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13.5 Nanoaerosol Characterization 417

2
p p
sU 0 q d C c U 0
Stk ¼ ¼ ð13:43Þ
d c 18ld c
where the characteristic dimension d c in the above equation depends on the specific
application. U 0 is the undisturbed air velocity. In standard air, a particle with
Stk ≫ 1.0 will continue in a straight line as the fluid turns around the obstacle. But
for Stk ≪ 1, particles will follow the fluid streamlines closely.
Example 13.4: Stokes numbers of nanoaerosol particles
Estimate the Stokes numbers of nanoaerosol particles with an aerodynamic particle
diameter of 100 nm in standard air flowing at 1 m/s perpendicular to a cylinder of
diameter 1 cm.
Solution
3
Given U 0 = 1 m/s, d c = 1 cm, q ¼ 1,000 kg/m , and d ¼ 100 nm
p p
Under standard conditions
Kn ¼ 2k=d p ¼ 2 66=100 ¼ 1:32

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

¼ 1 þ 1:32 1:142 þ 0:558 exp ¼ 4:36
1:32
2 9 2
q d C c U 0 1000 100 10 Þ 4:36 1 5
ð
p p
Stk ¼ ¼ 5 ¼ 1:34 10
18ld c 18 1:81 10 0:01
The extremely small Stokes number indicates that nanoparticles follow air under
STD conditions and it is difficult to separate them from the air simply by inertia.
However, it is doable under other conditions when the particle viscosity is reduced
and the particle Cunningham correction factor is enhanced. Under a carefully
engineered condition with low pressure, however, nanoaerosol particles can be
separated from the gas phase because of the relatively small amount of molecules
surrounding the nanoaerosol particles.
By this approach, nanoaerosol particles can then be focused to a beam after
expansion through an orifice, referred to as aerodynamic particle focusing. Aero-
dynamic focusing of particles has been employed for the accurate particle sizing
[13]. As depicted in Fig. 13.8, the trajectories of the aerosol particles depend on
their corresponding Stokes number. A well designed focusing orifice could isolate
particles down to a few nanometers [42]. Large particles cross the center line due to