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404 13 Nanoaerosol

The single fiber filtration efficiency for interception mechanism η it is [41]

2
1 a R 1:996Kn f
g ¼ 0:6 1 þ ð13:14Þ
it
Y 1 þ R R
Y is the Kuwabara hydrodynamic factor, defined using Eq. (13.15). It is a function
of filter solidity a

lna 3 a 2
Y ¼ þ a for Kn f 1 ð13:15Þ
2 4 4
Kn f is the fiber Knudesn number described in Eq. (13.16)

Kn f ¼ 2k=d f ð13:16Þ

where d f is the fiber diameter and R is the interception parameter defined in
Eq. (13.17).

d p
R ¼ ð13:17Þ
d f

Example 13.1: Nanoaerosol filtration efficiency
A filter is made of fiberglass with a solidity of 5 %, and it is 5-cm thick. The average
diameter of the fibers is 5 µm. When the face speed is 0.15 m/s, calculate and plot
the fractional transport efficiency as a function of particle aerodynamic diameter in
the range of 1–100 nm under standard conditions, by interception and diffusion,
respectively.
Solution
In this problem, the following parameters are considered as constant

d f ¼ 5 lm; a ¼ 0:05; l ¼ 1:81 10 5 Pa:s
2k
Kn f ¼ ¼ 0:0264
d f
lna 3 a 2
Y ¼ þ a ¼ 0:80
2 4 4
The following variables can be calculated in an Excel sheet for different particle
diameters

d p
R ¼
d f