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Clogging in nuclepore filters: Cap formation model
ArmspJwic E~iro~z Vol. 12, p. 1797-1802. 0 Pergamon Press Ltd. 1978. Printed in Gr+at Britain.
CLOGGING IN NUCLEPORE FILTERS : CAP FORMATION MODEL K. C. FAN, C. LEASEBURGE,Y. HYUN and J. GENTRY* Department of Chemical Engineering, University of Maryland, College Park, MD 20742, U.S.A. (First received 6 September 1977 and i~~na~~rrn 5 January 1978) Abstract-A theoretical and experimental study of the clogging of nuclepore filters was carried out using mon~is~~e latex particles with argon and methane as the carrier gas. A cap formation model based upon SEM photographs was developed. Using this model calculations of the ctogging rate as a function of time were made. Agreement between theory and experiment was good. INTRODUCTION
Nuclepore filters (NPF) were first produced in 1963 (Fleischer). Since that time they have become ever
more frequently used. In ambient sampling of particulates, the smooth, regular surface of the NPF are much more convenient for electron microscopy (SEM and TEM) than is the porous, twisted structure of membrane filters. Secondly, the regular, uniform pores are more amenable to theoretical calculations than are membrane filters. A number of investigations (Spurny and Lodge, 1972; Husar, 1974; Melo and Phillips, 1974; Liu and Lee, 1976a) have demonstrated the use of NPF in selective sampling. Laboratory measurements have shown that NPF are better suited for the analysis of microbiological aerosols (Spurny and Lodge, 1968b), for studies using X-ray fluorescence (Spumy et al. 1976a), and for the analysis of asbestos fibers in ambient air (Spumy and StGber, 1975; Spumy et al., 1976a), The problem of clogging has been discussed in the literature both for tiber filters and nuclepore filters. Juda employed the Fuchs-Stechkina equation calculating the pressure drop as a function of dust loading for a large number of systems with fiber filters (Juda and Chrosciel, 1970; Juda et al., 1973). Spumy and Lodge (1968a) and Spumy et al. (1975b) proposed a model based on uniform filling of the pores. This model has proved to be successful in a number ofcases, especially when the diameter of the partially clogged pores are calculated from the pressure drop (Fan et al., 1976). In this paper a model based on cap forming (CFM) is derived and compared to experimental measurements. It is found to be better than the UPM (uniform pore filling model) for the cases studied. SEM pictures were found to show that neither model applied all the time DlSCUSSlON
As previously mentioned the UPM model was the * TO whom correspondence
should be sent.
first attempt to explain clogging in NPF. However photographs taken with the SEM indicated that this did not always appear to be the mechanism of clogging. For example, the sequence of photographs in Fig. 1 shows the particles first collecting on the rim of the pore, then forming bridges as the particles collected on one another, and finally closing the pore with a cap. The flow rate in these ex~~ments was 9.91 min- ‘. Monodisperse, latex particles having diameters of 1.01 pm and NPF with a pore diameter of 3.0 pm were used. The particles generated from a Dautrebande type generator at these conditions had a concentration of 800 particles cm-‘. The generator was constructed following the model described by Dautrebande (1962). Argon was the carrier gas and the cross sectional area of the filter face was 5.07cm’. In these pictures three filters were used with the experiments lasting 2,4 and 10min. Recently Mercer (1977) was able to interrupt his experiments and repeatedly examine the same location of the filter at different times. These experiments, also, showed cap formation instead of UPM.
MODEL DEVELOPMENT The basic assumptions used in the model discussed in this paper are as follows: (1) The cap is formed uniformly layer by layer as indicated in Fig. 2; (2) When particles touch the surface of the filter or other particles they adhere together; (3) The cap is assumed to be a sector of a circular pore. The radius of the sector is given by R* = RJ cosa. R. is the radius of the pore and a is the angle between the horizontal and the radius connecting the pore rim and the center of the sector (Fig. 2); (4) Only inertial impaction, direct interception and electrostatic attraction were considered; (5) In this calculation electrostatic forces were accounted for using the method of Zebel (1974a, b). Like Zebel, the Wuest (1954)flow field was assumed. It should be noted that other flow fields such as the one described by Vrentas and Duda (1973) and used by
1797
1798
K. C.
FAN. C. LEASEBURGE. Y. HYUN
and J.
GENTRY
Fig. 2. Diagram of cap formation model.
and V, = 2nR,d,,([R**
- Rf]“.’ - [R* sin a - 0.5 d,])
(3)
The radius of the opening in the cap is designated by R, and is time dependent. The calculational algorithm proceeds as follows : (1) Since R*, a, d,, C, e’, and U. have constant values unaffected by clogging, for a value of X*, V, can be calculated from Equation (2). (2) For an incremental value At, the cap radius is calculated from Equation (3) with V, being given by Equation (1). (3) With the value of R, a trajectory calculation is carried out to find the new value of X* and the iteration of steps l-3 are repeated. (4) The efficiency of collection is determined by the ratio of the area lying outside X* to the total area of the cell. This expression is E = [Rb’ - X*‘]/R:.
(4)
(5) The initial value of R, is R, the pore diameter. Fig. 1. Particle size : 1.Ol pm. Filter : 3 pm.
Parker (1975) could be used without changing the essentials of the model ; (6) The volume of the cap filled in an increment of time can be expressed in terms of the packing density of particles E‘and the flow rate [V,,] through an annulus at the location X* by V, = V, At/&.
(1)
Particles passing through the annulus of thickness d, and radius 27rX* will be collected on the cap. Particles which pass through the parabola (Fig. 2) at values between X* and R, will be cdlected on the face of the filter or on the outer surface of the cap. For a particle concentration C and superficial velocity U,, the expressions for VPand V, are
The models chosen for the electrostatic field (Zebel, 1974a, b) and the velocity field (Wuest, 1954) enter through the trajectory calculation. This equation for the kth component of the spatial coordinate Yis
1
where Fp) is the kth component of the electrical field between the rim of the pore and the particle and U, is the kth component of the velocity. The two parameters are defined by Stk = A’
d* U rlR,
and
Ze=$$ 0
V, = [izd;]
2zX*CU,,d,
(2)
(5)
(7)
0
which are in terms of the particle mobility (B), the
1799
Clogging in nuclepore filters : cap formation model charge on the particle (JE), thecharge per unit distance of the rim of the pore (q) and the gas viscosity (v). Equations (l)-(7) are general and would be applicable for any velocity field that assumes a boundary region of flow undisturbed by the pore. The specific forms for the flow field used in this paper were taken from the literature (Zebel, 1974; Fan, 1977) and are quoted in the Appendix. In Fig. 3, the ex~~mental data for 0.36gm particles are compared with the CFM model and the UPM model The particle concentration was 4000 particles cma3. (The Phoenix photometer was calibrated for each particle size used in the study by collecting a sample at a constant reading of the photometer. The volume sample was known and by counting the particles which were removed by sieving through a NPF, the concentration could be measured.) In the experiment the gas velocity was 74cms-‘. Calculations were run for 16 min. The velocity at any time t was calculated from
I
1.0
U=
N,nR:
where Q is the flow rate and Np the number of pores. Calculations, carried out for Ze = -0.5 and Ze = 0, showed no significant differences. For the 3.0 pm filter, a value of 45” was found to give the best fit whereas a value of 60” gave the best fit for a 5.0pm filter. The smaller the angle, the higher the cap. This model predicts that for larger pores the caps will be flatter. This was in qualitative agreement with SEM. No quantitative data are available for comparison. Agreement between the trajectory calculation and CFM is very good. An analogous calculation for 0.79 ,um particles is shown in Fig. 4. The same angles a were used as for the 0.36gm particles. For these experiments the particle concentration was 1400 particles cmm3. Again the model fits well for short time periods. A possible explanation for the lower collection efficiency observed in the experimental data at longer times for the 3.0pm NPF is that as the opening in the
08
/1
0.7
--
0.36pm particles
UPM CFM
Time, min
Fig. 3. Comparison of CFM, UPM and rn~ur~~~ of coliection eff&eacy during clogging with 0.36pm particles.
-
UPM
--
CFM /
0.9-
3 pm pore
0.8 ,‘I3 0.7 ,
0 0=
/
/
0
D
D
00 v / A
0.5 -
“.‘I 0
Q
0.79 jbrn particles
2
4
6
8
Time,
IO
12
14
I6
min
Fig. 4. Comparison of CFM, UPM and measurements of collection efficiency with 0.79pm particles during clogging. cap becomes smaller, the velocity increases possibly resulting in re-entrainment. It is interesting that the difference between theory and experiment is greatest for the smaller pore size (3.0pm) and occurs sooner for the larger particles. These observations are consistent with the hypothesis suggested above. Comparisons were made with the uniform pore filling model. Because of the time required to fill the first layer, the ef&iency increases at a much slower rate. The semi-empirical equation of Spurny and Madelaine (1971) was used with the UPM model shown in Figs. 3 and 4. For these conditions the equations overestimate the collection efficiency. If a trajectory calculation were used with UPM, the initial value of the efficiency would be the same as pictured for CFM but with an even flatter curve. Although the CFM model was found in the SEM photographs for a majority of the cases studied (Fig. 5 for methane and 3.Opm NPF is typical), it was not universal, as is demonstrated in Fig. 6 where UPF appears to be the dominant mode. The conditions for determining which mode of clogging is dominant have not been resolved. It is interesting to note that in Fig. 5 there are pores without clogging+ Although electrostatic effects have been suggested as a possible explanation, it seems unlikely because of the simulations of particle trajectories (Zebel, 1974; Fan, 1977) and because of the experiments shown in Figs. 7 and 8. These experiments with 0.79ym particles represent the two different cases of charged and neutralized particles. The neutralized particles were passed through a *‘Kr generator while the charged particles were untreated. Qualitative measurements with a rod and cylinder precipitator
1800
Fig. 5. Electron
K. C.
micrograph
showing
FAN, C. LEASEBURGE.Y. HYIJPJand J. GENTK~
typical cap formation.
showed that the latex particles had a considerable residual charge although not as high as reported in the literature (Muhr and Loffler, 1974). The difference of 2.-3 % is within experimental error. Although the flow rate varies as R& the relative mon~is~rsity of the particles could not account for this effect (Caroff er al., 1973). A possible explanation might be the shielding of the pores by the support grid. At first glance the experiments of Mercer (I977) might preclude this explanation. However recent measurements of asbestos fibers in NPF (Gentry and Spumy, 1977) with a special filter holder without a support for the NPF showed that almost every pore had collected fibers. In
Fig. 6. Electron
micrograph
charwing uniform pore liliing.
the absence of more quantitative experiments the inhomogeneity of the deposition remains a mystery.
CONCtUSlON
SEM photographs of latex particles at different times in the clogging of NPF, showed two distinct modes-uniform pore filling (UPM) and the formation of the cap (CFM). In the majority of conditions examined, CFM was the pr~ominant mode. A mode was derived based on the formation of a
1801
Clogging in nuclepore filters : cap formation model
independently by measuring the elevation of the cap above the surface of the filter. Numerical simulations were carried out in which the Zehel model was used to describe the electrical field and the Wuest model was used to describe the flow field. Experimental measurements were in good agreement with the simulation. Numerical calculations using the UPM model did not agree with the data. The trend shown by 01with respect to pore size was in qualitative agreement with SEM. The simulations indicated that electrostatic effects would not make a significant change in the clogging condition. This was in agreement with experiment.
-
Charged
-
Neutralized
Time,
Acknowledgements-K. C. Fan wishes to acknowledge the Minta Martin Foundation, the Computation Center and the Center for Materials Research at the University of Maryland. Y. Hyun, C. Leaseburge and J. W. Gentry wish to acknowledge the support of NSF under Gr. No. 7609381.
min
Fig. 7. Comparison of collection efficiency during clogging for charged and uncharged parttcles. REFERENCES
-
IO-
Charged
0
I 0.1
I 0.2
I 0.3
Neutralized I 0.4
I 0.5
I 0.6
(
drop AP-AP,,(PsI)
Pressure
Fig. 8. Collection efficiency as a function of pressure drop.
sector over the pore. Other than the flow rate and physical properties of the gas, particles and filters, only the variable G(is needed. This value could be checked
Caroff M., Choudhary K. R. and Gentry J. W. (1973) Effect of pore and particle size distributions on efficiencies of membrane filters. J. Aerosol Sci. 4, 93-102. Dautrebande L. (1962) Microaerosols pp. l-22, Academic Press, New York. Fan K. C. (1977) The study of aerosol filtration using model grid filters and nuclepore filters. Ph.D. dissertation, University of Maryland. Fan K. C., Lee J. and Gentry J. W. (1976) The effect of gas composition on the collection efficiency of model grid and nuclepore filters for submicron aerosols. Enuir. Sci. 10. Fan K. C. and Gentry J. (1977) Pressure drop and collection efficiency of NPF as a function of gas composition. Unpublished manuscript. Fleischer R. L., Price, P. B. and Walker R. M. (1963)Tracks of charged particles in solids. Science 149, 383-391. Gentry J. W. and Spumy K. R. (1977) Unpublished data. Husar R. B. (1974) Atmospheric particulate mass monitoring with a B radiation detector. Atmospheric Environment 8, 1833188. Juda J. and Chrosciel S. (1970) A theoretical model of pressure loss increase during the filtration process. StaubReinhalt Luf 30, 196. Juda J., Chrosciel S. and Nowicki M. (1973) The influence of some filter parameters on the pressure loss increase in the filtration process. Staub-Reinhalt Luft 33, 159. LiuB.Y.H. and LeeK. W. (1976)Efficiencyofmembraneand nuclepore filters for submicron aerosols. Enuir. Sci. Technol. 10, 345-350. Melo 0. T. and Phillips C. R. (1974) Aerosol-sire spectra by means of membrane filters. Enuir. Sci. Technol. 8, 67-71. Mercer T. T. (1977) Private communication. Muhr W. and LGMer F. (1974) Elektrostatische Eigenshaften verschiedener Testaerosols. Jahrekongress GAF. Parker R. (1975) A fundamental study of particle deposition onto large pore nuclepore filters. Ph.D. dissertation, Duke University. Spumy K. R., Havlova J., Lodge J. P., Sheesley D. C. and Wilder B. (1975) Aerosol Filtration by means of nuclepore filters : filter pore clogging. hub-Reinhalt Luft 35, 77.
1802
K. C.
FAEI, C. LEASEBURGE, Y. HYUN
Sournv K. and Lodge J. P. t1968al Analvtical methods for ’ determination of aerosols by means of membrane ultrafilters XI. Structural and filtration properties of nuclear pore filters. Co/In Czech. them. Commun. Engl. Edn 33, 3679. Spumy K. R. and Lodge J. P. (1968b) Die Aerosolliltration mit Hilfe der Kernporenfilter. Sruub-Reinhalr Luff 28, 179. 186. Spumy K. R. and Lodge J. P. (1972) A note on the measurement of radioactive aerosols. J. Aerosol Sci. 3, 407-409. Spumy K. and Madelaine G. (197 1) Efficiency measurement of nuclepore filters by means of latex particles. Cohn Czech. them. Commun. Engl. Edn. 36, 2857-2866. Spurny K. R. and Stiiber W. (1975) Asbestos measurements in ambient air. Clean Air 9, 38.-41. Spurny K. R., Stober W., Ackermann E. R., Lodge J. P. and Spumy K. Jr. (1976a) The sampling and electron microscopy of asbestos aerosol in ambient air by means of nuclepore filters. .r. Air Pollut. Control Ass. 26, 496-498. Spurny K. R., Stober W., Opiela H. and Weiss G. (1976b) Microscopic et Analyse des aerosol d’amiante en air atmosphtrique. Atmospheric Pollution pp. 459-469. Elsevier, Amsterdam. Vrentas J. and Duda J. (1973) Flow of Newtonian fluid through a sudden contraction. Appl. Sci. Res. 27. Wuest W. (1954) Stromung durch Schlitz und Lochblenden bei kleinen Reynolds-Zahlen. Ing. Arch. 22, 357. Zebel G. (1974a) A simple model for the calculation of particle trajectories approaching nuclepore filter pores with allowance for electrical forces. J. Aerosol Sci. 5,473. Zebel G. (1974b) Ein einfaches Model1 zur Berechnung von Teilchenbahnen fiir Kernporenfilter mit elektrischen Ladungen. Jahreskongress GAF.
and J.
GENTRI~ APPENDIX
In terms of the distance from the pore rim to an arbitrary point ? given by i = [R; + X’ + Y’ - ZXR,COS~]~.~
(All
the components of the electrical field
F; = “R,
2n Y
~-~ do.
(A3)
” ?‘2 The components of the Wuest flow field were
“, = 3R; ____
.__w---v 4
(A4)
where IV, = [(R: + X)’ + Yz]o.5 W, = [(R, - X)’ + Y’]‘.’
(A5)
bw (A7)
CLOGGING IN NUCLEPORE FILTERS : CAP FORMATION MODEL K. C. FAN, C. LEASEBURGE,Y. HYUN and J. GENTRY* Department of Chemical Engineering, University of Maryland, College Park, MD 20742, U.S.A. (First received 6 September 1977 and i~~na~~rrn 5 January 1978) Abstract-A theoretical and experimental study of the clogging of nuclepore filters was carried out using mon~is~~e latex particles with argon and methane as the carrier gas. A cap formation model based upon SEM photographs was developed. Using this model calculations of the ctogging rate as a function of time were made. Agreement between theory and experiment was good. INTRODUCTION
Nuclepore filters (NPF) were first produced in 1963 (Fleischer). Since that time they have become ever
more frequently used. In ambient sampling of particulates, the smooth, regular surface of the NPF are much more convenient for electron microscopy (SEM and TEM) than is the porous, twisted structure of membrane filters. Secondly, the regular, uniform pores are more amenable to theoretical calculations than are membrane filters. A number of investigations (Spurny and Lodge, 1972; Husar, 1974; Melo and Phillips, 1974; Liu and Lee, 1976a) have demonstrated the use of NPF in selective sampling. Laboratory measurements have shown that NPF are better suited for the analysis of microbiological aerosols (Spurny and Lodge, 1968b), for studies using X-ray fluorescence (Spumy et al. 1976a), and for the analysis of asbestos fibers in ambient air (Spumy and StGber, 1975; Spumy et al., 1976a), The problem of clogging has been discussed in the literature both for tiber filters and nuclepore filters. Juda employed the Fuchs-Stechkina equation calculating the pressure drop as a function of dust loading for a large number of systems with fiber filters (Juda and Chrosciel, 1970; Juda et al., 1973). Spumy and Lodge (1968a) and Spumy et al. (1975b) proposed a model based on uniform filling of the pores. This model has proved to be successful in a number ofcases, especially when the diameter of the partially clogged pores are calculated from the pressure drop (Fan et al., 1976). In this paper a model based on cap forming (CFM) is derived and compared to experimental measurements. It is found to be better than the UPM (uniform pore filling model) for the cases studied. SEM pictures were found to show that neither model applied all the time DlSCUSSlON
As previously mentioned the UPM model was the * TO whom correspondence
should be sent.
first attempt to explain clogging in NPF. However photographs taken with the SEM indicated that this did not always appear to be the mechanism of clogging. For example, the sequence of photographs in Fig. 1 shows the particles first collecting on the rim of the pore, then forming bridges as the particles collected on one another, and finally closing the pore with a cap. The flow rate in these ex~~ments was 9.91 min- ‘. Monodisperse, latex particles having diameters of 1.01 pm and NPF with a pore diameter of 3.0 pm were used. The particles generated from a Dautrebande type generator at these conditions had a concentration of 800 particles cm-‘. The generator was constructed following the model described by Dautrebande (1962). Argon was the carrier gas and the cross sectional area of the filter face was 5.07cm’. In these pictures three filters were used with the experiments lasting 2,4 and 10min. Recently Mercer (1977) was able to interrupt his experiments and repeatedly examine the same location of the filter at different times. These experiments, also, showed cap formation instead of UPM.
MODEL DEVELOPMENT The basic assumptions used in the model discussed in this paper are as follows: (1) The cap is formed uniformly layer by layer as indicated in Fig. 2; (2) When particles touch the surface of the filter or other particles they adhere together; (3) The cap is assumed to be a sector of a circular pore. The radius of the sector is given by R* = RJ cosa. R. is the radius of the pore and a is the angle between the horizontal and the radius connecting the pore rim and the center of the sector (Fig. 2); (4) Only inertial impaction, direct interception and electrostatic attraction were considered; (5) In this calculation electrostatic forces were accounted for using the method of Zebel (1974a, b). Like Zebel, the Wuest (1954)flow field was assumed. It should be noted that other flow fields such as the one described by Vrentas and Duda (1973) and used by
1797
1798
K. C.
FAN. C. LEASEBURGE. Y. HYUN
and J.
GENTRY
Fig. 2. Diagram of cap formation model.
and V, = 2nR,d,,([R**
- Rf]“.’ - [R* sin a - 0.5 d,])
(3)
The radius of the opening in the cap is designated by R, and is time dependent. The calculational algorithm proceeds as follows : (1) Since R*, a, d,, C, e’, and U. have constant values unaffected by clogging, for a value of X*, V, can be calculated from Equation (2). (2) For an incremental value At, the cap radius is calculated from Equation (3) with V, being given by Equation (1). (3) With the value of R, a trajectory calculation is carried out to find the new value of X* and the iteration of steps l-3 are repeated. (4) The efficiency of collection is determined by the ratio of the area lying outside X* to the total area of the cell. This expression is E = [Rb’ - X*‘]/R:.
(4)
(5) The initial value of R, is R, the pore diameter. Fig. 1. Particle size : 1.Ol pm. Filter : 3 pm.
Parker (1975) could be used without changing the essentials of the model ; (6) The volume of the cap filled in an increment of time can be expressed in terms of the packing density of particles E‘and the flow rate [V,,] through an annulus at the location X* by V, = V, At/&.
(1)
Particles passing through the annulus of thickness d, and radius 27rX* will be collected on the cap. Particles which pass through the parabola (Fig. 2) at values between X* and R, will be cdlected on the face of the filter or on the outer surface of the cap. For a particle concentration C and superficial velocity U,, the expressions for VPand V, are
The models chosen for the electrostatic field (Zebel, 1974a, b) and the velocity field (Wuest, 1954) enter through the trajectory calculation. This equation for the kth component of the spatial coordinate Yis
1
where Fp) is the kth component of the electrical field between the rim of the pore and the particle and U, is the kth component of the velocity. The two parameters are defined by Stk = A’
d* U rlR,
and
Ze=$$ 0
V, = [izd;]
2zX*CU,,d,
(2)
(5)
(7)
0
which are in terms of the particle mobility (B), the
1799
Clogging in nuclepore filters : cap formation model charge on the particle (JE), thecharge per unit distance of the rim of the pore (q) and the gas viscosity (v). Equations (l)-(7) are general and would be applicable for any velocity field that assumes a boundary region of flow undisturbed by the pore. The specific forms for the flow field used in this paper were taken from the literature (Zebel, 1974; Fan, 1977) and are quoted in the Appendix. In Fig. 3, the ex~~mental data for 0.36gm particles are compared with the CFM model and the UPM model The particle concentration was 4000 particles cma3. (The Phoenix photometer was calibrated for each particle size used in the study by collecting a sample at a constant reading of the photometer. The volume sample was known and by counting the particles which were removed by sieving through a NPF, the concentration could be measured.) In the experiment the gas velocity was 74cms-‘. Calculations were run for 16 min. The velocity at any time t was calculated from
I
1.0
U=
N,nR:
where Q is the flow rate and Np the number of pores. Calculations, carried out for Ze = -0.5 and Ze = 0, showed no significant differences. For the 3.0 pm filter, a value of 45” was found to give the best fit whereas a value of 60” gave the best fit for a 5.0pm filter. The smaller the angle, the higher the cap. This model predicts that for larger pores the caps will be flatter. This was in qualitative agreement with SEM. No quantitative data are available for comparison. Agreement between the trajectory calculation and CFM is very good. An analogous calculation for 0.79 ,um particles is shown in Fig. 4. The same angles a were used as for the 0.36gm particles. For these experiments the particle concentration was 1400 particles cmm3. Again the model fits well for short time periods. A possible explanation for the lower collection efficiency observed in the experimental data at longer times for the 3.0pm NPF is that as the opening in the
08
/1
0.7
--
0.36pm particles
UPM CFM
Time, min
Fig. 3. Comparison of CFM, UPM and rn~ur~~~ of coliection eff&eacy during clogging with 0.36pm particles.
-
UPM
--
CFM /
0.9-
3 pm pore
0.8 ,‘I3 0.7 ,
0 0=
/
/
0
D
D
00 v / A
0.5 -
“.‘I 0
Q
0.79 jbrn particles
2
4
6
8
Time,
IO
12
14
I6
min
Fig. 4. Comparison of CFM, UPM and measurements of collection efficiency with 0.79pm particles during clogging. cap becomes smaller, the velocity increases possibly resulting in re-entrainment. It is interesting that the difference between theory and experiment is greatest for the smaller pore size (3.0pm) and occurs sooner for the larger particles. These observations are consistent with the hypothesis suggested above. Comparisons were made with the uniform pore filling model. Because of the time required to fill the first layer, the ef&iency increases at a much slower rate. The semi-empirical equation of Spurny and Madelaine (1971) was used with the UPM model shown in Figs. 3 and 4. For these conditions the equations overestimate the collection efficiency. If a trajectory calculation were used with UPM, the initial value of the efficiency would be the same as pictured for CFM but with an even flatter curve. Although the CFM model was found in the SEM photographs for a majority of the cases studied (Fig. 5 for methane and 3.Opm NPF is typical), it was not universal, as is demonstrated in Fig. 6 where UPF appears to be the dominant mode. The conditions for determining which mode of clogging is dominant have not been resolved. It is interesting to note that in Fig. 5 there are pores without clogging+ Although electrostatic effects have been suggested as a possible explanation, it seems unlikely because of the simulations of particle trajectories (Zebel, 1974; Fan, 1977) and because of the experiments shown in Figs. 7 and 8. These experiments with 0.79ym particles represent the two different cases of charged and neutralized particles. The neutralized particles were passed through a *‘Kr generator while the charged particles were untreated. Qualitative measurements with a rod and cylinder precipitator
1800
Fig. 5. Electron
K. C.
micrograph
showing
FAN, C. LEASEBURGE.Y. HYIJPJand J. GENTK~
typical cap formation.
showed that the latex particles had a considerable residual charge although not as high as reported in the literature (Muhr and Loffler, 1974). The difference of 2.-3 % is within experimental error. Although the flow rate varies as R& the relative mon~is~rsity of the particles could not account for this effect (Caroff er al., 1973). A possible explanation might be the shielding of the pores by the support grid. At first glance the experiments of Mercer (I977) might preclude this explanation. However recent measurements of asbestos fibers in NPF (Gentry and Spumy, 1977) with a special filter holder without a support for the NPF showed that almost every pore had collected fibers. In
Fig. 6. Electron
micrograph
charwing uniform pore liliing.
the absence of more quantitative experiments the inhomogeneity of the deposition remains a mystery.
CONCtUSlON
SEM photographs of latex particles at different times in the clogging of NPF, showed two distinct modes-uniform pore filling (UPM) and the formation of the cap (CFM). In the majority of conditions examined, CFM was the pr~ominant mode. A mode was derived based on the formation of a
1801
Clogging in nuclepore filters : cap formation model
independently by measuring the elevation of the cap above the surface of the filter. Numerical simulations were carried out in which the Zehel model was used to describe the electrical field and the Wuest model was used to describe the flow field. Experimental measurements were in good agreement with the simulation. Numerical calculations using the UPM model did not agree with the data. The trend shown by 01with respect to pore size was in qualitative agreement with SEM. The simulations indicated that electrostatic effects would not make a significant change in the clogging condition. This was in agreement with experiment.
-
Charged
-
Neutralized
Time,
Acknowledgements-K. C. Fan wishes to acknowledge the Minta Martin Foundation, the Computation Center and the Center for Materials Research at the University of Maryland. Y. Hyun, C. Leaseburge and J. W. Gentry wish to acknowledge the support of NSF under Gr. No. 7609381.
min
Fig. 7. Comparison of collection efficiency during clogging for charged and uncharged parttcles. REFERENCES
-
IO-
Charged
0
I 0.1
I 0.2
I 0.3
Neutralized I 0.4
I 0.5
I 0.6
(
drop AP-AP,,(PsI)
Pressure
Fig. 8. Collection efficiency as a function of pressure drop.
sector over the pore. Other than the flow rate and physical properties of the gas, particles and filters, only the variable G(is needed. This value could be checked
Caroff M., Choudhary K. R. and Gentry J. W. (1973) Effect of pore and particle size distributions on efficiencies of membrane filters. J. Aerosol Sci. 4, 93-102. Dautrebande L. (1962) Microaerosols pp. l-22, Academic Press, New York. Fan K. C. (1977) The study of aerosol filtration using model grid filters and nuclepore filters. Ph.D. dissertation, University of Maryland. Fan K. C., Lee J. and Gentry J. W. (1976) The effect of gas composition on the collection efficiency of model grid and nuclepore filters for submicron aerosols. Enuir. Sci. 10. Fan K. C. and Gentry J. (1977) Pressure drop and collection efficiency of NPF as a function of gas composition. Unpublished manuscript. Fleischer R. L., Price, P. B. and Walker R. M. (1963)Tracks of charged particles in solids. Science 149, 383-391. Gentry J. W. and Spumy K. R. (1977) Unpublished data. Husar R. B. (1974) Atmospheric particulate mass monitoring with a B radiation detector. Atmospheric Environment 8, 1833188. Juda J. and Chrosciel S. (1970) A theoretical model of pressure loss increase during the filtration process. StaubReinhalt Luf 30, 196. Juda J., Chrosciel S. and Nowicki M. (1973) The influence of some filter parameters on the pressure loss increase in the filtration process. Staub-Reinhalt Luft 33, 159. LiuB.Y.H. and LeeK. W. (1976)Efficiencyofmembraneand nuclepore filters for submicron aerosols. Enuir. Sci. Technol. 10, 345-350. Melo 0. T. and Phillips C. R. (1974) Aerosol-sire spectra by means of membrane filters. Enuir. Sci. Technol. 8, 67-71. Mercer T. T. (1977) Private communication. Muhr W. and LGMer F. (1974) Elektrostatische Eigenshaften verschiedener Testaerosols. Jahrekongress GAF. Parker R. (1975) A fundamental study of particle deposition onto large pore nuclepore filters. Ph.D. dissertation, Duke University. Spumy K. R., Havlova J., Lodge J. P., Sheesley D. C. and Wilder B. (1975) Aerosol Filtration by means of nuclepore filters : filter pore clogging. hub-Reinhalt Luft 35, 77.
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and J.
GENTRI~ APPENDIX
In terms of the distance from the pore rim to an arbitrary point ? given by i = [R; + X’ + Y’ - ZXR,COS~]~.~
(All
the components of the electrical field
F; = “R,
2n Y
~-~ do.
(A3)
” ?‘2 The components of the Wuest flow field were
“, = 3R; ____
.__w---v 4
(A4)
where IV, = [(R: + X)’ + Yz]o.5 W, = [(R, - X)’ + Y’]‘.’
(A5)
bw (A7)