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

2.3. Particle Charging
Particle-charging mechanisms generally considered relevant in electrostatic precipi-
tation are (1) field charging, also known as impact charging or ion bombardment, wherein
particles are bombarded by ions moving under the influence of the applied electric field,
and (2) diffusion charging, wherein particles are charged as a result of the motion of the
ions produced by the thermal motion of surrounding gas molecules. The field-charging
mechanism predominates for particles larger than 0.5 µm, whereas the diffusion-charg-
ing mechanism predominates for particles smaller than 0.1 µm. However, both mecha-
nisms are important in the size range 0.1–0.5 µm.
2.3.1. Field Charging
Assume that a spherical particle of radius a is placed in a uniform corona discharge
field E in a gas and that the particle bears no charge initially. As soon as a charge is
0
acquired by the particle as a result of ion bombardment, an electric field is created that
repels similarly charged ions. Some ions continue to strike the particle, but the rate at
which they do so diminishes until the charge acquired by the particle is sufficient to
prevent further ions striking it. This is the limiting charge that can be acquired by the
particle. Assume that the particle has acquired a uniform surface charge q. The particle
charge distorts the field E and imparts to it a radial component, which can be shown
0
(11) to be
  D −  1 a 3  q
E = E cosθ 2 +1 + r ≥ a (17)
r 0   3  2
 D +  2 r  4 π Kr
0
where D is the particle dielectric constant, r is the radial direction from the center of the
particle, and θ is the polar angle between r and the undistorted field E . An ion of
0
charged q is attracted to the particle if the ion approaches from an angle θ for which the
i
radial force F = q E is negative. Particle charging ceases at F = 0. Setting θ=π and
r i r r
r = a and defining
P = 3 D (18)
D + 2

the saturation or limiting surface charge acquired by the particle turns out to be
2
q =π K Pa E
4
max 0 0 (19)
Pauthenier and Moreau-Hanot (17) found that the particle charge as a function of time
is given by
q = q  t  (20)
f max  t +  τ

where τ, in seconds, is the particle-charging time constant, given by

τ = 4K 0 (21)
qm N
i
i
where N is the ion concentration and τ is the time required for 50% of maximum charge
to be acquired.