Table I. High-Volume and Personal Sampling Correlation Particulate concentration, mg/m3
Clean laboratory Sample 1 Sample 2 Sample 3 Outside industrial Sample 1 Sample 2 Inside industrial Sample 1 Sample 2 Sample 3
High-volume sampler
Personal monitor
0.051 0.050 0.037
0.049 0.038 0.032
0.073 0.079
0.076 0.089
0.80 0.55 0.43
0.77 0.57 0.42
-
values were obtained. It was these “dry” weights that were then used to calculate the particulate concentrations. Weight loss curves for several membrane filters prior to sampling are shown in Figure 3. Different percentage weight losses for the same area are illustrated because of differences in humidity in the area where the membranes were stored prior to use. After sampling, the particulate samples lose moisture in the dry weighing chamber depending on their average particle sizes and chemical nature. Figure 4 shows the weight loss curves for the three types of samples-those taken in a clean laboratory area, outside air in an industrial area, and inside a n industrial plant where oil mist is the predominant contaminant. As might be expected, the sample having the smallest average particle size desorbed the highest weight percent of moisture. The clean atmosphere sample was composed of small (0.1-1 p ) dust and soot particles and lost almost 70% of its original weight. The samples taken inside a n industrial plant, however, were composed of $O-80% oil mist which appeared to be hydrophobic, permitting the adsorption of only 20-3070 moisture. The samples taken outside a n industrial plant were generally larger in particle size (0.1-30 p ) and, therefore,
intermediate in their water adsorption capabilities, desorbing 35-45% of their total weight. Figure 5 is a compilation of photomicrographs showing typical particulate samples taken in the three areas on the high-volume glass fiber filters. As can be seen, the particle size of the clean laboratory sample is very small. In comparison, the inside industrial sample looks fairly clean, although it is approximately ten times the weight of the clean sample because of the difficulty in distinguishing the oil film on the industrial-sample filter. Table I shows typical particulate concentrations that have been obtained in the three areas by the two methods-high-volume sampling and personal monitoring. Correlation between the two sampling methods is generally good for the types of atmospheres studied. Experience has shown that the degree of correlation appears to depend on proper compensation for moisture adsorption on and the care in handling of the membrane filters where very small weight gains (0.1-3 mg) are involved and large errors can occur. The possibility exists that certain atmospheres could cause noncorrelation between the two sampling methods. However, correlation has continually been good for those atmospheres of interest. Conclusions Correlation between the two methods of particulate sampling, high volume and personal monitoring, for the types of atmospheres sampled can be obtained if proper techniques are used. Compensation for moisture adsorption on personal samples and care in handling the small membrane filters appear to be the two main correlation determining factors. Literature Cited (11Environmental Protection Agency, Fed. Regist., 36 (84) (April 30, 1971). (21 U.S. Department of Health, Education and Welfare, National Institute of Occupational Safety and Health, “Industrial Hygiene Measurements Course Manual,” Course No. 550. Cincinnati, Ohio, February 1973.
Receiced f o r reaieu: S e p t e m b e r 14, 1973. Accepted May 2,1973
CORRESPONDENCE
Capture of Aerosol Particles by Spherical Collectors SIR: We were interested in the calculations by H . F . George and G. W. Poehlein [Enczron Scz Techno!, 8 (1). 4&9 (1974)] on the combined influence of inertial and electrostatic forces on the collection efficiencies of aerosol particles on spherical collectors, since we have recently completed similar computations ( 1 ) . Our results do not agree in detail with those presented in Figures 4 and 5 of George and Poehlein’s paper, however, and we have examined George’s thesis (2) to determine the possible reasons for the disagreements. We have used the letter “a” to differentiate our same numbered figures from those of George and Poehlein. First, examination of the computer program used by George reveals t h a t , in our judgment. inadequate criteria were used for terminating calculations of particle trajectories in the electrostatic force case. leading to incorrect
evaluation of the limiting trajectory for collection. In the logic used, if the particle crosses the centerline (due to inertia) on the downstream side of the collector, it is considered that the particle will ultimately be collected and the numerical integration is stopped. Also. if the particle reaches a distance of 0.75 collector diameters ( D ,) beyond the center of the collector without having crossed the centerline, it is considered t h a t the particle will never be collected and the integration is stopped. T h a t these criteria are inadequate can readily be seen from the two trajectories computed by Nielsen using the potential fluid flow model and shown in Figure l a . In one case the particle crosses the downstream centerline without being collected, and in the other the particle reaches a distance of 0.75 I), beyond the center of the collector without having yet crossed the centerline and is collected. For the case in Volume 8 , Number 8 , August 1974
767
which the actual limiting trajectory crosses the centerline a t a distance of less than 0.75 D , downstream, using these incorrect conditions will result in a limiting trajectory that crosses the centerline at an exact distance of 0.75 D , downstream. This results in a value of the collection efficiency t h a t is too large. Likewise, for the case in which t h e actual limiting trajectory extends farther than 0.75. D , downstream without crossing the centerline, the use of these conditions will give a value of the collection efficiency that is low. Second, the trends shown by the smoothed curves in Figures 4 and 5 are somewhat misleading, since the curves have been developed from very few calculated efficiencies. Figure 4 is based on nine calculated efficiencies over three values of the inertial parameter 9 ,and Figure 5 is a crossplot of the smoothed curves of Figure 4. Third. t h e limiting case of \I/ = 0 in Figure 4, which seems to play a n important part in George and Poehlein's construction of the smoothed curves for 9 # 0, is a n inaccurate reproduction of the results of Kraemer and Johnstone ( 3 ) . The analytical solution for the collection effiD , is E = - ~ K E , ciency E for the case \I/ = 0 and D , where K L is the coulombic force parameter in Kraemer and Johnstone's notation,
which is nearly identical to ES in George and Poehlein's
paper. This result was obtained by Nielsen for the potential flow case. Kraemer and Johnstone had obtained this result for uniform flow in the limit of very large collection efficiencies, and earlier, Whipple and Chalmers ( 4 ) obtained the same result for Stokes flow. Nielsen has shown t h a t not only is the collection efficiency E t h e same for the three flows, but so is the local deposition density on the collector. Figure 4a is a reproduction of Figure 4 in which we have indicated the points computed by George and Poehlein and the analytical solution for the limiting case of \If = 0. I t should be noted that their curves for constant q/ do not approach the assumed asymptote for 9 = 0 as - K L becomes large. Although ES is named as the abscissa in Figure 4, we have not been able to tell from the thesis whether Equation 16 of the paper was used to calculate E S , or if Kt, was used instead. We have assumed that K E was actually used ( R = 0), although the correction to Figure 4a would be small, since K E = ES (1 where R = D,/D,. The correction factor has the values 1.21, 1.02, and 1.06 for \I/ = 0.117. 1.17, and 11.7, respectively. Fourth, the mathematical models used to calculate the electrostatic forces between t h e particle and collector are different for George and Poehlein than for our calculations. Whereas George and Poehlein used the method of images for conducting spheres, we used only the coulombic force contribution. Table I is a compilation of the characteristic parameters (Kraemer and Johnstone's nota-
+
A D
0.75
0,
-0.01
IGEOISE)
Curve 1 (solid line) IS the analytical solution for 9 = 0. Curves 2-5 are thosedrawn b y G e o r g e a n d Poehlelnfor \it = 0. 0.117, 1.17, and 11.7
-10.0
Figure 4b. Collection efficiency in potential flow as function of K E for various Q , computed b y Nielsen
-
Figure 4a. Collection efficiency in potential flow a s function of K E for various Q, computed by George and Poehlein
- 1 .o
-0.1
KE
'.
CALCULAT IONS OF N I E L S E U
w z
Environmental Science & Technology
.r=l'.'
4
Figure l a . Examples of particle trajectories computed by Nielsen that contradict George and Poehlein's criteria for particle collection. Potential fluid flow was used for these examples
768
C A L C b L A I l O N S OF V I E L S E N v=0.117 !GE3RGEl v = 1 . 1 7 !';EO?SE)
10
Y
Figure 5a. Collection efficiency in potential flow as function of for various K E , computed by Nielsen (solid lines) and by George (dashed lines)
Table I. Estimated Ratios of Induced Charge Force Parameters to Coulombic Force Parameter
* 0.117 1.17 11.7
Values correspond to the calculations by George and Poehlein. Nomenclature I S that of Kraemer and Johnstone (except for K l ( I * ) ) .Also included are ratios of gravitational to inertial parameters for the three values of Kv/KI
1.0 10 1.0
x x 10-4 x lo-'
Kr K I
K I I",/Ki
0.20 0.02 0.064
1 . 4 X lo-? 1 . 4 x lo-. 4.6 x
G/*
8.9 X IO-' 8.9 X 1 0 P 8.9 X 10-j
tion) for t h e image charge forces using George and Poehlein's values for particle and collector size and assuming the same fraction of maximum charge for particle and collector. In this table, t h e ratio of charged particle image force parameter to coulombic force parameter is
two sets of results. From Figure 4b it can be seen that for constant \If, the efficiencies calculated by George a n d Poehlein are generally higher t h a n ours. especially for large 1' ' a n d large - K E . T h e trend in differences is more obvious in Figure s a , where their results are much higher than ours whenever t h e effect of particle inertia begins to dominate over the influence of t h e electric force. In all cases. we are able t o explain qualitatively t h e differences in terms of the inadequate criteria described above for determining whether a particle t h a t has passed t h e collector will ultimately be collected. Our results presented here and those for several other electrostatic force and flow situations will be presented in complete form in the near future.
Achnocc iedgment We would like to t h a n k H. F. George a n d G . W. Poehlein for several helpful discussions and for providing additional unpublished information.
the ratio of charged collector image force parameter to coulombic force parameter is
Note A d d e d in Proof: Further d a t a provided by Poehlein indicate t h a t -KI. should indeed replace E S in Figures 4 and 5 , a s we had assumed, and t h a t some entries in Table I should be adjusted for certain computer runs.
and the ratio of the next higher order mutual interaction term (involving Q1&) to the coulombic term is
Literatitre Cited
The only noncoulombic term of possible significance in Table I is for t h e charged collector image force, which falls off with distance as r-5; b u t for 9 = 0.1, t h e limiting trajectory lies far away from the collector. and t h e term should be negligible. Consequently. we would expect that the method of images and the coulombic formula would give nearly identical results. Finally, tabulated results in the thesis indicate that gravitational forces were included in the calculation of particle trajectories in the electrostatic case, whereas we did not include them. The appropriate parameters are listed in Table I. The only case where the influence of gravity could be significant is for t h e low value of 9.In this case the electrostatic force dominates when G is small, as can be inf'erred from the analytical result for \I, = 0 and G > 0. E = -4K~;,'(1 - G ) . Figure 4b presents the results of our calculations in the same form as Figure 4. Included for comparison are t h e calculated results of George and Poehlein. T h e values of \I/ shown are t h e closest available to those used by George and Poehlein. T h e mechanism of interception was not included either in our calculations or those by George and Poehlein for the electrostatic force case. In Figure 5a we have presented our results in the same form as Figure 5 and have reproduced t h e curves from Figure 5 for comparison. Clearly, fundamental differences exist between these
(1) Nielqen, Kenneth A., M S thesis, Iowa S t a t e University, 1974. 1974 (2) George, Herman F., MS thesis, Department of Chemical E n gineering, Lehigh University, 1972. (3i'Kraemer. H . F . . .Johnstone. H. F., I n d . Eng. C h e m . , 45 (12). 2426-34 (1955). 14) W h i m l e . F. J . W.. Chalmers. .J. A , . Quart. ./. Ro\. M e t e o r o l Soc., 'id, 103-19 (1944).
Received for rerieu March 11, 1974. Accepted M a y 20, 1974. T h i s work mas supported by the Engineering Research Institute of Ioua S t a t e Unicersity.
Kenneth A. Nielsen James C. Hill"
Department of Chemical Engineering a n d Nuclear Engineering a n d Engineering Research Institute Iowa State University Ames. Iowa 50010
SIR: Xielsen and Hill clearly demonstrate that the convergence criteria used in our calculations were not adequate for the computation of some particle trajectories.
Gary Poehlein Department of Chemical Engineering Lehigh University Bethlehem, Pa. 18015
Volume 8 . Number 8 , August 1974
769
