Page 120 - Air pollution and greenhouse gases from basic concepts to engineering applications for air emission control

94 4 Properties of Aerosol Particles

irregular. The shape of a particle affects its aerodynamic behavior by influencing its
drag resistance. Therefore, a correction factor called the dynamic shape factor is
necessary to correct the Stokes’ law.
The dynamic shape factor, taking symbol S f herein, is defined as the ratio of the
actual drag force of the nonspherical particle to the drag force of a sphere having the
same volume and velocity as the nonspherical particle. The dynamic shape factor S f
is then given by

F D
S f ¼ ð4:7Þ
j
3pl u vjd e
which gives the drag on a nonspherical particle in Stokes regime as

j
F D ¼ 3pl u vjd e S f ð4:8Þ
where d e is the equivalent volume diameter. It is the diameter of a sphere having the
same volume as that of the nonspherical particle. Note that the shape factor is 1 for
spherical particles. Most of the dynamic shape factors are greater than 1.0.
Dynamic shape factors are usually determined experimentally by measuring the
settling velocity of geometric models in liquids. For irregular particles, settling
velocities were measured indirectly using the elutriation devices [11]. An elutriation
device separates particles based on their size, shape and density.

4.1.4 The Knudsen Number and Cunningham Correction
Factor

An important assumption of the Stokes’ law is that there is no slipping between the
gas and the aerosol particles. It is also referred to as continuum flow. However,
when the particle is getting smaller and smaller, approaching the mean free path of
the gas molecules, this assumption of continuum transport is no longer valid. The
dimensionless parameter that defines the nature of the aerosol is the Knudsen
number (Kn), which is the ratio of gas mean free path to particle radius.

Kn ¼ 2k=d p ð4:9Þ
When Kn 1, the particle diameter is much greater than the mean free path of
the gas, and the particle is in the continuum regime. This applies to the preceding
analyses. On the other hand, when Kn 1, the particle size is much smaller than
the gas mean free path, and its behavior is like a gas molecule. The particle size
between these two extremes defines the transition regime.
When the system is in noncontinuum regime, Cunningham correction factor
(C c ), is used to correct the drag force.