8
Aerosol
Filtration
by
Fibrous
Filter
Mats
Removal of Trace Contaminants from the Air Downloaded from pubs.acs.org by YORK UNIV on 12/05/18. For personal use only.
WILLIAM S. MAGEE, JR. and LEONARD A. JONAS Edgewood Arsenal, Aberdeen Proving Ground, Md. 21010 W E N D E L L L. ANDERSON Naval Weapons Laboratory, Dahlgren, Va. 22448
Abstract A s e m i - e m p i r i c a l formalism f o r a n a l y z i n g a e r o s o l filtration by f i b r o u s filters i s modified and compared t o s e v e r a l t h e o r i e s . Although approximate, the formalism i n t r o d u c e d by Dorman 3,4,5 proves t o be u s e f u l and instructive. The formalism is a p p l i e d t o a n a l y s i s o f p e n e t r a t i o n - v e l o c i t y profiles f o r ten d i f f e r e n t types o f filters, each challenged by dioctyl p h t h a l a t e (DOP) aerosols o f four distinct d r o p l e t s i z e s ( 0 . 2 6 , 0.28, 0 . 3 0 , 0.32 µm) in the velocity range, 7.2 t o 141.0 cm/sec. Q u a n t i t a t i v e comparison is made w i t h a simple theoretical model of Fuchs 6. Reasons f o r d i s c r e p a n c i e s are considered in terms o f modern concepts o f filtration. Introduction Even w i t h the a l t e r n a t i v e s o f f e r e d by current s o p h i s t i c a t e d technology f i b r o u s f i l t e r s are the choice f o r the e f f i c i e n t removal o f submicron s i z e d a e r o s o l c o n s t i t u e n t s from a i r streams. Although simple i n design and a p p l i c a t i o n such f i l t e r s i n v o l v e removal mechanisms "which r e s u l t i n complicated mathematical models for even the s i m p l e s t i d e a l i z e d c o n d i t i o n s . Consequently both the a n a l y s i s o f f i l t r a t i o n data and the q u a n t i t a t i v e r a t i o n a l e for comparison o f f i l t e r s are often ad hoc i n nature and l i m i t e d i n a p p l i c a b i l i t y . Moreover the b e t t e r t h e o r e t i c a l models, although reproducing some parametric dependencies, often give r e s u l t s d i f f e r i n g from experimental data by orders o f magnitude. The present study vas i n i t i a t e d t o provide at l e a s t a semie m p i r i c a l formalism for the study and assessment o f a e r o s o l f i l t r a t i o n by f i b r o u s f i l t e r s . This paper describes the b a s i s of the formalism and i t s a p p l i c a t i o n t o f i l t r a t i o n data f o r ten d i f f e r e n t types o f f i b r o u s f i l t e r s . The f i l t r a t i o n data c o n s i s t s of p e n e t r a t i o n - v e l o c i t y p r o f i l e s f o r each o f the types o f f i l t e r s challenged by d i o c t y l p h t h a l a t e (DOP) aerosols -with each o f four d i s t i n c t d r o p l e t s i z e s ( 0 . 2 6 , 0.28, 0 . 3 0 , 0.32 ym). P r o f i l e s 91
92
R E M O V A L OF
TRACE CONTAMINANTS F R O M THE
AIR
c o v e r t h e l i n e a r f a c e v e l o c i t y r a n g e , 7· 2 t o 1^1.0 cm/sec. The f o r m a l i s m c h a r a c t e r i z e s t h e d a t a i n terms o f t h r e e removal mechanisms: i n e r t i a l i m p a c t i o n , d i f f u s i o n and i n t e r c e p t i o n . A c o m p a r i s o n i s made t o t h e o r e t i c a l r e s u l t s g i v e n b y a s i m p l i s t i c m o d e l b y F u c h s . Reasons f o r d i s c r e p a n c i e s a r e d i s c u s s e d . Theory As a s t a r t i n g p o i n t we a d o p t a m o d i f i c a t i o n — o f a semie m p i r i c a l t r e a t m e n t b y Dorman-3_L-Ll^ w h i c h s t a t e s t h a t t h e p e r c e n t p e n e t r a t i o n , P_, o f t h e f i l t e r i s g i v e n by t h e r e l a t i o n 1
Ρ = 2 - k-LV*- k^LV 1 JJ
log
y
2
L
-k
(l)
η
where L i s t h e t h i c k n e s s o f t h e f i l t e r , V i s t h e l i n e a r f a c e v e l o c i t y , k^, k^ and k a r e Dorman p a r a m e t e r s c h a r a c t e r i z i n g t h e mechanisms o f i n e r t i a l i m p a c t i o n , d i f f u s i o n and i n t e r c e p t i o n r e s p e c t i v e l y , and χ and v_ a r e numbers c h o s e n e i t h e r f r o m t h e o r y or from f i t t i n g e q u a t i o n ( l ) t o data. P a r t o f t h e p r e s e n t study i s t o r a t i o n a l i z e c h o i c e s f o r χ and v_, v a r i o u s a u t h o r s -5- h a v i n g f o u n d 1< χ >
Η Ο Ο Η
Ο
$
ο Η
1
IT
$
ο
0.531
0.021
0.459
0.018
N15
Esparto
0.611
0.955
1.85
0.529
0.826
1.60
AA
AAA
75.7
81..1
70.8
40.9
2.12
28.5
30.5 43.8
32, .7 46,.9
0.798
1, .10
0,.702
26.9
0.13
0.14
0.15
0.002
0.,001
0.44
1.67
0.47
1.76
0.006
1.89
21.4
2,,02
22, .7
25.2
9.34
4.76
0.03
4.25
29. .3
33.6
12.4
6.33
5..52 10,.8
0
7.21
0
0 0
:
0.04
39.7
20.4
μ
0.32
0.04
ΙΛ
0
0..03
4. .93
34.9
30. .4 26.2
61.8
65.4
70.0
75-.0
10.1 8. .77 7.57
18.0
15. ,6
30.3
μ
μ
0.30
32.4
13.5
μ
0.28
34. .7
43.6
μ
0.26
46.2
μ
0.32
49.4
μ
0.30
—1 I n t e r c e p t i o n k^(cm )
53- ,0
μ
0.28
0.,005
2.4l
1.56
0.26
JJ
0.027
μ
Theory
0.,024
0.001
A
V i s e . 3.0D
1.5D
1.85
1.60
NI 3
Vise.
0.,912
0.794
0.687
Nil
2.,12
1. • 37
μ
1.19
μ
1.03
μ
0.26
lype 5
Mat
Filter
from Fuchs'
—1/3 —2/3 D i f f u s i o n a l k^(cm sec )
Dorman P a r a m e t e r
CALCULATED DORMAN PARAMETERS FOR FIBROUS F I L T E R MATS
—2 I n e r t i a l k^.(cm s e c ) 1 0.28 0.30 0.32
TABLE V I I .
104
R E M O V A L OF TRACE CONTAMINANTS
FROM THE
AIR
p o i n t t r a j e c t o r y c a l c u l a t i o n s u s i n g assumed f l o w f i e l d s show a s i g m o i d a l shape when p l o t t e d v e r s u s V . O n e s t u d y 91^-® r e p r o d u c e d t h i s s i g m o i d shape w i t h a r e l a t i o n i n the f o r m
a-J^ + a v2 + ^
(26)
2
Use o f e i t h e r V o r V as t h e v e l o c i t y d e p e n d e n c e o f t h e i n e r t i a l t e r m i s an a p p r o x i m a t i o n f o r t h i s . D e p e n d i n g on t h e relative m a g n i t u d e s o f t h e a^ i t a p p e a r s t h a t V i s more s u i t a b l e as t h e 2
l e a d i n g t e r m i n a n e x p a n s i o n o f (26). H o w e v e r , s u c h an e x p a n s i o n is only weakly j u s t i f i a b l e . The u s e o f t h e s i m p l e l i n e a r dependence on V appears t o be t h e cause o f t h e discrepancies between the e x p e r i m e n t a l and c a l c u l a t e d k ^ . Conclusion A l t h o u g h not t o t a l l y j u s t i f i a b l e on t h e o r e t i c a l g r o u n d s , o u r m o d i f i e d Dorman p r o c e d u r e i s a u s e f u l q u a n t i t a t i v e means t o compare f i l t e r s . The a d d i t i o n a l c o m p u t a t i o n s o f f u l l f l o w t h e o r y , a l t h o u g h more s a t i s f y i n g c o n c e p t u a l l y , seem u n w a r r a n t e d f o r practical applications. The f u l l t h e o r y i s , o f c o u r s e , n e c e s s a r y for s c i e n t i f i c studies. Glossary a^
numerical coefficients
b.
theoretical
d
coefficients
i n approximate in
inertial
log % penetration
f
diameter
of
the
aerosol
filtering fiber
dp
diameter
of
the
aerosol
particulate
h
one h a l f
the
k
f i l t e r i n g f i b e r s (cm) Dorman p a r a m e t e r f o r d i f f u s i o n a l f i l t r a t i o n
average
distance
between
term expression
(cm)
(cm) nearest
neighbor
(cm
sec
-2/3
—1 k
Dorman p a r a m e t e r
for
inertial
filtration
(cm
k^ I m χ y A D L No Ρ P^ R Τ
Dorman p a r a m e t e r f o r i n t e r c e p t i o n a l f i l t r a mean f r e e p a t h o f a i r m o l e c u l e s (cm) mass o f a e r o s o l p a r t i c l e (g) exponent of v e l o c i t y i n i n e r t i a l term exponent of v e l o c i t y i n d i f f u s i o n term numerical factor equal to unity i n d i f f u s i Diffusion coefficient of aerosol particles t h i c k n e s s o f f i l t e r mat (cm) ^ A v o g a d r o s number ( m o l e c u l e s mole ) Percent penetration of aerosols through a a t m o s p h e r i c p r e s s u r e , (cm Hg) ]_ _]_ U n i v e r s a l gas c o n s t a n t ( e r g s g mole deg A b s o l u t e temperature ( K)
tion
)
/
(cm
—2
\
sec)
on coefficient (cm sec )
T
filter ι )
)
8.
MAGEE ET AL.
V V Op CLj Op ε σ p_ I p^
Aerosol Filtration by Fibrous Filter Mats
105
1
l i n e a r face v e l o c i t y o f flow through f i l t e r (cm sec ) mean face v e l o c i t y defined by egn(6) (cm sec" ) dimensionless Fuchs c o e f f i c i e n t f o r d i f f u s i o n a l f i l t r a t i o n dimensionless Fuchs c o e f f i c i e n t f o r i n e r t i a l f i l t r a t i o n dimensionless Fuchs c o e f f i c i e n t f o r i n t e r c e p t i o n volume v o i d f r a c t i o n i n f i l t e r mat volume f i b e r f r a c t i o n i n f i l t e r mat d e n s i t y o f f i b e r m a t e r i a l (g cm" ) _o Bulk d e n s i t y of f i l t e r mat (g cm ) d e n s i t y o f DOP a e r o s o l p a r t i c l e (g cm" ) mechanical r e l a x a t i o n time owing t o v i s c o u s forces (sec) 1
f
1
3
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Jonas, L . Α . , Lochboehler, C . M . , Magee, W. S., E n v i r o n . Sci. T e c h n o l , 6, 821 (1972). Magee, W. S., Jonas, L . Α . , Anderson, W. L., E n v i r o n . Sci. T e c h n o l , 7, 1131 (1973). Dorman, R. G., "Aerodynamic Capture o f Particles," Pergamon P r e s s , Oxford, 1960. Dorman, R. G., Air Water Pollution, 3, 112 (1960). Dorman, R. G., Chapter V I I I in "Aerosol Science," C. N . D a v i e s , Ed., Academic P r e s s , New Y o r k , New Y o r k , 1966. Fuchs, Ν. Α., "The Mechanics of Aerosols," Pergamon P r e s s , M a c m i l l a n , New Y o r k , New Y o r k , 1964. Green, H. L . and Lane, W. R., "Particulate Clouds: Dusts, Smokes, and Mists," E . &F. N . SPON Ltd, London, 1957. D a v i e s , C. Ν . , "Air Filtration," Academic P r e s s , New Y o r k , New York 1973. P i c h , J., Chapter I X . in "Aerosol S c i e n c e , " C. N . D a v i e s , Ed., Academic P r e s s , New Y o r k , New Y o r k , 1966. L a n d a h l , H. and Hermann, K., J. C o l l o i d Sci. 4, 103 (1949).
