clogging in nuclepore filters

6
Clogging in Nuclepore Filters Kuo-chung Fan* and James W. Gentry Department of Chemical Engineering and Institute for Physical Science and Technology, University of Maryland, College Park, Md. 20742 Experimental measurements of the penetration and pressure drop across nuclepore filters (NPF) during clogging were made. The carrier gases for the pressure drop measure- ments consisted of argon, helium, methane, and different bi- nary mixtures of these gases. The semiempirical Spurny equation for pressure drop across NPF was modified to ac- count for carrier gases other than air and for polydispersity of pore sizes. Agreement of experiment with theory was good. Penetration measurements were carried out as a function of time for 3.0 and 5.0 wm NPF. Argon and methane were used as the carrier gas. Comparisons of the penetration as a func- tion of pressure drop were consistent with the clogging model proposed by Spurny. In the early 1960's, Fleicher et al. (1-5) developed a proce- dure for producing very uniform pores in a thin sheet of polycarbonate. The advantages of this new membrane filter, designated as nuclepore filters (NPF),over existing membrane filters for sampling [especially for electron microscopy (6-8) and for the examination of filtration theory (9)] have been discussed in the literature. An extensive set of experiments (10, 11) in which the pressure drop across nuclepore filters was measured as a function of pore size and gas velocity with air as a carrier gas led to the semiempirical expression cited below. In this paper the equation is extended to account for carrier gases other than air as well as for polydispersity of the pore size distri- bution. An extensive series of pressure drop measurements as a function of gas velocity and carrier gas composition is reported. Perhaps the earliest model to distinguish between clogging by solid and liquid aerosols was that of Spurny and Lodge (12). They reported that the penetration of solid aerosols (which maintain their shape after collection) decreased more rapidly than in the case of liquid aerosols. Later Spurny and coworkers (13, 14) proposed a model for clogging by solid aerosols, in which the pore is divided into two sections, an open central core where deposition occurs as in a capillary tube, and a packed outer annulus that collects particles by interception. In this paper penetration measurements were made and the experiments correlated with this model. Experimental Design The experimental procedure and design have been de- scribed previously (15 ). The aerosol was monodisperse latex spheres generated from a dilute, aqueous suspension using a Dautrebande-type nebulizer (16). The carrier gas was mixed to a predetermined ratio from the constituent gases before the nebulizer. After drying (successive cold traps of CaCl2-ice and acetone-dry ice) and electrostatic neutralization [s5Kr ion- ization source] the particles were either passed through the filter or directly into a smoke photometer (Phoenix-Sinclair Model 4000 AL). The pressure difference across the filter was observed with a mercury or water manometer, depending on the operating conditions. The penetration and the pressure drop (the pressure difference was used to trigger a pneumatic signal which could be transformed into a voltage) were re- corded simultaneously on a two-pen strip chart recorder. For the pressure drop measurements, the particle generator was bypassed. For the clogging studies, the flow rate through the filter was maintained constant. It was not possible to control the concentration of the aerosol stream. Calibration curves for three particle sizes (0.36, 0.5, and 0.79 km) were prepared. A predetermined quantity of gas and aerosol was filtered through a NPF at a constant reading of the photometer. Particles collected on the NPF were counted from photographs taken through a Type 96113 Mark 2A scanning electron microscope (SEM). The concen- tration determined by dividing the number of particles col- lected on the NPF by the total volume of carrier gas passing through the filter was plotted as a function of photometer setting to establish a calibration curve. Pressure Drop Measurements An extensive set of measurements (10,ll) of the pressure drop across NPF has established the semiempirical expres- sion where L, R,, and t are the pore length, pore radius, and po- rosity of the NPF; PI, q, and U, are the pressure, viscosity, and superficial velocity of the gas; and C, is a semiempirical con- stant proportional to the product of the mean free path and the total pressure. The effective radius R, and the mean velocity U, are re- lated to the flow rate Q by the relation where Np is the number of pores in the NPF. Previously reported applications (15,17) of Equation 1 have neglected the variation of C, with gas composition. In this section, a procedure for correcting C, for the variation in gas composition and a correction for polydispersity of the pore size are presented. Finally, comparison of experimental mea- surements for mixtures of argon, methane, and helium with Equation 1 is given. The value of C, for an arbitrary gas mixture can be ex- pressed in terms of the viscosity (v) and molecular weight (M) of the mixture by M* 0.5 C, = 0.0308 ($) (F) Torr-cm (3) where v* and M* are the viscosity and molecular weight of air. Equation 3 follows from expressing the ratio of the mean free path of the carrier gas to air in terms of the viscosities and molecular weights. The correction for polydispersity of the pore size distribu- tion is given by -- [W* - 1 + C,/R,Pi C &Pi ["I (1 + 3A2 + 0.75A4) + (1 + 1.5A2) (4) 1 1 + 3A2 =--- where A is defined by A = ficr/R, and [AP*] is the pressure drop across a NPF having a nonuniform pore size distribution. 0013-936X/78/0912-1289$01.00/0 @ 1978 American Chemical Society Volume 12, Number 12, November 1978 1289

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Page 1: Clogging in nuclepore filters

Clogging in Nuclepore Filters

Kuo-chung Fan* and James W. Gentry Department of Chemical Engineering and Institute for Physical Science and Technology, University of Maryland, College Park, Md. 20742

Experimental measurements of the penetration and pressure drop across nuclepore filters (NPF) during clogging were made. The carrier gases for the pressure drop measure- ments consisted of argon, helium, methane, and different bi- nary mixtures of these gases. The semiempirical Spurny equation for pressure drop across NPF was modified to ac- count for carrier gases other than air and for polydispersity of pore sizes. Agreement of experiment with theory was good. Penetration measurements were carried out as a function of time for 3.0 and 5.0 wm NPF. Argon and methane were used as the carrier gas. Comparisons of the penetration as a func- tion of pressure drop were consistent with the clogging model proposed by Spurny.

In the early 1960's, Fleicher et al. (1-5) developed a proce- dure for producing very uniform pores in a thin sheet of polycarbonate. The advantages of this new membrane filter, designated as nuclepore filters (NPF), over existing membrane filters for sampling [especially for electron microscopy (6-8) and for the examination of filtration theory (9) ] have been discussed in the literature.

An extensive set of experiments (10, 1 1 ) in which the pressure drop across nuclepore filters was measured as a function of pore size and gas velocity with air as a carrier gas led to the semiempirical expression cited below. In this paper the equation is extended to account for carrier gases other than air as well as for polydispersity of the pore size distri- bution. An extensive series of pressure drop measurements as a function of gas velocity and carrier gas composition is reported.

Perhaps the earliest model to distinguish between clogging by solid and liquid aerosols was that of Spurny and Lodge (12). They reported that the penetration of solid aerosols (which maintain their shape after collection) decreased more rapidly than in the case of liquid aerosols. Later Spurny and coworkers (13, 14) proposed a model for clogging by solid aerosols, in which the pore is divided into two sections, an open central core where deposition occurs as in a capillary tube, and a packed outer annulus that collects particles by interception. In this paper penetration measurements were made and the experiments correlated with this model.

Experimental Design The experimental procedure and design have been de-

scribed previously (15 ). The aerosol was monodisperse latex spheres generated from a dilute, aqueous suspension using a Dautrebande-type nebulizer (16) . The carrier gas was mixed to a predetermined ratio from the constituent gases before the nebulizer. After drying (successive cold traps of CaCl2-ice and acetone-dry ice) and electrostatic neutralization [s5Kr ion- ization source] the particles were either passed through the filter or directly into a smoke photometer (Phoenix-Sinclair Model 4000 AL). The pressure difference across the filter was observed with a mercury or water manometer, depending on the operating conditions. The penetration and the pressure drop (the pressure difference was used to trigger a pneumatic signal which could be transformed into a voltage) were re- corded simultaneously on a two-pen strip chart recorder.

For the pressure drop measurements, the particle generator

was bypassed. For the clogging studies, the flow rate through the filter was maintained constant.

I t was not possible to control the concentration of the aerosol stream. Calibration curves for three particle sizes (0.36, 0.5, and 0.79 km) were prepared. A predetermined quantity of gas and aerosol was filtered through a NPF a t a constant reading of the photometer. Particles collected on the NPF were counted from photographs taken through a Type 96113 Mark 2A scanning electron microscope (SEM). The concen- tration determined by dividing the number of particles col- lected on the NPF by the total volume of carrier gas passing through the filter was plotted as a function of photometer setting to establish a calibration curve.

Pressure Drop Measurements An extensive set of measurements ( 1 0 , l l ) of the pressure

drop across NPF has established the semiempirical expres- sion

where L, R,, and t are the pore length, pore radius, and po- rosity of the NPF; P I , q, and U , are the pressure, viscosity, and superficial velocity of the gas; and C, is a semiempirical con- stant proportional to the product of the mean free path and the total pressure.

The effective radius R, and the mean velocity U, are re- lated to the flow rate Q by the relation

where N p is the number of pores in the NPF. Previously reported applications (15,17) of Equation 1 have

neglected the variation of C, with gas composition. In this section, a procedure for correcting C, for the variation in gas composition and a correction for polydispersity of the pore size are presented. Finally, comparison of experimental mea- surements for mixtures of argon, methane, and helium with Equation 1 is given.

The value of C, for an arbitrary gas mixture can be ex- pressed in terms of the viscosity (v) and molecular weight ( M ) of the mixture by

M* 0.5 C, = 0.0308 ($) (F) Torr-cm (3)

where v* and M* are the viscosity and molecular weight of air. Equation 3 follows from expressing the ratio of the mean free path of the carrier gas to air in terms of the viscosities and molecular weights.

The correction for polydispersity of the pore size distribu- tion is given by

-- [ W * - 1 + C,/R,Pi C

&Pi ["I (1 + 3A2 + 0.75A4) + (1 + 1.5A2)

(4) 1

1 + 3A2 =---

where A is defined by A = f icr /R, and [AP*] is the pressure drop across a NPF having a nonuniform pore size distribution.

0013-936X/78/0912-1289$01.00/0 @ 1978 American Chemical Society Volume 12, Number 12, November 1978 1289

Page 2: Clogging in nuclepore filters

5 p NPF 4Ar-6CH4 6Ar-4CHn *

He 10

0. CH4

.8 0 25 50 75 100

VELOCITY (CMr’SEC)

Figure 1. Ratio of theoretical (Equation 1) to experimental pressure drop as a function of flow rate and gas composition (5 flm NPF)

3pm NPF 4Ar-6 CH4 6 A r - 4 C H 4 * IAr -2He -

0 6 0 . .-

0 . m . * w LL e

VELOCITY (CMISEC)

Figure 2. Ratio of meoretical (Equation 1) to experimental presswe drop as a function of flow rate and gas composition (3 pm NPF)

The derivation for Equation 4, presented in the Appendix, assumes that the pores are distrihuted normally with a mean R, and a standard deviation r. The pore distribution f ( R ) has the form

For typical NPF, A is of the order of 0.05; consequently, the correction in Equation 4 is less than 1% and can usually he neglected.

Experiments were carried out for mixtures of argon, helium, and methane. NPF a t two pore sizes (3 and 5 Gm) were used. The superficial velocity varied from 30 to 100 cmls. Pressure drop measurements were carried out in the absence of parti- cles with the same NPF used for all the measurements. The viscosities of argon, helium, methane, and the argon-helium mixtures were taken from the literature (18) The viscosities of the argon-methane mixtures were determined experi- mentally from pressure drop measurements with model grid filters (19), assuming that the Fuchs-Stechkina equation was valid.

In Figures 1 and 2 the ratio of the experimental pressure drop to that given hy Equation 1 is presented as a function of the superficial velocity for seven gas compositions. If Equation 1 were valid, the ratio should he independent of velocity and composition. The data in Figure 1 indicate that for the 5 p m NPF, the estimated pressure drop (Equation 1) is low by a factor of 1.20 with a standard deviation of 0.08. For the 3.0 pm NPF, the estimated pressure drop was low by a factor of 1.10 with a standard deviation of 0.08.

There are several possihle explanations for the ratio dif- fering from one. Noncompensating errors in the porosity and thickness of the NPF of less than 10% could account for this discrepancy. A more likely explanation is the obstruction of the pores by the supporting screen. Many observers have noticed (19,20) an irregular deposition of particles on NPF. For example, of the 24 pores shown in Figure 3,20 are com-

1290 Environmental Science a Technology

Figure 3. Electron micrograph showing irregular deposition of latex aerosol suggesting partial obstruction of some pores

pletely clogged and 4 are almost particle-free. Using a SEM to examine particle clogging a t different time intervals, Mercer (19) found that some pores were only temporarily obstructed and later clogged. Numerical simulations (21) and experi- ments (22) seemed to discount the effect of electrostatic at- traction. Recent experiments with an unsupported NPF showed particles collected a t each pore (23).

The effect of obstructed pores would he to decrease the porosity, predicting an increased pressure drop. A simple geometric model (23) predicts that 29% of the pores for the 5.0 pm NPF and 23% of the pores for the 3.0 pm NPF would be obstructed. The pressure drop measurements reported in Figures 1 and 2 would he accounted for hy obstruction of 17% of the pores in the 5 pm NPF and by 9% of the pores in the 3.0 pm NPF. The 3 pm NPF shown in Figure 3 had 17% of its pores obstructed, There are three reasons that suggest that obstructed pores might explain why the ratio of experimental and theoretical pressure drop was not one.

Obstructed pores would result in an increase in the pressure drop and a corresponding decrease in the ratio.

From geometric considerations, the discrepancy would he greater for larger pore sizes. Also, the ratio would he less than 1.4 for 5 pm NPF and less than 1.3 for 3 pm NPF. This is

Page 3: Clogging in nuclepore filters

Table 1. Particle Concentrations Leaving Generator .6

t V

8 k . 4 - 0

W

carrier partlcle gas slze ( p m )

- concn

(partlcles/cm3)

argon 0.79 1.5 x 103 0.50 7.4 x 102 0.36 4.1 X lo3 (5.0 pm NPF)

3.0 X lo3 (3.0 p m NPF) methane 0.79 6.2 X lo2

0.50 2.5 X lo2 0.36 4.0 x 103

consistent with experiment. The extent of obstruction would be independent of gas

composition and little affected by flow rate. This is consistent with the data in Figures 1 and 2.

Measurements of Clogging In these tests, the flow rate through the filter was main-

tained constant a t approximately 180 cm3/s corresponding to a superficial velocity of 36 cm/s.

The experimental design included an option where the ionization source could be bypassed. Comparisons between penetration for the neutralized and unneutralized aerosol gave results that agreed within experimental error (2-3%), although the charged particles showed a consistently lower penetration. A subsequent measurement of the electrostatic charge dis- tribution with a rod and cylinder mobility analyzer (24) showed that the aerosols had a small but significant charge leaving the cold traps. I t did not appear that electrostatic charges played a significant role in these experiments.

The particle concentration determined from the photom- eter reading of the unfiltered aerosol stream with the cali- bration charts prepared from the SEM photographs is given in Table I for the experiments reported in this study. Three particle sizes and two carrier gases were used.

As had been previously reported (16), collection efficiency can be correlated as a function of (P - Po) where Po is the initial pressure drop across the NPF. In Figures 4 and 5 the experimental data using a 5.0-pm NPF are plotted for argon and methane, respectively. The larger the particle size, the more rapidly the collection efficiency increases with pressure. I t is interesting to note that the pressure drop increases less steeply with time when argon rather than methane is used as the carrier gas. A possible explanation might be different modes of clogging. Preliminary data indicate qualitatively that there are a t least three modes of clogging-the formation of caps, uniform pore filling, and collection on bridges between adjacent pores-which appear to depend on flow rate, gas composition, and particle size. For the majority of conditions reported here, cap formation seemed to be the dominant mode.

Clogging: Comparison of Theory with Experiment In comparing experiment with theory, an indirect method

is most commonly used. In this method, it is necessary to as- sume a specific clogging model-a mathematical description of where the particles are deposited around or in the pore. Next, it is necessary to have mathematical expressions relating the collection efficiency and pressure drop to a parameter in the clogging model. The basic method is to determine the value of the parameter from the pressure drop measurements. Then the efficiency is determined from this value of the pa- rameter. In essence the indirect method compares the col- lection efficiency as a function of pressure drop, given by the clogging model, with experiment.

The clogging model used in this study is the two region model developed by Spurny and coworkers (11, 12). This

0 1 IO

5pm NPF-ARGON

PARTICLE SIZE

. 7 9 u m 0

. 5 0 y m A

3 6 p m 3

1 , 100 1000 1000(

PRESSURE DROP [ A P - A t ] (PASCALS)

Figure 4. Collection efficiency as a function of pressure drop and par- ticle size (5 Frn NPF with argon as carrier gas)

PARTICLE SIZE

.50 prn -

.36 prn - 250 500 750 A P - A t (PASCALS)

Figure 5. Collection efficiency as a function of pressure drop and par- ticle size (5 p m NPF with methane as carrier gas)

model assumes the pore to consist of two regions-a clogged area that collects particles by interception and a particle-free core where collection is as if the pore were unclogged. For this model the collection efficiency is given by

E T = (1 - b ) E ; + b (6)

where b is the fraction of the pore that is clogged, and E > is the collection efficiency for a pore with a radius Rt. The value of b is given by

and E ; was calculated by the relation of Spurny and Made- laine (25) . This equation is an empirical expression combining the partial efficiencies due to inertial impaction (26), diffusion (27, 28), and interception (25) .

Subsequent work by Smith and Phillips (29), Smutek and Pich (30), and Parker (31) has indicated that trajectory cal- culations with more realistic velocity profiles give better values for the inertial impaction than the analytical expression of Pich (26) used to compute E;. The primary difficulty with the Pich expression is that the impaction term is underesti-

Volume 12, Number 12, November 1978 1291

Page 4: Clogging in nuclepore filters

i I

,

,I PARTICLE SIZE

. 7 9 p c

. 5 0 p m 0

.36pm f‘ SPURNY MADELAINE -

-,**’ UNIFORM PORE FILLING --- r PORE DIAMETER = 5pm

CARRIER GAS ARGON

I 0 2 4 6 8 1 0 1 2

, ,

Ro-R, / R,

Figure 6. Collection efficiency as a function of change in apparent pore diameter and particle size (5 k m NPF with argon)

mated for large particles. Since the experiments reported here are for particles less than 0.8 pm a t relatively low velocities, the use of the original Pich expression does not result in sig- nificant error.

The two region model has been criticized in that the uni- form pore filling implied by the model is not always observed in SEM photographs and the rate of clogging was found to be too slow to fit some experimental measurements (32). How- ever, the model gives a consistent method for relating effi- ciency and pressure drop.

The calculational procedure is as follows: The value of Rt is determined from the pressure drop across

the filter using Equation 1. The variable Rt replaces R, in this equation.

The initial pressure drop AP, is given by Equation 1 with

The fraction of the pore that is clogged ( b ) is given by Equation 7.

The porosity is calculated from Equation 2 with the variable Rt replacing R,.

The collection efficiency E ; is determined from the Spurny-Madelaine equation (25).

The overall collection efficiency is obtained from Equation 6.

It should be stressed that the calculation does not depend on or provide information regarding the rate of clogging. I t does indicate whether the curves of collection efficiency as a function of pressure drop are consistent with the clogging model.

In Figures 6 and 7 the collection efficiency is plotted as a function of (R , - R t ) / R , for three particle sizes and two car- rier gases-methane and argon. The pore size of the NPF is 5.0 pm. In Figure 7 the dashed curves represent the case in which the collection efficiency was calculated directly from the Spurny-Madelaine expression assuming uniform pore filling rather than Equation 6. In the uniform pore filling the pores fill in concentric circular annulae of a thickness equal to one pore diameter. The efficiency of particle collection is then calculated as if the filter could be represented by a clean nuclepore filter with a reduced pore diameter.

The curves show that the model predicts a higher collection efficiency than the experimental points. For argon the

Rt 5 R,.

PORE DIAMETER 5um CARRIER GAS CHI

0 .2 .4 .6 .8 1.0

[Ro-RJ /Ro

Figure 7. Collection efficiency as a function of change in apparent pore diameter and particle size (5 p m NPF with methane)

Table II. Experimental Measurements of Collection Efficiency ( E ) as a Function of Pressure Drop [AP* = AP - AP,] and Particle Size for 3 pm NPF

0.79 pm AP*

(10-3

N/m2)

0.09 0.17 0.32 0.57 0.69 1.18 1.59 1.84 2.20 2.64 3.10

0.04 0.07 0.16 0.26 0.39 0.50 0.64 0.80 0.96

‘ E

0.87 0.88 0.89 0.90 0.91 0.92 0.93 0.94 0.95 0.96 0.96

0.63 0.65 0.68 0.70 0.72 0.75 0.78 0.80 0.81

0.50 pm AP*

(10-3

N/m2) E

methane 0.02 0.64 0.34 0.70 0.44 0.73 0.51 0.75 0.61 0.78 0.68 0.81 0.75 0.82 0.83 0.83 0.92 0.85 1 .oo 0.86 1.22 0.88 1.34 0.89 1.45 0.90 1.57 0.90 1.69 0.91

argon 0.11 0.5 1 0.20 0.56 0.41 0.62 0.69 0.68 1.01 0.74 1.19 0.80 2.25 0.87 2.99 0.91 3.87 0.94 4.60 0.96 5.91 0.98 6.92 0.99

0.36 pm AP*

(10-3

N/m2) E

0.04 0.49 0.07 0.55 0.22 0.61 0.43 0.67 0.68 0.72 1.01 0.76 1.36 0.80 1.81 0.83 2.42 0.86 3.06 0.89 3.90 0.92 4.94 0.94 6.28 0.95 9.97 0.96

0.02 0.31 0.04 0.33 0.10 0.36 0.18 0.39 0.25 0.42 0.35 0.45 0.44 0.48 0.55 0.50 0.72 0.53

agreement between theory (solid curve) and experiment is very good. For methane the Spurny-Madelaine equation ov- erestimates the collection efficiency accounting for the quantitative discrepany between theory and experiment.

In Tables I1 and 111, data analogous to that plotted in Fig- ures 4-7 are presented for 3 pm NPF instead of 5 pm NPF. No

1292 Environmental Science & Technology

Page 5: Clogging in nuclepore filters

Table 111. Comparison of Experimental Data ( Eexp) and Theoretical Calculations ( E 1 ) of Collection Efficiency for 3 pm NPF

0.36-prn particles 0.5-prn particles 0.79-prn particles (Ro - R f V R o E E X ~ 6 (Ro - Rt V R o EExp 6 (Ro - R t V R o E E X ~ 6

argon 0.05 0.47 0.44 0.03 0.62 0.58 0.04 0.84 0.79 0.09 0.61 0.50 0.05 0.72 0.60 0.08 0.85 0.81 0.20 0.84 0.64 0.12 0.86 0.68 0.14 0.94 0.85

0.20 0.94 0.75 0.17 0.95 0.87

0.01 0.61 0.05 0.72 0.11 0.83 0.13 0.86 0.16 0.89 0.23 0.94 0.25 0.95 0.28 0.96

methane 0.61 0.03 0.7 0.67 0.04 0.76 0.74 0.04 0.81 0.76 0.06 0.82 0.77 0.08 0.855 0.82 0.09 0.88 0.83 0.10 0.89 0.85 0.1 1 0.9

0.14 0.91

significant qualitative differences were observed for the smaller pore size.

Conclusions A series of measurements of the collection efficiency for

latex aerosols a n d b e pressure drop across nuclepore filters during clogging was carried out. Three particle sizes, two pore sizes of NPF, and two gases (argon and methane) were used in the study.

When an effective pore radius was calculated from pressure drop measurements (using the Spurny equation), agreement with the clogging model of Spurny and Madelaine was good.

Comparisons of the Spurny equation for pressure drop across NPF with experimental measurements resulted in a constant ratio independent of carrier gas composition or flow rate. The ratios (1.1 for 3 pm NPF and 1.2 for 5 pm NPF) probably differed from unity because of the partial obstruc- tion of some of the pores by the supporting screen for the fil- ter.

Appendix The effect of polydispersity is accounted for by relating the

velocity through a pore of radius R, (Uz l t ) to the mean ve- locity U,/c which is defined by Equation 2.

Q t = N,,ZRiU, ( 2 )

The following three assumptions are made in this deriva- tion:

The pore size distribution function is given by a normal distribution with a mean pore radius R , and a standard de- viation u.

The pressure drops across all pores in the filter are equal. The pressure drop is given by the approximate form of the

Spurny equation.

(8) 1.14 X l o p 2 &U - 1.14 X V L U ; AP = - 2tR2(1 + CIRP1) 2tR2(1 + C/RPI)

From Equation 8, the velocity Ult through a pore of arbitrary radius R can be related to U: by

R 2 (1 + C/RP) R i ( 1 + C/R,P)

u= u;- Since the flow rate through a filter is given by

0.78 0.02 0.87 0.89 0.79 0.05 0.91 0.90 0.8 0.06 0.93 0.91 0.81 0.08 0.95 0.92 0.82 0.11 0.96 0.93 0.83 0.83 0.84 0.84

Q = N p ( Z R 2 ) ( U l t ) f ( R ) d R (10) 0

the velocity U:/t can be expressed uniquely in terms of the flow rate if the pore size distribution f ( R ) is known, by ex- pressing Uit using Equation 1.

Specifically for a normal distribution

tQ = nRgu'Np [ ( I + 3 A 2 + 0.75 A 4 ) (1 + C/R,P)

C ROP

+ - ( 1 + 1.5 A ' ) ] (11)

Since the pressure drop is proportional to U: (from Equa- tion 8) for a NPF with a nonuniform pore size distribution

1 + C/R,P C

ROP

-=A- - [AP]* u*

1 uo [ 1 + 3 A 2 + 0.75A4 +- (1 + 1.5A2)

1 ( 1 2 ) x-

1 + 3 A 2

The ratio U*,/U, is obtained by relating Equations 2 and 3.

Literature Cited (1) Fleicher, R. L., Price, P. B., Walker, R. M., Reu. Sci. Instrum., 34,

(2) Fleicher, R. L., Price, P. B., Symes, E. M., Science, 143, 249

(3) Fleicher. R. L., Price, P . B., Walker, R. M., ibzd., 149, 383

(4) Price, P. B., Walker, R. M., J. A p p l . Phys., 33,2625, 3400, 3407

( 5 ) Price, P. B., Walker, R. M., Phys. Reu Lett., 8, 217 (1962). (6) Frank, E. R., Spurny, K. R., Sheeley, D. C., J. Microsc. (Paris),

9,735-40 (1970). (7) Spurny, K. R., Ackermann, E. R., Lodge, J. P., Tesarova, I., Proc.

of 3rd Inst. Clean Air Congress, pp 17-20, VDI-Press, Dusseldorf, Germany, 1973.

(8) Liu, B.Y.H., Kuhlmey, G. A,, Proc. Symp. on X-ray Fluorescence Analysis, Chapel Hill, N.C., 1976.

(9) Spurny, K., Chern. Tech., 6,69-73 (1976). (10) Havlova, J., Hrbek, J., Hampl, V., Spurny, K., Collect. Czech.

Chem. Commun., 35,2087 (1970). (11) Kirsch, A. A., Spurny, K., J. A p p l . Mech. Phys. (Russ.) , 3,109

(1969). (12) Spurny, K., Lodge, J. P., Collect. Czech. Chem. Cornmun., 33,

3479-93 (1968).

510 (1963).

(1964).

(1965).

(1962).

Volume 12, Number 12, November 1978 1293

Page 6: Clogging in nuclepore filters

(13) Spurny, K., “Assessment of Airborne Particles”, T. T. Mercer et al.. Eds., P 60, Thomas. 1972.

(14) Spurny, K:, Havlova, J., Lodge, J. P. , Sheesley, D. C., Wilder,

(15) Fan. K. C.. Lee. J.. Gentrv. J. W.. “The Effect of Gas Comoosi- B., Staub-Reinhal t L u f t , 35 ,77 (1975).

tion on the Collection Efficiency of Model Grid and Nuclipore Filters”, 50th Int. Conf. on Colloid and Surface Sci., San Juan, Puerto Rico, 1976.

(16) Fan, K. C., Lee, J., Gentry, J. W., in “Colloid and Surface Science 11”, M. Kerker, Ed., Academic Press, New York, N.Y., 1976.

(17) Chapman, S., Cowling T. G., “The Mathematical Theory of Non-Uniform Gases”, pp 151-67, Cambridge, 1960.

(18) Fan, K. C., PhD dissertation, University of Maryland, College Park, Md., 1977.

(19) Mercer, T. T., “Collection of Ti02 Particles Using Nuclepore Filters, 10th Aerosol Technology Meeting, Albuquerque, N.M., 1977.

(20) Zebel, G., J . Aerosol Sci., 5,2473-82 (1974). (21) Leaseburge, C., Hyun, Y., Shen, P., Gentry, J., unpublished data,

(22) Gentry, J., Spurny, K., ibid (23) Dautrebande, L., “Microaerosols”, pp 1-22, Academic Press,

1977.

New York, N.Y., 1962. (24) Hyun, Y., Gentry, J., “A Variable Frequency Electrostatic Mo-

bility Analyzer”, 13th IRCHA Colloquium, Paris, France, 1978. (25) Spurny, K., Madelaine, G., Collect. Czech. Chem. Commun. , 36,

2749 (1971). (26) Pich, J., ibid. , 29, 2223-7 (1964). (27) Gormley, P. G., Kennedy, M., Proc. Royal Irish Acad., 52A, 163

(28) Twomay, S., Bull. Obs. Pug de Dome , p 173 (1962). (29) Smith, T., Phillips, C., Environ. Sei. Technol., 9, 564-8

(30) Smutek, M., Pich, J., Aerosol Sei., 5, 17-24 (1974). (31) Parker, R., PhD dissertation, Duke University, Durham, N.C.,

(32) Fan, K. C., Leaseburge, C., Hyun, Y., Gentry, J., Atmos . Enui-

(1949).

(1975).

1975.

ron., submitted for publication (1978).

Receiued for reuieu: September 6,1977. Accepted J u n e 12,1978. Work supported by N S F u n d e r Grant No. 76-09381. K.C.F. receioed sup- port f r o m t h e M i n t a Mar t in Foundat ion of the Universi ty of Maryland.

Effects of Nitrogen Dioxide and Water Vapor on Oxidation of Sulfur Dioxide over V205 Particles

Brigitte Barbaray, Jean-Pierre Contour, and Gerard Mouvier * Laboratoire de Physico-Chimie Instrumentale, Universite Paris VII, 2, place Jussieu, 75221 Paris Cedex 05, France

8 The effect of nitrogen dioxide and water on the adsorption and oxidation of sulfur dioxide over V2O5 is studied by x-ray photoelectron spectroscopy (XPS). SO2 does not chemisorb onto V2O5 below 150 “C, and it oxidizes a t 200 “C into ad- sorbed sulfate and sulfur trioxide. But if nitrogen dioxide or water is added in the adsorption cell, SO2 is chemisorbed and oxidized into sulfate from 25 “C. These results indicate that in the absence of nitrogen oxide or water, the VzO5 aerosols contribute little to the production of atmospheric sulfuric acid and that the nitrogen oxide enhances the , 5 0 2 oxidation as in the homogeneous reactions.

Numerous studies on the homogeneous oxidation of SO:, in the presence of other gaseous pollutants (NO2, hydrocar- bons, H20, 0 3 , OH, HOP, R 0 2 . . .) show that nitrogen oxides and hydroxyl radicals play a very important role in the oxi- dation of SO2 and formation of fine aerosol particles that constitute “acid smog” (1-3). However, two other processes are involved in the oxidation of atmospheric SO2: oxidation in the aqueous phase ( 4 , 5 ) , and heterogeneous oxidation in the presence of solid particles (6-9).

These two mechanisms have not been as widely published. In particular, the catalytic action of certain solid particles has never been clearly demonstrated (9, 10). We have therefore studied the adsorption and the oxidation of SO2 upon contact with Vz05 particles in the presence of preadsorbed nitrogen dioxide and water vapor.

Recent reports have revealed the utility of X-ray photo- electron spectroscopy (XPS) in the determination of the chemical state of adsorbed pollutants (6, 8, 11) . I t seemed interesting to us to apply this technique to the study of the adsorptions and the surface reactions occurring in the S02- NOz-H:,O-V:,05 system. The chemical reactions between SO2 and V205 have long been studied (12 ,13) , but photoelectron spectroscopy, which is a technique for surface analysis, makes it possible to investigate more precisely the initial phase of these reactions.

Experimental Conditions We used very high-purity V2O5 (Merck), treated before

adsorption by heating a t 200 “ C and to 10-9 torr in the prep- aration chamber of the spectrometer for 14 h. The SO2 (Merck) was used without any further purification (SO2 =

The spectra were recorded on an AEI ES 200 B spectrom- eter operating with FAT 130 scanning mode and equipped with a Mg anticathode (Mg K a = 1253.65 eV). The binding energies were determined by using the Is peak of carbon contamination as internal reference. The binding energy of these electrons is set a t 285 eV, relative to the Fermi level (14) .

The preparation of the sample and the adsorption are performed in the spectrometer preparation chamber. The adsorption pressure is set a t IO-* torr, and the temperature can be varied from 25 to 450 O C . After adsorption the SO:, is pumped out at the adsorption temperature, and the chamber is evacuated until a pressure of lop8 torr is reached. This pressure is maintained in the spectrometer while the spectra are recorded. These experiments were carried out in the ab- sence of light to avoid any photochemical contribution to the SO2 oxidation (1 , I O ) .

When the effect of NO2 and H20 on SO2 oxidation was studied, the following experimental procedure was adopted: NO2 adsorption at 10-2 torr or HzO adsorption a t 1 torr during 15 min, followed by evacuation of NO:, until a pressure of lops torr is reached; after pumping down to torr during 15 min, introduction of SO2 and adsorption as described above. These procedures were chosen in preference to the introduc- tion of a mixture of NO:, and SOz, since it makes it possible to study the NO2- or HiO-SO:, interactions in the adsorbed state by eliminating the possibility of homogeneous gas-phase reactions (10).

Results and Discussion Adsorption of SO2. The spectra were recorded before and

after SO2 adsorption (Table I). Under these conditions,

99.95%, HzO = 0.02%).

1294 Environmental Science & Technology 0013-936X/78/0912-1294$01.00/0 @ 1978 American Chemical Society