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Electrostatistic Precipitation 169

which is the Deutsch–Anderson equation. A is the area of collecting plates and Q is the
volumetric gas flow rate.
This equation can be applied to both wire–cylinder and wire–plate (duct-type) pre-
cipitators. For a cylinder of radius R and length L and gas flow at velocity v,
A = 2π RL
Q =π R v
2

hence,
η = 1 − exp (−2wL Rv ) (40)

Similarly, for a duct precipitator of plate length L, plate height H, and the wire-to-plate
spacing b,
A = 2 LH
Q = DHv

hence,
− (
η= 1 − exp wL bv ) (41)
Comparison of Eqs. (40) and (41) shows that for a given collection efficiency, a
cylindrical precipitator may be operated at twice the gas velocity of a duct precipitator
of equal length and electrode spacing.
Equation (39) holds for conductive spherical particles in the size range for which
Stokes’ law is valid (i.e., laminar flow). In practice, laminar flow is rarely achieved.
However, at the boundary layer, the gas flow is laminar, and particles entering the bound-
ary layer will be collected. Nonspherical shapes and dielectric factors may very well
change the numerical coefficients but not the basic form of the equation. The
Deutsch–Anderson equation indicates clearly that for a given particle size, the collection
efficiency increases with increasing particle migration velocity or collecting surface
area, whereas the collection efficiency decreases with increasing gas flow rate. For a
constant volume of gas passing through the electrostatic precipitator, the maximum col-
lection efficiency occurs when the velocity is uniform. Collection efficiency decreases
as gas viscosity increases. The density and concentration of the particle do not appear
in the Deutsch–Anderson equation; however, they may exert a secondary influence. For
example, light and fluffy particles on the collecting surface are harder to remove; they
tend to fall more slowly to the hoppers and are subject to re-entrainment. High parti-
cle concentrations mean a greater mass of materials to be collected and disposed of.
Thus, particulate buildup on the collecting electrodes will be greater and rapping of the
electrodes may become critical.
The temperature and pressure of the flue gas have several important effects on the
performance of an electrostatic precipitator. First, gas viscosity increases with temper-
ature. An increase in gas viscosity would reduce migration velocity proportionally, as
defined previously in Eq. (32). Second, the gas volume V is directly proportional to the
absolute gas temperature T and inversely proportional to pressure P, as expressed in the
universal gas law PV = nRT, where n and R are the number of moles and universal gas
volume, respectively, resulting from higher temperatures. Finally, the gas temperature