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168 Chung-Shin J. Yuan and Thomas T. Shen

Fig. 5. Schematic of gas flow passing through two plates in an electrostatic precipitator.

known as the Deutsch–Anderson equation. The derivation of the Deutsch–Anderson
equation is based on the following assumptions:

1. The particle concentration at any cross-sectional area normal to the gas flow is uniform
2. Gases move downstream at constant velocity with no longitudinal mixing
3. The charging and collecting electrical fields are constant and uniform
4. Particles move toward the collecting electrodes with a constant migration velocity
5. Re-entrainment of collected particles on the surface of collecting electrodes is negligible.
Consider a dusty gas flow in a rectangular channel confined by two parallel collecting
plates in an electrostatic precipitator, as illustrated in Fig. 5. The concentration of particles
decreases gradually with distance because of the migration of particles toward the col-
lecting plates. A material balance on particles flowing into and out of a control volume
shows that the difference between the mass of particles flowing through the slice ∆x
must equal the mass of particles collected at the collecting plates:
vH D 2) C − vH D 2) C x+∆ x = w C x+∆ x 2/ H x (36)
(
(
∆
x
where v is the gas flow velocity, H is the height of the plate, D is the width of the plate,
C is the particle concentration, and w is the migration velocity of particles. Dividing
through Eq. (36) by ∆x and taking the limit as ∆x approaches to zero
− ( vHD 2 )(dC dx ) = wHC (37)
Integrate Eq. (37) for distance x from 0 to L and for particle concentration C from inlet
particle concentration C to outlet particle concentration C ,
in out
ln C ( out C ) =−2 wHL vHD) (38)
(
in
Define the particle collection efficiency of an electrostatic precipitator η in terms of
inlet and outlet particle concentrations,
1
1
η= − C C = − exp( −wA Q)
out in (39)