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Emerging Pollution Control Technologies 455

For small spherical particles that are in the low-Reynolds-number region, Eq. (8) can
be resolved to produce Stokes’s equation for the terminal settling velocity V :
s
2
V = d (ρ −ρ ) g / (18 µ ) (13)
s p g g
This yields good results for particles from about 3 to 30 µm in diameter. Particles
with diameters less than 3 µm tend to slip through the gas molecules, and the terminal
settling velocity must be corrected by multiplying Eq. (13) by the Cunningham slip
correction factor C:

−4
3
C = 1 + [(2T × 10 )/d] {2.79 + 0.894 exp − [(2.47 × 10 )(d) / T]} (14)
Note that in this equation, T is the absolute temperature in degrees Kelvin and D is the
particle diameter in micrometers.
In settling devices, it is usually assumed that the particles fall in a quasistationary
manner; that is, particles reach terminal-settling velocity instantaneously. However, it is
necessary to consider the forward motion of the particles to make sure that the particles
are not thrown out of the other side of the device. Entering particles are assumed to be
moving at the same velocity as the entering gas. This makes it necessary to evaluate a
non-steady-state force balance where the resultant force is essentially equal to the sum
of gravitational force, and particle-stopping distance X is obtained by resolving this
s
equation at low Reynolds number for spherical particles:
2
X = V d ρ /(18µ ) (15)
s 0 p g
where V is the initial velocity. The distance for particles of less than 3 µm in diameter
0
is obtained by correcting Eq. (15) by multiplying by C.
The size of particle that can be completely removed in a gravity separator can be
found using

d = (36 V h µ /ρ gL) 1/2 (16)
m 0 g p
where V , h, and L are shown in Fig. 4.
0
The settling chamber fractional efficiency η for specific size particles can be esti-
mated using
η= 0.5 V L/(V h) (17)
s 0
4.3. Other Methods
Many forces, including gravity, which was just discussed, are available for use in
particle collection devices. Systems that use centrifugal and electrostatic forces are cov-
ered in other chapters. This leaves devices that use forces such as inertial impaction
phoretic forces, interception, and thermal, sound, and magnetic forces for operation.
Additionally, there are hybrid systems utilizing various combinations of forces.
Interception, which is the sticking of a particle that just grazed the collector as it passed,
is often not distinguished from impaction. Magnetic forces are usually only used for
very large material. Thermal precipitators and sonic agglomerates are specialty systems
and have not been used for control of particulates on a large scale.
In Sections 4.3.1–4.3.3, inertial impaction, phoretic forces, and hybrid devices are
briefly considered. In these subsections, particular emphasis will be placed on fine