(5) Zbid., TN 3410, 1955. (6) Brun, R. J., Gallagher, H. M., Vogt, D. E., Zbid., TN 3047, November 1953. (7) Zbid.. TN 3155. Julv 1954. (8) Brun, R. J., Lewis: ‘W., Perkins, P. J., Serafini, J. S.,Zbid., Rept. 1215, 1955. (9) Davies, C. N., Peetz, C. V., Proc. Roy. SOG.(London), A234, 269-95 (1956). (10) Dorsc‘h, R.’G., Brun, R. J., Natl. Advisory Comm. Aeronaut. TN 3153, 1954. (11) Dorsch, R. G., Brun, R. J., Gregg, J. L., Zbid., TN 3099, 1954. (12)Dorsch, R. G., Saper, P. G., Kadow, Ch. F., Zbid., TN 3587, November 1955. (13) .Fuks, N. A., “The Mechanics of Aerosols,” pp. 33-5, Acad. Sci. U.S.S.R., Moscow, 1955 (in Russian). (14) Guibert, A. G., Janrsen, E., Robbins, W. M., Natl. Advisory Comm. Aeronaut. R M 9A05, February 1949. (15) Langmuir, I., J. Mrteorol. 5, No. 5, 175-92 (1948). (16) Langmuir, I., Blodgett, K. B., U. S. Army Air Force Tech. Rept. No. 5418, Feb. ’L9, 1946; U. S. Dept. Commerce Publ. PB 27565 (February 1946). (17) Lewis, W., Brun, R,. J., Natl. Advisory Comm. Aeronaut. TN 3658, 1956.
(18) Levin, L. M., Doklady Akad. Nauk S.S.S.R. 91, No. 6, 1329-32 (1953). (19) Millikan, R. A., Phys. Rev., Ser. 222, 1-23 (1923). (20) Ranz, W. E., Dept. Eng. Research, Penn. State Univ. Bull. No. 66; U. S. Public Health Serv. Research Grant S-19, Tech. Rept. No. 1, December 1956. (21) Ranz, W. E., Univ. Ill., Eng. Expt. Sta. Tech. Rept. No. 3, March 31, 1951. (22) Ranz, W. E., Wong, J. B., IND.END. CHEM.44, 1371-81 (1952). (23) Richardson, E. G., ed., “Aerodynamic Capture of Particles,” Pergamon, London, 1960. (24) Sell, W., Forsch. Gebiete Zngenieurw. 2, Suppl. No. 347 (August 1931). (25) Taylor, G. I., Gt. Brit. Aeronaut. Research Council, Repts. and Memo. No. 2024 (probably 1940). (26) Weyssenhoff, J., Ann. Physik. 62, No. 9, 1-45 (1920). ( 2 7 ) Wong, J. B., Ranz, W. E., Johnstone, H. F., J . Appl. Phys. 26, NO.2, 244-9 (1955). RECEIVED for review September 22, 1961 ACCEPTED August 17, 1962 Work sponsored in part by Arnold Engineering Development Center, Tullahoma, Tenn., under Contract No. AF 40(600)-710.
COLLECTION EFFICIENCY OF JET IMPACTORS A T REDUCED PRESSURES S. C . S T E R N , H . W . Z E L L E R , A N D A . I . S C H E K M A N ’ Electronics Group, General Mills Znc., Minneapolis, Minn.
The collection (efficiencies of circular and rectangular jet impactors have been determined a t reduced pressures using monodispersed, solid, homogeneous aerosols. Variables include particle size, jet-to-slide spacing, jet size, jet velocity, and pressure. The data are compared with theoretical and experimental results b y other investigators. Areas of agreement and disagreement are discussed. The experiments verify the significant role of the Cunningham correction for slip a t reduced pressures.
CHARACTERISTICS of particulate sampling devices of the jet impingement type have been studied theoretically by Davies and Aylward ( 1 ) , Ranz and \Yong ( 6 ) , and Einbinder (2). They developed theoretical solutions for the aerosol collection efficiency of rectangular and circular jets based on approximations of the velocity field in the region where the aerosol jet stream impinges on a n infinite plane. If these approximations are realistic-to the extent that they properly describe aerodynamic flow through the jet, particle trajectories, and impaction on an infinite plane-performance of jet impactors may be predicted. These investigators have shown that collection efficiency of
ERFORM.IASCE
Present address, Information Science Center, Collins Radio Co., Newport Beach, Calif.
either a circular or rectangular jet is a function of a nondimensional inertial parameter IC. defined as :
The Cunningham correction for slip, based on Millikan’s (4)data, is defined aq: C = 1
+ DP - 1.23 + 0.41 d - 0 . 4 4 D p / h ) ] 2x [
(2)
+
Physically, the inertial parameter is the ratio of the stopping distance to a characteristic dimension D ifor a particle moving in a fluid with a relative velocity of V. In some cases, a comparison of the theoretical solutions of these investigators show3 disagreement in the functional relationship between collection efficiency and the inertial parameter $. The differences are illustrated in Figure 1, where solutions of Ranz and Wong, Einbinder, and Davies and Aylward for a rectangular jet are compared. The extent VOL. 1
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INERTIAL PARAMETER,
Y
Figure 1. Comparison of theoretical collection efficiency curves for rectangular jet impactors a t large clearance ratios A.
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Figure 3. Combined experimental efficiency data for rectangular impactors A. B.
Einbinder
S / D , = 1.0; C = 1.6 to 2.4 S / D , = 0.3 to 0.51 C = 1.6 to 15.2 0 0.56 micron 0.81 micron A 1.17 microns
B. Ranz and Wong C. Davies and Aylward
of their disagreement depends mainly on the nature of the flow field assumed by each investigator and consequently on the accuracy of their calculations for particle trajectories. I t is evident that there is no agreement on the characteristic value of +l'* for which the collection efficiency is equal to 50%. Carefully designed and controlled experiments have been conducted to determine the validity of these impaction theories. Kotable are the studies of May ( 3 ) , Ranz and Wong ( 6 ) , and Mitchell and Pilcher (5). These tests were generally conducted under conditions where the Cunningham correction for slip was small. May employed a cascade-type rectangular jet impactor and a heterogeneously sized liquid aerosol of dibutyl phthalate. Mitchell and Pilcher used polystyrene beads and a liquid dibutyl phthalate aerosol to investigate the effect of slide separation from the nozzle orifices of circular jets. Ranz and \\Tong tested both rectangular and circular
ANEROID BAROMETER
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MANOMETER r\
Experimental
SAMPLE CONTROL
-u
ROTAMETER
Figure 2. Test apparatus used to determine collection efficiencies of impactors a t reduced pressures 274
impactors using a liquid glycerol aerosol dispersed from a La Mer generator. The research described in this article had three objectives: to obtain experimental collection efficiencies for rectangular and circular jet impactors for a series of solid spherical homogeneous aerosols under conditions where the Cunningham correction for slip is significant (this situation exists when impaction occurs a t reduced pressures) : to compare the experimental results with those reported in the literature; and to compare the results with existing theory. These results were expected to reveal any significant difference between the collection of solid and liquid aerosols and to determine the validity of existing theories for jet impaction a t reduced pressures. The ability to conduct tests over a range of homogeneous particle sizes a t conditions where Cunningham correction for slip is significant permitted high collection efficiency tests to be made with jet velocities below the speed of sound. Previous investigators (7) found that when jet velocities approached the speed of sound, erroneous data were obtained from re-entrainment of particles or from fragmentation of impacted particles.
l&EC FUNDAMENTALS
Test Apparatus. The test apparatus developed in this laboratory was unique because impactor collection efficiencies could be determined at low pressures. The equipment shown in Figure 2 includes these major components: an aerosol generator, a wind tunnel section which housed an impactor test stand, a vacuum system, and a light-scattering microphotometer to assay aerosol concentration. The aerosol generator was a modified all-glass, filtered, air-operated Vaponefrin nebulizer which disperses a liquid aerosol from a n aqueous suspension of polystyrene spheres. Monodispersed homogeneous polystyrene aerosols are produced by the subsequent evaporation of those liquid droplets that contain a single polystyrene particle. The chance of two
or more particles bei.ng present simultaneously in a single evaporating water dro.plet was reduced by diluting the initial concentrated polystyrene latex suspension (Dow Chemical Co.) with specially prepared and filtered ”particle-free” water. T h e maximum concentrations used ranged from 1 ml. of concentrated 1.8-micron polystyrene latex suspension per 100 ml. of water to about 0.03 ml. of the 0.56-micron latex suspension per 100 ml. of wat’er. These concentrations were selected because the modified Tiaponefrin nebulizer disperses a liquid aerosol having a n experimentally measured mass median diameter of about 4 niicrons. When the size distribution is taken into account? less than 10% (by mass) of the aerosol droplets will contain more than one polystyrene bead. Aerosol size was checked by electron microscopic examination, and monodispersion was checked by microscopic examination of impacted aerosol samples collected during short runs of a few seconds. The wind tunnel test facility, shown in Figure 2>was fabricated from t\ro pieces of aluminum tubing. The upstream section contained a Stairmand diffuser and a n axially centered aerosol sampling tube positioned 10 cm. from the test fixture. The second section of the tunnel had a n axially centered aerosol sampling tube located 10 cm. downstream from the test section. The impactor under test was located between the two sections of the wind tunnel. The test facility was designed so that a single impactor, two impactors in series, or two impactors in series backed up by a filter could be tested for collection efficiency. As shoirn in Figure 2! five pressure taps were located in the wind tunnel sections, One tap was connected to a Wallace and Tiernan microbarometer which measured absolute pressure in the \rind tunnel. The other pressure taps \rere connected to a differential manometer to measure pressure drops across either of the impactor stages or the filter. The vacuum system served two purposes. It was used to reduce and maintain a desired air density in the wind tunnel and to provide air flow through the wind tunnel section. .4n auxiliary vacuum system was used to bleed aerosol samples upstream and downstream of the impactors into a light-scattering microphotometer. Procedure. T h e wind tunnel was first evacuated to a desired reduced pressure, and a n aerosol was generated by admitting dry filtered air into the nebulizer. Sampling valves to the photometer were then opened, and the air inlet valve and sample control valve were adjusted so that the vacuum system maintained both desired reduced pressure and air flow through the tunnel. At least three efficiency tests were made for each particle size ,and free stream velocity. Each test required about 3 minutes. During this period, aerosols upstream and downstream from the jet impactors were passed sequentially through the quartz window aerosol cell that was positioned in a dark chamber in the light-scattering photometer. I n computing impactor efficiency from the output of the photomultiplier, the expansion of gas on the downstream side of the jet caused by pressure drop through the impactor was taken into consideration. Jet Impactors. Nine rectangular and circular jet impactors were studied to determine the relationship between collection efficiency ij and the inertial parameter $. Physical dimensions of the critical parts of these impactors are given in Table I . The interior dimensions of impactors 2 through 5 were similar to those tested by May. The remaining impactors had inlet diameters of 15 cm. and over-all lengths of approximately 20 cm. Collections were made on either glass slides or circular Plexiglas disks coated with Dow Corning
1 2
Table 1. Jet Dimensions TY@ D , , Cm. L , Cm. Rectangular 0,224 11 . 2 Rectangular 0.083 0.578
3 4 5 6
Rectangular Rectangular Rectangular Circular
0.109 0.147 0,195 1.05
7
Circular
1.15
8
Circular
1.33
9
Circular
1.43
KO.
LID, 50
7 7 7 7
0.755 1.03 1 ,37
SID, 0.50 1 .O 0.47 0.47 0.34 0.31 3.0
n
33
3.0 0.33 3.0 0.33 3.0 0.33
high-vacuum silicone grease, The spacing between the collection surface and the jet opening was adjustable and could be varied from 0.3 to 3 times the value of D,. T h e large rectangular impactor and the four circular impactors were designed for flow rates of about 750 liters per minute of ambient air a t atmospheric pressures bemeen 246 X lo3 and 13 X lo3 dynes per sq. cm. The small rectangular jets were designed for the same pressure range, but with a flow rate of 12.5 liters per minute. As a result of these design criteria, air velocities through the jets varied betLveen 5 X lo3 and 1.8 X lo4 cm. per second, with most tests being conducted a t velocities between 5 X IO3 and 1 X lo4 cm. per second. I n practice, tests \\’ere conducted a t approximately 246 X lo”, 187 X lo3: 71 X lo1, and 27 X lo3 dynes per sq. cm. Results and Discussion
Results of experiments with the five rectangular impactors have been pooled and are shown in Figures 3 and 4. Some scatter in the data was experienced. However. a n analysis
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&
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Figure 4. Combined experimental efficiency data for circular impactors A. B.
S/D, = S/D, = 0 W
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Stern, Zeller, and Schekman, experimental, S / D , = 1.0 Ran2 and Wong, theoretical, S / D i 1.O May, experimental, S / D , = 1.0 D. Ranz and Wong, experimental, S / D , = 2 to 3 E. Davies and Aylward, theoretical, S / D j = 0.35 F. Stern, Zeller, and Schekman, experimental, S/D, = 0.3 to 0.5 G. Davies and Aylward, theoretica!,S/D, = 0.64
>
B. C.
of the data revealed that the scatter could not be related in any systematic way to particle size, test pressure, or other variables. The circular impactors, because of their relatively greater design flow rates, required large amounts of make-up air, resulting in dilute test aerosols. The signal level in the 1ight.scattering photometer thus obtained was, in many instances. only slightly greater than the residual background level, causing a subsequent loss of precision in the data. Sufficient data were obtained to define the performance of both types of impactors a t large and small clearances. The fact that the data obtained at different pressures and with a variety of particle sizes can be accommodated by a single curve is rather significant. It justifies the existence of a functional relationship between f j and $, and illustrates the major dependence of $, and in turn f j , on the Cunningham correction for slip C. Variation of C with particle size for a given pressure is shown in Table 11. Because of the increase in C with reduction in pressure, collection efficiency increases for any given particle size a t constant velocity.
Table II. Calculated Values of C a s a Function of Particle Size and Pressure at 22’ C. C
D,,Microns
Sq. Cm.
7.8
7.77
0.87
0.56
x x x x
1.38 1.50 2.47 5.19
1.60 1.81 3.35 7.58
1.90 2.22 4.50 10.6
2.35 2.83 6.18 15.1
246 187 71 27
103 103 103 103
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Yk
Figure 6. Comparison of circular impactor data with theoreiical and experimental results by other investiga tors A.
B. C. D.
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Figure 5. Comparison of rectangular impactor data with theoretical and experimental results b y other investigators A.
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>
Ranr and W t n g , theoretical, S / D , 1 .O Siern, Zeller, and Schekman, experimental, S / D , = 3.0 Ranz and Wong,experimentaI,S/Dj = 2 to 3 Stern, Zeller, and Schekman, experimental S/D, = 0.33 Mitchell and Pilcher, experimental, S / D , = 0.375, small slide-to-wall clearance Mitchell and Pilcher, experimental, S/D, = 0.375, large slideto-wall Clearance
The data in Figures 3 and 4 are compared directly with the theoretical and experimental result4 of other investigators in Figures 5 and 6. Principal areas of agreement and disagreement are the following: The data for rectangular impactors at large clearance ratios agree very well with Ranz and LSong’s theoretical predictions. However, these same data and May’s experimental data show greater collection efficiencies for equal values of when compared with Ranz and Wong’s experimental results. The data for rectangular impactors at small clearance ratios agree with theoretical predictions by Davies and Aylward. Experimental data for rectangular impactors at small clearance ratios are not available through normal research channels. Results reported here, therefore, represent new data. Considering the scatter of the data. these results agree with Ranz and LYong’s experimental and theoretical data for circular impactors a t large clearance ratios. In addition, these data are in agreement with the results of other investigators who state that circular jets are more efficient collectors than rectangular jets for equal values of 4’ z. The data for circular impactors at small clearance ratios agree with Mitchell and Pilcher’s results. Although no theoretical predictions are available for comparison, Einbinder (2) has indicated that increasing collection efficiency can be expected with decreasing clearance ratio. These data, in general, tend to exhibit higher collection efficiencies for identical values of $Az than those reported by other investigators, although some of the differences can be accounted for by the spread of the data. Reasons for discrepancies are not known but may be related to differences in collector surface treatment and differences in the adhesion or cohesion of liquid and solid particles after impaction. Particle bounce and the re-entrainment of collected material may be a problem, particularly when the collection surface has not been treated with some “sticky” subqtance. Thomas and Lapple ( 8 ) have indicated that the
length of the sampling interval is critical because small deposits of material on the collection surface may cause increased collection efficiency through interception effects. I n addition to the problems mentioned, variations of the basic flow pattern because of boundary-layer growth and changing velocity profiles in the impactor jets might be expected a t reduced pressures. These phenomena are particularly evident when making pressure drop measurements because the relative pressure differential across a nozzle must be increased as the absolute pressure is decreased to maintain a constant-volume flow rate. For the range of pressures studied and the impactor configurations tested, however, examination of the data has not revealed any significant variations in collection efficiencies not already taken into account by the inertial parameter. This problem, nevertheless, should be considered in any atteimpt to use published data as a basis of predicting the performance of impactors with small jet dimensions a t pressures less than those reported here. Nomenclature
C = Cunningham slip correction, dimensionless D, = diameter of round jet or width of rectangular jet, cm. D, = diameter of aerosol particle, cm. L
= length of rectangular jet, cm.
S V
= impactor jet-to-slide distance, cm = velocity of aerosol particle in jet, cm./sec.
Z ij
= mean molecular velocity, cm./sec. = total collection efficiency, %
h
= mean free path length,
P
= = = =
2/J =, cm. PV
p p,
+
viscosity, grams/(cm.) (sec.) air density, grams/cc. particle density, grams/cc. inertial parameter, dimensionless
literature Cited
(1) Davies, C. N., Aylward, M., Proc. Phys. SOC. (London) B64, 889 (1951). (2) Einbinder, H., Battelle Memorial Inst., Tech. Rept. BMI 2409-1,Contract DA-18-064-CML-2569, March 1955. (3) May, K. R., J. Sci. Znstr. 22, 187 (1945). (4) Millikan, R. A.,Phys. Rev. 22, 1 (1923). (5) Mitchell, R. I., Pilcher, J. M., IND. ENG.CHEM.51, 1039 (1959). (6)’ Ranz, W. E., Wong, J. B., Ibid., 44, 1371 (1952). (7) Schadt, C., Cadle, R. D., Anal. Chem. 29, 864 (1957). (8) Thomas, D. G., Lapple, C. E., A . I. Ch. E. J . 7, 203 (1961). RECEIVED for review September 11, 1961 ACCEPTED September 12, 1962 Research sponsored by Division of Biology and Medicine, U. S. Atomic Energy Commission under Contract A T 11-1-401.
METHOD FOR RAPID DETERMINATION OF DIFFUSION COEFFICIENTS Theory and Application J .
CALVIN
GlDDlNGS AND SPENCER
L. SEAGER
Department of Chemistry, Lrniniversily o f Utah, Salt Lake City 12, Utah
A method similar in operation to chromatographic techniques has been theoretically and experimentally extended for measuring a wide range of diffusion coefficients. Design of the experimental apparatus is guided b y chromatographic theory. For very slow diffusion processes, such as those occurring in liquid systems, it is possible to magnify the over-all diffusion effect so that it is measurable after a very short period of time. The experimental work deals with gaseous diffusion coefficients measured a t various flow velocities, concentration levels, etc. Where data are available for comparison, agreement with other methods is satisfactory. Although the potential speed of the method has not yet been developed, it appears that diffusional ancilysis b y this method is already much more rapid than b y most conventional methods of similar accuracy.
method for mearsuring gas phase diffusion coefficients (76). T h e apparatus used consisted of a commercially available gas chromatography unit, with an empty tube replacing the packed column. The theory applying to the system is a special case (73) of a more general theory (7, 70, 7 7, 74) of chromatography, although Taylor (26) first derived the special case used here in 1953. The extension of the method to a wide range of diffusion measurements, involving both gas and liquid phases, is highly feasible in view of the aforementioned general theory. NEW
A was proposed in am earlier communication
Further extensions of the method are discussed here and additional experimental results on gas phase systems are reported. The principal feature of the present method is the speed with which diffusion measurements can be made. Although this paper reports the more general characteristics of the method, and no attempt has been made to increase speed, it has nonetheless been found possible to take and interpret the data for 200 separate determinations of the diffusion coefficient ( D ) in 36 hours. Consequently, the compilation of extensive tables of diffusion data should be much more feasible than before. VOL 1
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