Page 202 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

6.5 Filtration 177

and the Peclet number is

U 0 d f
Pe ¼ ð6:80Þ
D p
where U 0 is the air velocity approaching the filter fiber, and D p is particle diffusion
coefficient that can be calculated using Eq. (6.81).

kTC c
D p ¼ ð6:81Þ
3pld p
Peclet number shows the effect of convective transport over diffusive transport
of particles.
Later on, Lee and Liu [20] further simplified the Eq. (6.78) for diffusion as,

1=3
1 a 2=3
g ¼ 2:6 Pe ð6:82Þ
D
Y
This simplified equation shows that g / Pe 2=3 for a filter with a fixed solidity.
D
A general equation for single fiber filtration by interception can be described as
(Lee and Liu [20], p. 152)
1 þ R h a 2 a 2 i
g ¼ 2 ln 1 þ RÞ 1 aÞ þ 1 ð 1 þ RÞ ð 1 þ RÞ ð6:83Þ
ð
ð
it
2Y 2 2
Equation (6.83) is a complete expression based on Kuwabara flow fields with a
wide range of R and a. Simpler forms are given by Lee and Liu [20], p. 152 with
limitations. The respective simplified equations for the cases R 1or a 1 are as
follows:

ð 1 aÞ R 2
g ¼ for R 1 ð6:84Þ
it
Y 1 þ R
1
ð
ð
21 þ RÞ ln 1 þ RÞ 1 þ RÞ 1 þ RÞ
ð
ð
g ¼ for a 1 ð6:85Þ
it
2Y
6.5.1.1 Electrostatic Attraction
In most filtration models, electrical attraction is ignored, not because of its little
importance, but rather the complex in the quantification of its effect. Nonetheless,
Brown [3] gave a review of the theory of particle separation by electrostatic
attraction. He introduced the single fiber efficiency for a neutral fiber and a particle
with charge q as