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178 6 Separation of Particles from a Gas

e r 1 q
2
g ¼ 1:5 2 ð6:86Þ
E
e r þ 1 12plU 0 e 0 d p d f
where ε r = relative permittivity of the fiber and e 0 = permittivity of a vacuum. Note
that this equation was validated with the experimental measurements using glass
fiber filters.
As introduced in Sect. 6.2, gravitational settling is not effective for micron
particles, and it works only for large particles. Similarly, it does not play an
important role in filtration compared to other mechanisms. We will skip its ana-
lytical solution.

6.5.1.2 Total Efficiency of a Single Fiber

With the filtration efficiency of each mechanism determined, the total efficiency of a
single fiber per unit length is

g ¼ 1 1 gð it Þ 1 g ip ð 1 g Þ 1 gð E Þ ð6:87Þ
D
sf
In the computation of each component, the value should be less than or equal to
1.0.
Although each of the five filtration mechanisms plays a role in many cases, their
relative importance is size dependent. As shown in Fig. 6.12, the contribution of
diffusion drops with the increase of the particle diameter, whereas the effects of
other mechanisms increase with particle diameter.
Example 6.4: Filtration efficiency based on different mechanisms
A fiber filter has a solidity of 3 %. The average diameter of the fiber is 5 µm.
Estimate the single fiber efficiency based on, interception, impaction, and diffusion,
respectively, when the face velocity is 0.05 m/s.
Solution
In this example, the following parameters are considered as constant
2k 2ð0:066Þ
d f ¼ 5 lm; a ¼ 0:03; Kn f ¼ ¼ ¼ 0:0264
d f 5
lna 3 a 2
Y ¼ þ a ¼ 1:033; l ¼ 1:81 10 5 Pa s
2 4 4
The following variables can be calculated in an Excel sheet for different particle
diameters