Page 121 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

4.1 Particle Motion 95

j
3pld p u vj
F D ¼ ð4:10Þ
C c
The Cunningham correction factor for aerosol particles can be determined using
the following equation recommended by Allen and Raabe [2]

0:999
C c ¼ 1 þ Kn 1:142 þ 0:558 exp ð4:11Þ
Kn
where k is the gas mean free path that was introduced in Sect. 2.1.7.
There are several alternative equations for the Cunningham correction factor,
differing only in the numerical factors. For example, Whitby et al. [28] (cited by
Otto et al. [19]) used a formula as

C c ¼ 1 þ 1:392Kn 1:0783 ð4:12Þ

And Flagan and Seinfeld [9] give a more complex one as follows.
8
1 þ 1:257Kn 1:0 Kn\0:001
<

1:10
C c ¼ 1 þ Kn 1:257 þ 0:40 exp 0:001\Kn\100 ð4:13Þ
Kn
1 þ 1:657Kn Kn [ 100
:
Equation (4.11) is used in this book unless otherwise specified. However,
readers are suggested to choose the equations in accordance to their specific
applications.
Both Knudsen number and Cunningham correction factor are dimensionless
parameters. Since the theoretical value of C c is always greater than 1, the drag force
experienced with slipping effect considered is always smaller than the value cal-
culated with nonslipping assumption.
For a small particle with irregular shape, both slip factor and shape factor are
supposed to be considered for particle dynamics analysis. However, the task is so
complicated that it outvalues the outcome. In air emission engineering, it is well
acceptable to use the approximate factor calculated for the equivalent volume
sphere for most irregular particles. The slip factor for randomly oriented fibers
(L=d\20) is 0–12 % greater than that for the equivalent volume sphere. Drag
coefficients of different particle shapes are available in the literature (e.g., [12, 15]).

4.2 Rectilinear Particle Motion

Steady rectilinear particle motion is the simplest yet important type of particle
motion in particle dynamics. It is the foundation for the mechanisms of particle
separation from air stream, namely particulate air pollution control.