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Electrostatistic Precipitation 165

Fig. 4. Free-body diagram of a charged particle.

The above expression for particle space-charge density can be utilized to obtain a more
rigorous expression—more rigorous than Eq. (11)—for the effect of particle space charge
on the cylindrical corona field. Using σ , as given in Eq. (28), in Poisson’s equation, Eq.
p
(2), and solving for E gives

    2  i  i 
E =    r  0  E c 2 − 1  + 1 ( 2  e −2 PSr
r 
     2π Km  4π Km PSr)  
i
0
0
i
1/2

− i 1  2 + 1  (28)


4π Km PSr ( PSr) 
2
0 i  
A plot of field strength E versus radial distance from the above expression will show
that particle space charge works to lower the field near the wire surface (r ) and to raise
0
it at the cylinder wall (r ). The field reduction at the wire occurs because the space charge
1
tends to shield the discharge wire from the cylinder.
2.4. Particle Collection
Particle collection in electrical precipitators occurs when the charged particles move
to the surface of the collecting electrodes and are trapped by the electrostatic field. The
particles are accelerated toward the collecting electrodes by Coulomb forces, but iner-
tial and viscous forces resist the motion. Consequently, a particle in the precipitation
field attains a velocity, known as particle migration velocity, which is a fundamental
parameter important to all theories of particle precipitation.
2.4.1. Particle Migration Velocity
The motion of a charged particle is governed by the dynamics of the force system
acting on the particle, as illustrated in Fig. 4. The various forces acting in the precipita-
tion system are gravitational, inertial, viscous, and electrical forces. For fine particles of
interest in electrostatic precipitation, gravitation forces are quite insignificant and,
therefore, may be neglected. Abalance between the remaining forces on the particle yields