Page 124 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

98 4 Properties of Aerosol Particles

Table 4.1 Time required for particles of standard density to reach their terminal velocity at
standard conditions
Particle diameter, 95 % of its maximum settling speed, Time to reach 0:95v TS
d p (μm) 0:95v TS (m/s) t ¼ 3s
0.01 0.0000001 0.0000000
0.1 0.0000008 0.0000003
1 0.0000331 0.0000107
10 0.0028980 0.0009329
100 0.2863625 0.0921817

2
q d gC c
p e
v TS ¼ ð4:23Þ
18lS f
Example 4.1: Terminal settling time
Consider a spherical glass particle with a diameter of 30 μm and a density of
3
2,500 kg/m is released from rest in still air. How long it will take to reach its
terminal velocity?

Solution
3
From d p ¼ 30 lm, q = 2,500 kg/m , and l ¼ 1:81 10 5 Pa s, we can get
p
0:066 lm
Kn ¼ 2k=d p ¼ 2 ¼ 0:0044
30 lm
Since 0:001\Kn\100, the Cummingham correction factor is calculated using

0:999
C c ¼ 1 þ Kn 1:142 þ 0:558 exp
Kn

0:999
¼ 1 þ 0:0044 1:142 þ 0:558 exp ¼ 1:055
Kn
The time it takes for the particle to reach its terminal speed is,

! !
2 6 2
q d C c 2500 30 10 1:055
p p
t ¼ 3s ¼ 3 ¼ 3 ¼ 0:0073 s
18l 18 1:81 10 5
Example 4.2: Sneezing droplet settling
Scientific research results indicated the total average size distribution of the droplets
by coughing was 0.58–5.42 μm, and 82 % of droplet nuclei were centered in
0.74–2.12 μm. A spherical droplet with a diameter of 5 μm and density of 1,000 kg/m 3
is discharged from the mouth horizontally in still air.