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102 4 Properties of Aerosol Particles

Example 4.4: Stokes number
Estimate the Stokes number of a 1 μm spherical particle with a density of 8,000 kg/m 3
in an air flowing at 1 m/s normal to a cylinder of diameter 10 cm, assuming standard
conditions.
Solution
3
Given d e =1 μm, u o = 1 m/s, d c = 10 cm, ρ p = 8000 kg/m , we get
Kn ¼ 2k=d p ¼ 2k=d e ¼ 2 0:066=1 ¼ 0:132

0:999
C c ¼ 1 þ Kn 1:142 þ 0:558 exp ¼ 1:166
Kn
2 6 2
q d C c u 0 8000 1 10 1:166 1 4
p p
Stk ¼ ¼ 5 ¼ 2:86 10
18ld c 18 1:81 10 0:1
Note that the geometric diameter is used in calculating the Knudsen number
because Kn is a geometric ratio rather than an aerodynamic property.

The small Stokes number indicates that this particle follows the air under
standard conditions and it is difficult to separate the particle from the air simply by
inertia. However, it is feasible under other conditions, when the particle viscosity is
reduce and the particle Cunningham correction factor is enhanced by great air mean
free path. In-depth analysis will be introduced in Chap. 13.

4.2.5 Diffusion of Aerosol Particles

Diffusion of gas borne particles takes place when there is a gradient of particle
concentration in the space. It results in a net transport of particles from a region of
higher concentration to that of lower concentration. The transport flux of the gas
borne particles is defined by Fick’s first law of diffusion. In the absence of external
forces, Fick’s law is the same as that for gases,

dn
J ¼ D p ð4:28Þ
dx
where J = flux of particles, expressed in terms of the number of particles per unit
2 2
area per unit time (#/s•m ), D p = diffusivity of the particles in the gas (m /s), and
dn=dx = gradient in number concentration of particles (1/m).