converging nozzle expansion, they
assumed parallel sonic gas velocity at the nozzle exit plane and velocity
equilibrium between the gas and the suspended particles. Beam dynamics in the
vacuum chamber other than parallel, constant velocity motion were therefore
assumed caused by the free jet expansion. Furthermore, they assumed the free
jet flow was adequately characterized by planar, two dimensional flow as would
occur in the central region of a long, narrow slit nozzle. They solved for
this two-dimensional flow field using the method of characteristics.
Israel and Whang calculated the particle trajectories in the calculated
flow field to obtain beam diameter (radial expansion) versus downbeam distance
for various aerosol particle sizes and compared these results to their measured
data. The data generally supported the calculated results. Israel and Whang's
55
-------
investigation, besides providing interesting details, suggests the general re-
sult that the dynamics of aerosol beams of submicron particles generated in
long slende:: nozzles are predominantly due to the acceleration of the beam
particles in the free jet expansion. This conclusion is also suggested by the
results obtained using much shorter nozzles in the present author's laboratory,
provided tho beam particles are < 0.1 ym diameter. For larger particles a
substantial velocity difference can occur between the particles and gas so that
beam dynamics are strongly influenced by flow in both the nozzle and free-jet
regions, as shown in Table 2.
Since t:he above investigations, several techniques have been reported
which provide improved estimates of the flow properties in nozzles, orifices
and capillaries. These techniques have been recently reviewed by Edwards (60).
Although a general, solution of the Navier-Stokes equations for compressible
flow in a cs.pillary, orifice or nozzle has not yet been reported, experimental
investigations and model calculations have provided considerable information
about these flow systems. None of these data or techniques have yet been
applied in aerosol beam calculations.
4. Applications of Aerosol Beams
Aerosol beams have been used in several applications and proposed for
others. Examples include systems for the size sorting of fine powders (1),
for measuring particle drag (3), particle bounce and particle adhesion energy
(41,42), particle size or mass distributions (1,4,9,32,34-36), composition of
particles (39,40) and the electrical charging of particles (37,38,45,48). All
of the systems used in these investigations were experimental in the sense
that they attempted to incorporate a new technique for which little precise
information was available into a system capable of accurate measurements. For
this reason alone, the results of each of these investigations are useful be-
cause, in addition to demonstrating the advantages and limitations of the var-
ious applications, they provide useful information about the properties of
aerosol beams.
One application of aerosol beams, namely, time of flight aerosol beam
spectrometry (TOFABS) (1,4,7,9) will be described in detail. Although this
particular application was rather arbitrarily selected, it comprises an im-
portant application and illustrates some of the unique features of aerosol
beams. It also illustrates an important current need in aerosol beam
56
-------
technology, namely, the development of adequate techniques for detecting and
measuring small particles in the beam.
TOFABS instruments can be used for measuring the size distribution of air-
borne particles. This type of instrument infers a particle's aerodynamic size
by measuring its TOF in the vacuum chamber, as described previously. Example
results from Reference (1) showing the capability of this technique are shown
in Figure 8. These data show the number of particles counted versus particle
TOF between two focused laser beams of 1.077 cm separation. The aerosol
samples measured were monodisperse latex spheres and aggregates (doublets,
triplets, etc.). Two sample aerosols were separately measured containing
spheres of 1.25 ym diameter (solid curve) and 2.02 ym diameter (dashed curve),
respectively. The aerodynamic size difference between the singlet spheres
and doublet aggregates in air at NTP is 19%. The TOFABS easily resolves dif-
ferences of this magnitude and seems capable of resolving smaller differences.
Because of the relatively large separation of the light beams in the
above apparatus, the particle TOF values were large. This had the consequence
that only rather dilute aerosols could be measured. For aerosol number den-
3 3
sities > 10 particles/cm coincidence counting errors would have become sig-
nificant.
To solve this problem the single beam TOFABS of Figure 9 was built. In
this version, the vertical downward aerosol beam intersects a single horizontal
laser beam at its focus. As each beam particle passes through the laser beam,
it scatters light into the spherical mirror which focuses the scattered light
signal onto a small deflector mirror which directs the signal onto a photo-
multiplier tube (PMT). The instantaneous amplitude of the PMT signal there-
fore corresponds to the instantaneous location of the particle in the laser
beam.
Because the intensity distribution in the laser beam was Gaussian, the
PMT signals were Gaussian in time as the particles traversed the laser beam
at constant velocity, provided the particles were small compared to the laser
beam thickness of 72 ym. Such Gaussian signals are shown for monodisperse
latex spheres of 2.02 ym diameter as the upper oscilloscope trace of Figure
10. The lower trace is a logic pulse of constant amplitude and of width equal
to the particle TOF across the laser beam. This logic pulse was provided by
the circuitry shown in Figure 11, which assured that the particle TOF was
57
-------
always measured for a fixed path length.
Figure 2 shows experimental calibration data obtained using latex spheres,
compared to an analytical calibration curve fitted to the data by selecting
the laser beam thickness giving the best agreement (72 ym).
An example size distribution measured with this instrument is shown in
Figure 12. The sample was a heterodisperse NaCl aerosol obtained by spraying
an aqueous solution in air and allowing the droplets to dry. The vertical axis
is number of particles measured while the horizontal axis is TOP (particle
aerodynamic size). The maximum in the distribution curve occurred at 0.9 ym
diameter.
This TOFABS can measure particles between 0.3 and about 10 ym diameter.
The lower size limit occurs because the scattered light signals are sufficient-
ly weak for smaller particles so that statistical or "shot" noise, due to
statistical fluctuations in the small number of photons reaching the PMT, pre-
vents accurate measurement of the instantaneous location of smaller particles
in the laser beam.
Because of substantial interest in particles of smaller size (the "res-
pirable" siza range covers particle diameters between a few hundredths to a
few ym) currant research in the author's laboratory is investigating methods
for detecting beam particles of small size and thereby extending the measur-
able size ra:age of TOFABS instruments. Since these particles can be isolated
from their suspending gas, very sensitive detection techniques capable of sen-
sing particliis much smaller than 0.1 ym should be usable in detecting small
particles wi:hout removing them from the beam or attenuating their velocity.
One promising detection technique is electron beam scattering. The fol-
lowing analysis of the scattering of an electron beam by charged aerosol beam
particles illustrates the important features of the process and suggests that
particle detection by this technique should be possible. The complete analy-
sis is too complex to summarize here. Only the simplest prototype problem;
will be consi.dered. However, this prototype problem shows all the important
features of l:he scattering process and provides an order of magnitude approx-
imation of the attainable signal level. A more complete analysis will be des-
cribed elsewhere.
Consider an aerosol beam passing through a crossed electron beam which
charges the team particles, as in the experiments of Hall and Beeman (48).
58
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The design and performance of such electron beams are described in References
61-64. The aerosol beam particles, now charged, will scatter electrons in
passing through other electron beams and may thereby be detected and measured.
We wish to determine .the magnitude of the signals obtainable by electron beam
scattering and whether this detection method seems useful for small aerosol
beam particles.
In order to prevent the disintegration of small droplets when the repul-
sion of their surface charges exceeds their surface tension, i.e., to prevent
the droplet charge from exceeding the Rayleigh limit, we assume the electron
beams of such a system to be low energy beams. High energy beams and detec-
tion of particles by secondary electron emission will not be considered here.
Thus, the energy and current of the first electron beam is controlled so that
particles obtain a desired (size dependent) saturation charge in this electron
beam. They retain this same charge while passing through a subsequent beam or
beams. (In fact, measurement of particle charge may also be useful in infer-
ring the size of the aerosol beam particle.)
Rutherford (65) analyzed the deflection of a small charged particle (an
electron in the present problem) by coulombic interaction with a more massive
charged particle. He assumed the interaction of point charges and used con-
servation of angular momentum to calculate the angle by which the electron's
final trajectory is deflected from its initial trajectory. He obtained
cot($/s) = 2 r/b (13)
where r is the minimum separation between the initial electron trajectory and
the charged particle. The trajectory of the more massive particle is not sig-
nificantly altered by the interaction. In fact, we can regard the more mas-
sive particle as stationary.
The quantity b is given by
b = 2 Ne2/(mu2)
where, for the present application, N is the number of electronic charges on
the aerosol beam particle, e the unit electronic charge, m the electron mass
and u the electron velocity. The quantity b represents a simple physical
quantity, namely, the minimum separation of the two point charges obtained
when the initial electron trajectory intersects the charged particle.
59
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Rutherford Vs result for is therefore exact for charged particles of radius
a provided 11 « b or r » a. If one of these conditions is not satisfied the
point chargu assumption may no longer be adequate. We shall assume and later
demonstrate that (13) is an adequate approximation in the present calculations
for low energy electron beams.
Rutherford's result for applies irrespective of the sign of the charge
on either particle, since the same deflection angle R and outer radius R-' , is located an axial distance L from the
scattering particle.
Electrons with initial trajectory at r will fail to intercept C.. if their
deflection angle <$> given by (13) exceeds the angle ij;1, where
tan \|>' = (Rj - r)/L.
That is, whe:i
2 arctan {b/2r> > arctan {(R| - r)/L>.
Since only electrons at small r obtain sufficient deflection, this expression
applies when r « R ' . Thus, electrons will fail to strike CL because their
deflection angle is too large when
r < rQ = b/{2 tan j arctan (R|/L)}. (14)
The first orcler or paraxial approximation of (14), valid when R' « L, is
r = bL/R!.
o 1
Electrons between r and R will strike CL if > if), where
tan \l> = (R-j^ - r)/L.
That is, to first order approximation, electrons will strike C.. if
r2 - R + bL > 0.
60
-------
The equality has the roots
1 1 91/9
rl = I Rl " I Rl(1 " A bL/Ri > S bL/Ri
i i 91/9
r2 = I Rl + I V1 ~ 4 bL/Ri ) S Ri - bL/RT
Four r ranges are thus specified. Electrons initially in the range 0 < r < r
o
will not strike C.. because their deflection is too large. Electrons in the
range r < r < r.. will strike C.. because they pass near the scattering par-
ticle and obtain sufficient deflection. Electrons in the range r1 < r < r
will not strike C- because their deflection is too small. Electrons in the
range r. < r < R (assuming r~ < R) will strike C.. because they require only a
small deflection.
As a numerical example, consider the case where L/R1 = 100, R-I/R, = 10
12 111
and -r mu =1 eV. Calculated values of b, r , r.., r0 and scattered electron
/ o 1 /
current J. are shown in Table 4 for various N values.
These calculated data show several interesting results. First, water
droplets can be charged to below their Rayleigh limit, shown as N in Table 4
for droplet radius r (46), and cause significant scattering of the electron
-6
beam down to droplet diameters of 10 cm. Thus, water droplets of this size
and larger seem to be detectable by electron beam scattering.
Second, the distance of nearest approach b between an electron and a
droplet charged to near its Rayleigh limit exceeds the particle radius by an
order of magnitude and since r exceeds b, Rutherford's scattering theory
based on the assumption of coulombic interaction of point charges seems to be
an adequate approximation for all electrons having r > r , i.e., for all elec-
trons reaching the collectors CL and C«.
Third, because R^ - r~ = r.. is small except when N becomes quite large,
a preferred detector design would not attempt to collect scattered electrons
on GI from the outer annulus r_ < r < R because this would require the elec-
tron beam radius R to be nearly as large as R-. In this case, background
noise due to poorly collimated or unfocused electrons and to space charge ex-
pansion of the electron beam would probably cause poor signal to noise ratio
(SNR). An optimum SNR value can only be obtained by both minimizing the back-
ground noise level and maximizing the signal level. (The importance of the
61
-------
former has sometimes been overlooked in light scattering systems.) We there-
fore require. R to be significantly less than R which generally eliminates a
scattered electron signal from the outer annulus r_ < r < R, since r? > R.
Fourth, because r.. exceeds r by an order of magnitude the scattered
electron signal current I., is adequately given by
I1 = TtCbL/R^2 IQ (16)
2
where I. is the current density (amps/cm ) at the electron beam axis.
A similar analysis of the scattering from a sheet electron beam passing
through a slit of width 2t in the collector, analogous to the orifice of diam-
eter 2 R- In collector C-, gives the scattered electron signal
I1 = TT/2 (bL/t)2 IQ (17)
which is exactly one-half that derived above for a circular beam with R- = t.
Thus, the scattered electron signals from a sheet electron beam have comparable
magnitude to those for a circular electron beam.
The electron beam current density I cannot be very large in a narrow,
low energy beam like the one we are considering because space charge expansion
of the beam Dccurs too quickly at large I . At a beam energy of 1 eV and
2 °
current density I of 30 yamp/cm the electron beam experiences negligible
expansion over a path length L of 1 cm. Beyond this distance space charge
expansion of the beam is rapid. A current density of this magnitude is easily
obtainable, =ven by thermal electron emission which is space charge limited
2
at low beam energies (62). A current density of I =32 yamp/cm was assumed
in calculating the signal currents I. of Table 4.
Of counse space charge expansion of the electron beam can be reduced by
increasing the electron velocity. For sufficiently small expansion (small L),
the beam expiinsion is given by the first order approximation (62-64)
AR/R, = I e L2/(4emu3) <* I /u3 (18)
i o o
where AR is (:he increase in beam radius over the initial radius R. and e the
permittivity of vacuum. This idealized expression was obtained by solving
Newton's law for a parallel, circular electron beam having uniform current
density and electron energy. It is valid when
62
-------
L <
LV
since higher order terms become important for larger L values.
According to expression (16) the signal current increases with beam energy
according to
(2Ne2Ll2
Thus, increase in both I and u so as to maintain constant signal I always
causes an increase in space charge expansion of the electron beam according to
(18). Nevertheless, an electron beam energy somewhat higher than 1 eV may be
optimum because higher energy beams can be better focused. Of course, the
above analysis assuming point charge interaction only applies for beams of
sufficiently low energy.
The signal currents of Table 4 cannot be detected without amplification.
Q
If the collector C.. is an electron multiplier, amplification of 10 and some-
9
times 10 is possible. (However, acceleration of the scattered electrons may
be required to induce secondary emission in the multiplier.) A gain of 10
together with a load resistance of 100 ft would give voltage pulses of max-
imum amplitude between 1 mV and 10 V. Since the current density distribution
is approximately Gaussian in electron beams (61), the resulting current or
voltage signals will be roughly Gaussian of width equal to the particle TOF
through the electron beam.
Although we have ignored complexities such as electron beam convergence,
divergence and other distortions (64,66,67), background and shot noise and
saturation of the electron multiplier, the foregoing prototype calculations
suggest the detection of charged aerosol beam particles by electron beam
scattering is a feasible technique for water droplet diameters > .01 ym and
for even smaller solid particles.
The calculations therefore suggest the TOFABS technique for measuring
aerosol size distributions, previously demonstrated for particles > 0.3 ym,
should be usable with electron beam detection for measuring size distributions
over a much broader range. Although substantial development work remains, it
63
-------
seems justified by these results and the need for a single instrument capable
of rapid, accurate measurement of the particle size distribution over the size
range from 0.01 to 10 ym.
Acknowledgement: The author is pleased to acknowledge the assistance
of Dr. Yung Sung Cheng .in collecting the references on velocity
selectors and for helpful discussions on this subject and others, and
of Dr. Dilip Padliya who provided the calculations on which Figs. 2,
4-6 and Tables 2 and 3 were based, as well as helpful discussions.
This paper is based on work partially performed under contract with
the U.S. Energy Research and Development Administration at the
Univers ity of Rochester Biomedical and Environmental Research
Project and has been assigned Report No. UR-3490-1031. Partial
support for the work this paper describes was provided in the form
of research grants from the U.S. National Institute of Environmental
Health Sciences and the U.S. Environmental Protection Agency.
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Instruments," in J. L. Potter, Ed., Rarefied Gas Dynamics, AIAA, New
York, Part II (1976).
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AIAA, Ne.w York, Part II (1976).
9. M. H. Schwartz and R. P. Andres, Aerosol Sci., ]_, 281 (1976).
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64
-------
Molecular Beams, Academic Press, New York, 1959, p. A3.
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Selector," AEC Report COO-1328-15, Sept. 1965.
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7_, 3054 (1971).
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32. G. W. Israel and J. S. Whang, in H. M. Englund and W. T. Beery, Eds.,
Proceedings of the 2nd International Clean Air Congress, Academic Press,
New York, 1971. See also G. W. Israel and J. S. Whang, "Dynamical
Properties of Aerosol Beams," Technical Note BN-709, Institute for Fluid
Dynamics and Applied Mathematics, University of Maryland, College Park,
July, 1971.
65
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33. J. Gebhart, J. Heyder, C. Roth and W. Stahlhofen, in B. Y. H. Liu, Ed.,
Fine Particles, Academic Press, New York, 1975, p. 794.
34. W. Hollander and J. Schbrmann, Atmos. Environ., J3, 817 (1974).
35. A. P. Avy and M. Benarie, Staub, 24, 343 (1964).
36. M. Benarie and J. P. Quetier, Aerosol Sci., 1., 77 (1970).
37. J. D. Hopburn, F. S. Chute and F. E. Vermeulen, A.I.A.A. Journ., 11, 370
(1973).
38. J. D. Htipburn, F. S. Chute and F. E. Vermeulen, A.I.A.A. Journ., 13, 249
(1975).
39. R. L. Myers and W. L. Fits, Environ. Sci. Techn., 9., 334 (1975).
40. W. D. Davis, "Continuous Mass Spectrometric Analysis of Particulates
using Surface lonization," Report No. 76CRD069, General Electric Corporate
Research and Development, Schenectady, April 1976.
41. B. Dahne
-------
57. H. Ashkenas and F. Sherman, in J. H. de Leeuw, Ed., Rarefied Gas Dynamics,
Vol. 2, Academic Press, New York, 1966.
58. J. B. French, A.I.A.A. Journ., 3> 993 (1965).
59. J. B. Anderson, in P. P. Wegener, Ed., Molecular Beams and Low Density
Gasdynamics. Marcel Dekker, New York, 1974, p. 1.
60. R. H. Edwards, in J. L. Potter, Ed., Rarefied Gas Dynamics, AIAA,
New York, Part I (1976).
61. H. Moss, Narrow Angle Electron Guns and Cathode Ray Tubes, Supplement 3
of "Advances in Electronics and Electron Physics," Academic Press, New
York, 1968.
62. K. R. Spangenberg, Vacuum Tubes, McGraw-Hill, New York, 1948.
63. 0. Klemperer, Electron Optics, 3rd edition, Cambridge University Press,
1971.
64. A. B. El-Kareh and J. C. J. El-Kareh, Electron Beams, Lenses and Optics,
Vols. 1 and 2, Academic Press, New York, 1970.
65. E. Rutherford, Philos. Mag., Series VI, 21, 669 (1911).
66. C. C. Cutler, J. Appl. Phys., 27, 1028 (1956).
67. R. L. Kyhl and H. F. Webster, IRE Trans, of the Professional Group on
Electron Devices, ED-3, 172 (1956).
67
-------
Table 1 Compounds detected in airborne participates by
Davis (40) using surface ionization mass spectrometry.
Acetone
Toluene
Mesitylene
Naphthalene
Dimethylnaphthalene
Pyrene
Ethyl Alcohol
t-Butyl Alcohol
Aniline
Nicotine
Camphor
Cinchonine
Uranyl Acetate
CsN03
BaC03
BiC03
CaC03
SrCO,,
Cr2°3
Pb3°4
NiSO.
4
MgO
CuO
MoO
68
-------
Table 2 Calculated gas velocities and properties and the calculated particle velocities that result
for unit density spheres. These data apply for nozzle 1 of Fig. 4 except for a 0.1 mm
length of constant diameter at the nozzle exit not present in nozzle 1.
Distance
from nozzle
inlet plane,
0.1
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
1.9
2.1
2.3
2,5
V
Gas
M/sec
2,07
4,94
!Qr86
24P07
54,42
12Qf46
238,36
313,27
571,93
663, 82
700,48
716,89
724f46
velocity
M
.006
.014
.032
.070
.159
.355
.731
1.000
2.500
3.856
5.000
5.858
6.404
and properties
T,
°K
293.0
293.0
292.9
292.7
291.5
285.8
264.7
244.2
130.2
73.7
48.8
37.3
31.8
P,
Torr
730.0
729.9
729.5
727.5
717.2
669.0
511.8
385.6
42.7
5.8
1.4
0.5
0.3
d «? q.l ym
M/qec
3- 06
4,. 93
1Q.82
23.87
53,,43
116,. 02
2,23,. 09
31Q.74
439,. 79
473,97
489.50
493.46
4,95.60
Particle velocity
d = 1.0 ym
M/sec
2.. 00
4.65
9-70
19.61
38.56
73.45
129.03
188.80
238.54
255.93
260.46
262.11
262.99
d = 10. ym
M/sec
1.08
1.97
3.47
6.08
11.12
21.18
38.77
59.50
76.00
82.59
84.84
85.77
86.27
VD
-------
Table 3 Calculated increase in particle diameter due to condensational
growth. The various vapors were added to an air aerosol so
that the mixture was at NTP and the partial pressure of the vapor
equalled its saturation pressure.
Condensible
Vapor
Vapor Pressure
at 293 °K
(Torr)
Final Diameter for Initial
Particle Diameter of:
0.5 ym 0.1 ym
(ym) (ym)
Water
Acetone
Benzene
Ethanol
17.404
177.810
74.662
42.947
0.5004
0.5084
0.5007
0.5021
0.1004
0.1080
0.1007
0.1021
70
-------
Table 4 Calculated values for a circular electron beam scattered by a
particle at its center having N electronic charges.
N
10
20
50
100
200
500
1000
rRL'
cm
2xlO~7
3xlO~7
5x1 0~7
8xlO~7
IxlO'6
2xlO~6
4xlO~6
b,
cm
1.44xlO~6
2.88xlO~6
7.20xlO~6
1.44xlO~5
2.88xlO~5
7.20xlO~5
1.44xlO~4
V
cm
1.45xlO"5
2.89xlO"5
7.20xlO~5
1.45xlO"4
2.89xlO~4
7.20xlO"4
1.44xlO~3
n=Rrr2»
cm
1.44xlO~4
2.88xlO~4
7.20xlO~4
1.44xlO~3
2.88xlO~3
7.20xlO~3
1.44xlO~2
V
yamp
2.56xlO~6
1.02xlO~5
6.40xlO~5
2.56xlO~4
1.02xlO~3
6.40xlO~3
2.56xlO~2
L/R = 100, L/R' = 10, IQ = 32 yamp/cm2, -|mu2 = 1 eV
O / Q
, a = 75.6 dynes/cm.
71
-------
Figure 1 Comparison of measured and calculated particle velocities in an
aerosol beam generated by expansion of latex sphere aerosols at
NIP through a converging nozzle 2.1 mm long and 0.4 mm in diameter.
A normal shock was assumed just upbeam of a collimator located
2 mm from the nozzle exit plane. The shock wave location was
selected to give the best agreement of the calculated and
measured data.
3.0-
1.0J
0
— THEORY FOR a =1.05 gm/cm3
O DATA,/>= 1.027 gm/cm3
o DATA,/> = 105 gm/cm3
200 300 400
TERMINAL VELOCITY (m/sec)
500
72
-------
Figure 2 Comparison of measured and calculated particle TOF through a
focused laser beam. The laser beam thickness of 72 ym was
assumed because it gave best agreement between the measured and
calculated data. The beam was generated by expansion of latex
sphere aerosols initially at NTP. These results are comparable
to the data of Table 2.
1.0
VI
a.
u.
O
I I
I II II 1
I I
I I I I I
0.1
0.1
I I I I I I I I
1.0
Dp.
10.
73
-------
Figure 3 Measured particle velocities vs. particle diameter for beams of
Latex spheres generated by expanding helium and air aerosols at
NTP through a capillary of 0.5 mm diameter and 300 mm length.
600
V,
m/
'sec
500
400
300
0.5
Helium Aerosol
^
ir Aerosol
1.0
1.5
2.0
d,
-------
Figure 4 Calculated particle TOF vs. particle diameter for beams of unit
density spheres generated by assumed expansion of air aerosols
at NTP through the three nozzles specified. A flight path of
100 ym beginning 2 mm from the nozzle exit plane was assumed.
O
Ul
1.0
0.1
O.I
NOZZLE-I 2
DIMENSIONS IN MM
I j I I
D
1.0
_| • lit II
10.
75
-------
Figure 5 Calculated particle TOF vs. particle diameter for nozzle 2 of
ligure 4 with three nozzle diameters. An air aerosol at NTP
containing unit density spheres was assumed expanded through
the nozzle to generate the beam. The TOF was calculated for
a flight path of 100 ym beginning 2 mm from the nozzle exit
plane.
NOZZLE DIAMETER --0.1 mm
I I I I I I II
I I I I I I
76
-------
Figure 6 Calculated particle TOF vs. particle diameter for assumed
expansion of air aerosols at NTP containing spheres at the
three mass densities shown through nozzle 2 of Fig. 4.
Particle TOF was calculated for a flight path of 100 ym
beginning 2 mm from the nozzle exit plane.
i i i i r i M i
I III IT I I
1.0
o
UJ
- 1.5gm/cc
0.1
I I I I I I I I I
I I I I I I I I
0.1
1.0
Dp.
10.
77
-------
Figure 7 Measured beam diameter D vs. particle diameter D for beams of
latex spheres generated in a converging nozzle of 0.4 mm throat
diameter, 2.1 mm length and total flow of 1390 cc of air at NTP
per min. Open and closed circles represent beam diameters at
10 and 20 mm from the nozzle exit plane, respectively. Beam
diameter was reduced an order of magnitude by restricting the
aerosol sample to a small central fraction (28 cc/min) of the
total flow. Except for the smaller particle sizes in such
focused beams, which apparently tend to unfocus by particle
diffusion, the data all fit an expression of the form
D, = D exp(-mD ) where D and m are constant.
bo p o
10.
s
2
"jo
Q
1.0
0.1
AEROSOL FLOW = 1390 cc/min _
AEROSOL FLOW = 28 cc/min
0
1.0
D,
2.0
78
-------
Figure .8 Frequency (no. of particles) vs. TOF for air aerosols at NTP
containing uniform latex spheres of a single size and aggregates
of these spheres. The unusually high fraction of aggregates
was obtained by spraying undiluted aqueous suspensions of the
spheres into an air stream.
40 42
44 46 48 50
TIME OF FLIGHT (/xsec)
79
-------
Figure 9 Schematic diagram of a time of flight aerosol beam
.spectrometer (TOFABS) using a single, focused laser
Deam to detect and measure airborne particles.
80
-------
Figure 10 Upper oscilloscope trace: superimposed PMT signals generated by
the light scattered as 2.02 ym diameter latex spheres traverse
the focused laser beam. The horizontal scale is 0.2 ysec per
major division. Lower trace: superimposed logic pulses of
fixed amplitude and width equal to particle TOF through the laser
beam. The logic pulse time scale is delayed 0.5 ysec relative
to the PMT signal.
31
-------
Figure 11 Schematic diagram of the electronics system that processes
the PMT signals of Fig. 10 to obtain the logic pulses of
Fig. 10 and stores and displays the data as shown in Fig. 12.
DISMAY 01
PIINIOU?
82
-------
Figure 12 Measured TOF distribution for a polydisperse NaCl aerosol.
Vertical axis is number of particles while horizontal axis
is TOF. The maximum corresponds to an aerodynamic diameter
of 0.9 ym, that is, a unit density sphere of this diameter
will obtain the same TOF.
t
-------
Figure 13 Schematic diagram of a scattered electron beam detector.
.Aerosol beam particles previously charged in passing through
;in electron beam can be detected in passing through
subsequent electron beams because the charged particles
scatter electrons onto the collector (electron multiplier)
parallel, circular
electron beam —
Ian
-r) XL-
scattered
electron
trajectory
•initial
electron
trajectory
. 84
-------
TECHNICAL REPORT DATA
(Please read Instructions on the reverse before completing)
1. REPORT NO.
EPA-600/2-77-229
2.
3. RECIPIENT'S ACCESSION-NO.
4. TITLE AND SUBTITLE
TIME-OF-FLIGHT AEROSOL BEAM SPECTROMETER FOR PARTICLE
SIZE MEASUREMENTS
5. REPORT DATE
November 1977
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Barton Dahneke
8. PERFORMING ORGANIZATION REPORT NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
Department of Radiation Biology and Biophysics
University of Rochester
Rochester, New York 14642
10. PROGRAM ELEMENT NO.
1AD712, BE-23 (FY 77)
11. CONTRACT/GRANT NO.
R803065
12. SPONSORING AGENCY NAME AND ADDRESS
Environmental Sciences Research Laboratory - RTF, NC
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, N.C. 27711
13. TYPE OF REPORT AND PERIOD COVERED
FINAL 6/74 - 3/77
14. SPONSORING AGENCY CODE
EPA/600/09
15. SUPPLEMENTARY NOTES
16. ABSTRACT
A time-of-flight aerosol beam spectrometer (TOFABS) is described. The instrument
has been designed and constructed to perform in situ real time measurements of the
aerodynamic size of individual aerosol particles in the range 0.3 to 10 ym diameter.
The measurement method consists of (1) allowing a sample aerosol to undergo expansion
through a nozzle into a vacuum chamber, such that each particle acquires a terminal
velocity depending on its aerodynamic size, then (2) measuring the terminal velocity
by determining the time taken for each particle to traverse a laser beam of fixed
width. An experimental calibration curve relating time-of-flight and aerodynamic
size, based on the use of polystyrene latex spheres, is shown to be in good agreement
with a theoretical calibration obtained from the gas - particle dynamics equations.
A comprehensive discussion of the properties and uses of aerosol beams is included
as an appendix.
17.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.lDENTIFIERS/OPEN ENDED TERMS
c. COSATl Field/Group
*Air pollution
*Aerosols
*Particle size distribution
Aerodynamic characteristics
Rarified gas dynamics
Stokes law
13B
07D
20D
18. DISTRIBUTION STATEMENT
RELEASE TO PUBLIC
19. SECURITY CLASS (This Report!
UNCLASSIFIED
21. NO. OF PAGES
93
20. SECURITY CLASS (This page)
UNCLASSIFIED
22. PRICE
EPA Form 2220-1 (9-73)
85
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