Page 206 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

6.5 Filtration 181

Q
U 1
U 0 ¼ ¼ ð6:90Þ
1 a ð 1 aÞA c
The number concentration of particles lost per unit volume from the bulk air
over the distance dx equals to that captured by the fiber with a single fiber efficiency
g corresponding to an approaching flow rate of U 0 d f ds f ; where d f ds f defines
sf
the cross section area of the fiber with the length of ds f and the diameter of d f .

Q dC N ðxÞ¼ g C N ðxÞU 0 d f ds f ð6:91Þ
sf
3
where C N is the number concentration of particles (#/m ), the single fiber efficiency
g is determined by Eq. (6.87).
sf
The LHS stands for the decrease in particle number per unit time after air passes
through the bulk filter thickness dx, whereas the RHS stands for the reason of this
decrease calculated as if all these particles passed through a single fiber with a cross

with an approaching speed of U 0 and a single fiber
section area of d f ds f
efficiency of g . Equations (6.88) and (6.91) give,
sf
4aA c dx
A c U 1 dC N ðxÞ¼ C N ðxÞg U 0 d f
sf 2
pd
f
ð6:92Þ

dC N ðxÞ U 0 g 4a
sf
¼ dx
C N ðxÞ U 1 pd f
Consider Eq. (6.90), we have

dC N ðxÞ g 4a
sf
¼ dx ð6:93Þ
C N ðxÞ ð 1 aÞpd f
At any instant, all the parameters in the bracket on the right-hand side are
constants for the particle size of d p , which allows us to integrate from inlet to outlet
of the filter:
C Z No dC N xðÞ Z L g 4a
sf
¼ dx ð6:94Þ
C N xðÞ ð 1 aÞpd f
C Ni 0
which gives the overall fractional penetration through the filter

sf
C No g 4aL
Pd p ¼ ¼ exp ð6:95Þ
C Ni ð 1 aÞpd f
Consequently, we can get the overall fractional filtration efficiency of the filter as