Page 187 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

162 6 Separation of Particles from a Gas

1
s ¼ ð6:37Þ
pN i0 K E eZ e
where Z e ¼ mobility of the ions, and the average value of the mobility of air ions is
2
about 1:5 10 4 m /V s. A typical charging constant is s ¼ 0:01 0:1 s using the
above equation.
The number of ions that is eventually charged to a particle depends on charging
time, the concentration of ions in the charging zone, and the electric mobility of
these ions, which determines the moving speed of the ions in response to the
electric field E. In a typical industrial application, the particle residence time t is of
the order of 10 s. Therefore, t s and we can assume maximum field charging,
which is from Eq. (6.36).

Ed 2
p 3e r
n max ¼ ð6:38Þ
4eK E 2 þ e r
6.3.2.3 Combined Charging

Combined charging takes into consideration both charging mechanisms. The total
number of ions charged to a particle is calculated using

2
d p kT d p K E c i pe N i0 Ed 2 p 3e r t
ntðÞ ¼ 2 ln 1 þ t þ ð6:39Þ
2e K E 2kT 4eK E 2 þ e r t þ s
On the right-hand side of the equation, the first term is for the effect of diffusive
charging and the last for field charging. The relative importance of diffusive and
field charging depends on the size of the particles to be charged. Since both dif-
2
fusive and field charging are a function of d , which indicates that it is not the
p
aerodynamic diameter but rather the actual surface area that affects the charging
effect.
Figure 6.5 shows the relative importance of diffusive and field charging; cal-
culation was based on the following parameters:

4
2
9
14
2

K E ¼ 9 10 Nm C 2 Z e ¼ 1:50 10 m Vs N io ¼ 5:00 10 ion m 3
e ¼ 1:60 10 19 C c i ¼ 240 m=s k ¼ 1:38 10 23 J=K
6
T ¼ 293 K E ¼ 1:0 10 V=m t ¼ 0:1s, e r ¼ 1
It shows that diffusion charging is an important mechanism for particles smaller
than 200 nm in diameter, whereas field charging dominates for particles larger than
2 μm.
In order to implement the charging mechanisms, diffusive, field, or both, there
have to be enough ions generated. Among the ion generation technologies, corona
discharge has been believed to be the most effective in producing sufficient ions. It
has been well known that ozone and aerosol particles, especially smaller ones, are