Page 23 - Air Pollution Control Engineering

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4 Lawrence K. Wang et al.

molecules (l); (2) next is the Cunningham group, which consists of particles with diam-
eters about equal to l; (3) the largest is the Stokes group, which consists of particles with
diameters much larger than l. The reported values of l are quite varied, however, for air
at standard conditions (SC) of 1 atm and 20ºC and range from 0.653 × 10 −5 to 0.942 ×
10 −5 cm. One can also estimate l for air at a constant pressure of 1000 mbar using
l = 223 ×10 −8 T (1)
.
where l is the mean free path of air (cm) and T is the absolute temperature (K).
One also can estimate the terminal settling velocity of the various size spherical par-
ticles in still air. The Stokes equation applies for that group and gives accuracy to 1%
when the particles have diameters from 16 to 30 µm and 10% accuracy for 30–70 µm:
v = d g ρ 18 µ g (2)
2
p
s
where v is the terminal settling velocity (cm/s), d is the diameter of the particle (cm),
s
2
g is the gravitational acceleration constant (980 cm/s ), ρ is the density of the particle
p
−4
3
(g/cm ), and µ is the viscosity of the gas (g/cm s, where µ for air is 1.83 × 10 ).
g g
Particles in the Cunningham group are smaller and tend to “slip” through the gas
molecules so that a correction factor is required. This is called the Cunningham correction
factor (C), which is dimensionless and can be found for air at standard conditions (SC):
C =1+ T( ( { 2 ×10 −4 )) }{ 2 79 + 0 894 exp − d ( [ 1 2 47 ×10 −3 T ) ]} (3)
.
.
.
d
1
where T is the absolute temperature (K) and d is the particle diameter (µm). When Eq.
1
(2) is multiplied by this factor, accuracy is within 1% for particles for 0.36–0.80 µm and
10% for 1.0–1.6 µm. Particles of the molecular kinetic size are not amenable to settling
because of their high Brownian motion.
Liquid particulate and solids formed by condensation are usually spherical in shape
and can be described by Eqs. (1)–(3). Many other particulates are irregularly shaped, so
corrections must be used for these. One procedure is to multiply the given equations by
a dimensionless shape factor (K):
( )
.
.
K = 0 843log K′ 0 065 (4)
where K′ is the sphericity factor and
K = 1 for spheres
K = 0.906 for octahedrons
K = 0.846 for rod-type cylinders
K = 0.806 for cubes and rectangles
K = 0.670 for flat splinters
Concentrations of air pollutants are usually stated as mass per unit volume of gas (e.g.,
3
µg/m , or micrograms of pollutant per total volume of gases) for particulates and as a vol-
ume ratio for gases (e.g., ppm, or volume of pollutant gas per million volumes of total
gases). Note that at low concentrations and temperatures (room conditions) frequently
present in air pollution situations, the gaseous pollutants (and air) may be considered as
ideal gases. This means that the volume fraction equals the mole fraction equals the
pressure fraction. This relationship is frequently useful and should be remembered.
Special methods must be used to evaluate the movement of particulates under conditions
in which larger or smaller particles are present, of nonsteady state, of nonrectangular