Acoustical Particle Sizing Device Stephen R. Coover” and Parker C. Reist Department of Environmental Sciences and Engineering, School of Public Health, 20 1H, University of North Carolina at Chapel Hill, Chapel Hill, N.C. 27514
Acoustical particle counters have been described on a number of occasions in the literature in recent years. Heretofore, the devices offered no capabilities for sizing particles. This paper reports on the development of a n acoustical particle counter that exhibits a variable threshold diameter. Threshold diameter is selected by adjustment of the airflow rate to achieve a preselected Reynolds number for the airflow in the sensor. Determination of counts a t “n” Reynolds numbers can be resolved into an “n”-point particle size distribution by schemes that are presented. H
An acoustical particle sensor was developed in the early 1950s by researchers a t the Physics Department of the University of Mississippi under contract to the Chemical Corp Biological Laboratory ( I ) . Passage of a n aerosol particle through a specially designed orifice at high velocity was found to produce an acoustical pulse. The project was discontinued as the sensor was considered not to be practical. T h e results of the study were not published in the open literature. Gerhard Langer of the National Center for Atmospheric Research rediscovered the acoustical particle sensor in the early 1960s (2-5). Langer’s papers stimulated a renewed interest in the device. Langer and other investigators utilizing similar acoustical sensors discovered that the acoustical sensor exhibited a lower particle size threshold of about 5-15 p m (6). Mechanisms for the production of the acoustical pulse have heen proposed (6, 7-91, but the mechanism heretofore has not been clearly delineated. A number of attempts have been made to relate pulse amplitude a t the entrance of the capillary t o particle size, but the attempts have been unsuccessful (10-12). One study has claimed to successfully relate pulse amplitude a t the exit of the capillary to particle size, but little subsequent information has been presented to substantiate this claim (13). The acoustical particle sensor has existed for over 25 years. Reported applications have been limited to ice nuclei counting ( 1 4 , 1 5 )and condensation nuclei counting (16).These applications merely scratch the surface of the device’s overall potential. We have studied the acoustical particle sensor in a n effort to characterize its response so that it might be applied t o “large” particle counting and sizing problems. Our research has culminated in the development of a scheme by which the acoustical particle sensor can be used to size as well as count aerosol particles.
element consists of a 1.0 ern diameter X 15.0 ern long entry section, which tapers to a 15 mm X 6.0 ern capillary section via a 10’ half-angle conical contraction. Figure 1 B is a schematic of the experimental apparatus used to evaluate the device. T h e acoustical pulse that is triggered by the passage of an aerosol particle through the acoustical element is detected by a miniature electret microphone and amplified by a linear integrated circuit operational amplifier. A voltage comparator is used as a discriminator to discriminate between acoustical pulses and “noise”. Discrimination against noise is readily achieved as the signal to noise ratio [(S N ) / N ]is of the order of 1OO:l. Our current design is immune to ordinary room noise. A trigger with presettable dead time, set to slightly longer than the acoustical pulse duration, prevents multiple triggering on the sinusoidal wave form of the pulses. A digital scaler records the acoustical pulses. Flow rate through the acoustical element is selected with a rotameter. A membrane filter a t the exit of the acoustical element prevents contamination of the subsequent flow system with particulates and dampens mechanical noise infiltrating back from the vacuum pump.
Apparatus Figure 1A presents a diagram of the acoustical particle counting element utilized in this study. The polyester plastic 0013-936X/80/0914-0951$01.00/0
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1980 American Chemical Society
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Particle Size Threshold Four varieties of defatted monodisperse pollens and spores ranging in size from 6-pm wheat smut spores to 45-pm beech tree pollen were used as test aerosols. Precisely weighed samples of the pollens or spores were dispersed in a 1-ms acrylic plastic chamber by a blast of air. We have utilized this technique of aerosol generation for a number of years and have found that it produces an aerosol relatively free of agglomerates. We observed that the passage of an aerosol particle through the acoustical counting element could trigger a n acoustical pulse only if the air flow in the capillary section of the element exceeded a certain particle size specific Reynolds number. As such, the acoustical particle counter exhibits a threshold for particle size detection that can be selected by adjustment of the air-flow rate to achieve the desired Reynolds number in the capillary section of the acoustical element. Figure 2 presents a calibration curve of threshold particle diameter vs. Reynolds number. Note that the calibration is linear and independent of capillary diameter. Experiments with monodisperse pollens and spores (approximate density 1 g/cm3), divinylbenzene microspheres (density 1.05 g/cm3), and glass microspheres (density 2.45 g/cm3) revealed that the critical Reynolds number for spherical particles is independent of particle density. Experiments with flocking fibers indicated that the acoustical particle sizing device appears to size nonspherical particles on the basis of projected particle diameter perpendicular t o air flow. Volume 14, Number 8, August 1980
951
looo
1
Dimensions are diameters of spheres mlcromelers
1
Eapansion Chamber Membrane Filter
B
-ACOUSTICAL
FLOW REYNOLDS NUMBER, IN UNITS OF 103
ELEMENT
Figure 3. Absolute detection efficiency for spheres (1.5-mrn diameter acoustical element)
\MICROPHONE PRESETrABLE
ADJUSTABLE
Capillary
CONTROLLER
Figure 1. (A) Acoustical particle sizing element. (B) Analyzer sche-
matic
$ 4 0 1 i d
z
g u
3530'
2 0
6 I ln
o = l5mm
\\
'i
Lycopodium Spores
a
W
x
\
2520-
-
l5-
w 10 (r I + 5O7
8 9 IO I1 CRITICAL FLOW REYNOLDS NUMBL.., I N UNITS OF 103
Figure 2. Acoustical particle sizing device particle threshold diameter vs. critical flow Reynolds number
Absolute Detection Efficiency Knowledge of the absolute detection efficiency of the acoustical particle counter is required if the device is to be used for quantitative analyses. Absolute detection efficiency was determined with a Coulter Counter. The acoustical element was placed in a rubber stopper in the neck of a 500-cm3 filtering flask containing 100 cm3 of 2% saline. Particles exiting from the acoustical element were impacted and retained in the saline. The number of particles that had passed through the acoustical element was determined from the analysis of an aliquot of the saline with a Coulter Counter Model Z equipped with a 100-channel analyzer and a logarithmic scale expander. Coulter analysis provided not only particle counts but verification of monodispersity of the test aerosol. Figure 3 presents a plot of absolute detection efficiency for 952
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five monodisperse particle sizes vs. Reynolds number. All sizes of particles exhibit plateaus in their detection efficiency curves, but the larger sizes establish plateaus a t higher efficiencies and a t lower Reynolds numbers than the smaller sizes. Absolute detection efficiency data confirm the existence of particle size thresholds but indicate that the thresholds are not truly discrete.
Particle Sizing by Matrix Solution As the particle size thresholds are not truly discrete and the absolute detection efficiency for all sizes is not loo%, the distribution of counts per unit volume of air sampled vs. Reynolds number cannot be directly interpreted as an integral particle size distribution. However, the count data conveys information that can be resolved into an integral or differential particle size distribution. A matrix technique may be used to resolve the crude count data into a particle size distribution. The observed counts per unit volume at a given Reynolds number is given by: C, =
n
EirNi
i= 1
where C, = counts per unit volume a t Reynolds number r , EL, = detection efficiency for size i a t Reynolds number r , and Ni = particles per unit volume a t size i . More generally, the relationship can be expressed in matrix terminology as:
where Cr,l = matrix of counts per unit volume taken a t r Reynolds numbers, E , , = matrix of detection efficiencies of n sizes of particles at r Reynolds numbers, and N,,J = matrix of particles per unit volume of n sizes. As Cr,l and E , , can be determined and N,,J is desired, the solution is:
where -1 signifies the inverse matrix. The above relation is solvable if r 1 n, i.e., there are a t least as many counts a t different Reynolds numbers as size intervals to be determined, and matrix E is nonsingular, Le., rows or columns not dependent or not filled with zeroes. If the conditions are met, a computer can be used to solve the matrix equation for Nn,l,the concentration of particles in n different size intervals. The solution may contain negative values as it is a mathematical solution. Negative values have no physical significance. A technique of successive elimination may be
used to impart physical significance to the matrix solution. The column of matrix E which corresponds to the particle size interval yielding a negative concentration is deleted from matrix E and zero is assigned to that size interval. The matrix equation with the reduced matrix is solved. If negative solutions are returned again, the procedure is repeated until a nonnegative solution is produced. In essence, this technique produces a physically significant solution by elimination of size intervals that fit the data poorly. Rationale for “successive elimination” is purely intuitive. Mathematical rigor of the technique has not been established.
Particle Sizing by Curve Stripping Another technique that can be employed to resolve the crude count data into a particle size distribution is curve stripping, a technique widely used in nuclear counting (17). The basic premise of this technique is the existence of discrete thresholds. When applied to the acoustical particle sizing device, this implies that only the largest particles are counted a t the lowest Reynolds number and, as such, counts recorded a t the lowest Reynolds number can be exclusively assigned to the largest particle size interval. Using efficiency data for the largest particle size interval, the crude counts recorded a t the lowest flow are translated to a concentration of particles of the largest size interval. Contributions of the large size interval to crude counts a t all other Reynolds numbers are assessed and “stripped” by subtraction from the crude data. The process is repeated for the next larger size interval a t the next higher Reynolds number. Curve stripping continues until concentrations of particles in all size intervals of interest have been evaluated. As the acoustical particle sizing device’s thresholds are imperfect, Le., not truly discrete, curve stripping produces only an approximate particle size distribution. Particle Sizing Resolution Table I illustrates the resolution of a bimodal mixture by the successive approximation matrix solution and curve stripping techniques. The data indicate that both techniques resolve the distribution into the correct intervals, although the curve stripping places some counts in the large size intervals. Both techniques place approximately the correct number of counts in the lycopodium spore interval, b u t both place overly high numbers of counts in the ragweed pollen interval. High counts in the ragweed pollen interval have been attributed to a “particle matrix effect”. Detection efficiency for ragweed pollen, which is normally very low, appears to be enhanced in the presence of the larger lycopodium spores. An illustration of the sensitivity of resolution of the acoustical particle sizing device is presented in Figure 4. Five bimodal ragweed pollen/lycopodium spore mixtures were
Table I. Resolution of a Bimodal Aerosol Mixture (20 mg of 19-pm Ragweed and 10 mg of 28-pm Lycopodium) sire interval, Ctm
curve strip
45 36 28 19 6
5.7 93.7 424 7218 0
particies/iiler observed expected successive Coulter injection approximation counter sizea
0 0 378 10 198 0
X X
450 f.61 6222 f 403 X
0 0 482 4069 0
Assumes homogeneous distribution in 1.06-m3chamber following a 100% effective injection corrected for decay during counting. a
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t
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io00
c
I00
,
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I
Figure 4. Resolution of bimodal mixture, concentration = 19 mg/m3, ratio of 19 p m ragweed to 28 pm lycopodium by weight: inverted triangles = 1:O;upright triangles = 3.1;diamonds = 1:l; circles = 1:3; squares = 0:l
analyzed at 10 Reynolds numbers to provide crude count data. The crude data were resolved into two intervals by the matrix solution method. Log-normal particle size distributions were assumed and drawn through each of the two sizes. Proper dispersions of the log-normal distributions were calculated on the basis of adjacent interval spillover when analyzing a pure species of each of the test aerosols.
Theory of Operation Acceleration of air in a smooth gradual conical contraction establishes an unstable, superlaminar flow in the capillary section of the acoustical particle sizing element (11). An aerosol particle present in the air stream is also accelerated in the conical contraction but at a much lower rate due to its much greater density as compared to air (a 1 g/cm3 particle is 770 times as dense as air). Because of different accelerations, a differential velocity is established between the particle and the air stream (8, 9). When the differential velocity between the particle and the air stream reaches a level such that the particle Reynolds number exceeds 40, the particle begins shedding vortices into its wake (18).Vortices in the particle’s wake are initially of laminar character but become fully turbulent as the particle Reynolds number exceeds about 150 (18). At a particle Reynolds number between 120 and 900, the wake of the particle becomes sufficiently turbulent to trigger transition of the flow in the capillary from superlaminar to turbulent (19).The probability t h a t a turbulent transition occurs depends upon two factors: (a) the degree of instability present within the capillary that is a direct function of the capillary flow Reynolds number, and (b) the magnitude of the perturbation that is a direct function of particle Reynolds number and ultimately particle diameter for a given location and flow Reynolds number. As.such, the onset of turbulence occurs a t a specific capillary flow Reynolds number for each particle diameter. Transition from laminar to turbulent flow is accompanied by an abrupt rise in flow resistance as frictional losses in turbulent flow are proportional to the second power of flow velocity, whereas frictional losses in laminar flow are proportional to the first power of flow velocity. The abrupt increase in friction retards flow in the capillary, which produces a momentary pressure rise a t the capillary inlet and a momentary pressure reduction a t the capillary exit as the system adjusts to the new flow rate. The momentary pressure rise a t the capillary inlet perturbs the air column in the inlet section of the acoustical particle sizing element and causes it to resonate as a closed end organ pipe. Oscillation of the air in the inlet section is perceived as an audible “click”. When the particle exits from the capillary, perturbations to the capillary cease and flow in the capillary returns to superlaminar conditions. The entire system returns to equilibrium in a few more milliseconds as oscillations in the inlet section die out. Volume 14,Number 8, August 1980 953
Orlflce COlibrQIlon Threshold S m fw Spheres micrometers
35
8 0 7C 6 0 5 0 40 3 0 20 10
E 2 5 1 0 = 38
PARTICLE REYNOLDS NUMBER
Figure 6. Fiber diameter vs. particle Reynolds number at onset of tur‘ 4 6 8 IO I2 FLOW REYNOLDS NUMBERS, IN UNITS OF I 0 3
Figure 5. Increase in orifice resistance to flow produced by monofilament fiber in orifice mouth
Empirical Evidence for the Mechanism of Operation Measurement of acoustical pulse amplitude indicates the pulses originate in the capillary entrance. This confirms the work of other investigators (8,9).Using a storage oscilloscope, we have determined that both frequency and amplitude of the pulses are independent of the size of the triggering particle. The frequency of oscillation is solely a function of inlet geometry and may be readily calculated from the length of the inlet section as though it were a closed end organ pipe, Le., 1/4 wavelength resonant cavity: length of inlet, cm 7.1 11.6 17.3 26.2 63.0
resonant frequency, Hz obsd calcd 1207 1211 714 741 476 497 313 328 138 133
Linear regression between threshold diameter and flow Reynolds number shows that a linear relationship exists between threshold diameter and Reynolds number. The acoustical particle sizing device fails to count a t flow Reynolds numbers below 4000, which is the classical transition point between turbulent flow and transitional flow. In addition, the apparatus counts but fails to provide size discrimination for particles with diameters larger than 80 pm. Particles larger than 80 pm would require critical flow Reynolds numbers below 4000 if they were to be sized. Monofilament nichrome and tungsten filament wires were inserted into the capillary of the acoustical element to simulate the presence of a particle. The wires passed completely through the center of the capillary and were held taut by a weight suspended from the end of the wire in the exit chamber. As the wire did not significantly change the cross-sectional area of the capillary, any increase in pressure drop across the capillary over reference flow conditions has been attributed to increased turbulence. Significant increases in flow resistance were observed when the wire was inserted into the capillary and the flow Reynolds number exceeded a size specific critical Reynolds number, Figure 5. The critical Reynolds number for each wire diameter corresponds to the threshold Reynolds number for a spherical particle with a diameter the same as the wire. Particle Reynolds numbers (based on wire diameter) were computed for each of the wires a t the flow Reynolds number a t which the flow resistance increased most rapidly, Figure 6. Criticality occurs a t a particle Reynolds number in the range of 100-500, which agrees with the theory
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Environmental Science & Technology
bulence
of obstruction-induced turbulence (19). Extrapolation of the data in Figure 6 to a particle Reynolds number of “zero” yields a minimum detectable diameter of 4.7 pm, which is in agreement with the observed detection ( 4 ) limit for acoustical particle counters (5 pm).
Conclusions Passage of an aerosol particle through a specially designed orifice can produce an audible acoustical pulse if a critical air flow Reynolds number is exceeded in the capillary of the special orifice. The critical Reynolds number is specific for each size particle. Determination of particle counts a t “n” different Reynolds numbers can be resolved into an “n”-point particle size distribution. Acoustical particle sizing devices are rugged, compact, and are expected to cost an order of magnitude less than direct reading light scattering particle size analyzers. Wide applications of acoustical particle sizing devices to pollen counting, industrial hygiene, air pollution, clean room monitoring, and industrial process control are envisioned. Literature Cited (1) Chemical Corps, Cheniical Corps Biological Laboratory Contract DA-18-064-CML-2296,Quarterly Reports, 1952-1955. ( 2 ) Langer, G., J . Colloid Sci., 20,602-3 (1965). (3) Langer, G., U.S. Patent No. 3 434 335, March 25,1969. (4) Langer, G., Staub-Reinhalt Luft, 28 (9), 13-4 (Sept 1968). ( 5 ) Langer, G., Res. Dev. Ind., 40-2 (June 1963). (6) Hofmann. K. P.. Mohnen. V.. Staub-Reinhalt L u f t . 28 (9). 15-20 (Sept 1968). (7) Lanper. G., Powder Technol., 2.307-9 (1969). (8) Scariett, B., Sinclair, I., Part. Size Anal., Proc. Conf., 393-403 (1975). (9) Sinclair, I., et al., Part. Size Anal., Proc. Conf., 1970, 61-71 (1970). (10) Hemenwav. D. R., Ph.D. Thesis, DeDartment of Environmental Sciences and Engineering, Universitiof North Carolina, Chapel Hill, N.C., 1974. (11) Laneer. G.. Powder Technol.. 6.5-8 (1972). (12) Rei;, P. C., Burgess, W. A.,’Am. Ind. Hyg. Assoc. J., 123-38 (March-April 1968). (13) Karuhn, R. F., Part. Technol., Proc. Int. Conf., l s t , 1973, 202-7 (1973). (14) Langer, G., J . Appl. Meteorol., 12,1000-11 (1973). (15) Langer, G., et al., J. Appl. Meteorol., 17,1039-48 (1978). (16) Cadle, R. D., et al., Arch. Meteorol. Geophys. Bioklirnatol., Ser. A , 28,l-10 (1979). (17) Neame, K. D., Homewood, C. A., “Liquid Scintillation Counting”, Wiley, New York, 1974, pp 115-28. (18) Blevins, R. D., “Flow Induced Vibration”, Van Nostrand Reinhold, New York, 1977, p 14. (19) Schlichting, H., “Boundary Layer Theory”, 6th ed., McGrawHill, New York, 1966, pp 509-15. Received for review September 4 , 1979. Accepted April 4, 1980
