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6.5 Filtration 183

g 4aL
sf
g d p ¼ 1 exp ð6:98Þ
ð 1 aÞpd f
The results are shown in Fig. 6.14.

Up to this point we assumed that filter fibers are oriented normal to the incoming
air flow. It is clearly not the case in most engineering applications. Fiber orientation
also affects the filtration efficiency and resistance to the air flow. The overall fil-
tration efficiency is affected by the three-dimensional randomness of the fiber ori-
entations too [31]. A filter with fibers randomly arranged in planes perpendicular to
the approaching air velocity is more efficient than a filter with fibers randomly
arranged in three dimensions.
The other assumptions in the preceding analysis of fibrous filtration are that all
the aerosol particles are spherical and that the adhesion efficiency is 100 %. These
simplifications do not introduce much of error because the likelihood of an aerosol
particle adhering to a fibrous filter depends on not only the air flow velocity but also
the particle–filter interfacial characteristics. Nonspherical particles are more likely
to be captured than spherical ones. And, functions that correct for imperfect
adhesion can be empirically derived for particular cases.

6.5.3 Fibrous Filter Pressure Drop

The pressure drop across a fiber filter is caused by the combined effect of each fiber
resisting the flow of air past it. Davies [8]defined a dimensionless filter pressure
coefficient as

DP
C DP ¼ . ð6:99Þ
4lU 0 L d 2
f
With a known pressure drop coefficient, the pressure drop can be calculated as

4lU 0 L
DP ¼ C DP 2 ð6:100Þ
d
f
By dimensionless analysis and experimental correlation, Davies [8] obtained
C DP as a function of solidity in the range of 0.06–0.3 as follows,

C DP ¼ 16a 1:5 1 þ 56a 3 ð6:101Þ

Combination of Eqs. (6.100) and (6.101) leads to the total pressure drop over a
bulk filter as