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

and pressure also influence the voltage–current relationship as a result of changing gas
density because ion mobility decreases with gas density.
The particle size of the dust is also very important in the determination of the value
of migration velocity for design purposes. The variations in migration velocity result
largely from particle size variations. With improved particle sizing techniques, the
Deutsch–Anderson equation may be modified as

 wA 
i
η =− exp  −  (42)
1
 Q 
i
where η is the fractional collection efficiency for the ith particle size, w is the migration
i i
velocity of the ith particle size, and the overall collection efficiency η is the summation
of fractional collection efficiency η times mass fraction f :
i i
n
η = ∑ η f (43)
i mi
= i 1
where f is the mass fraction of the ith particle size.
mi
Penney commented that the Deutsch–Anderson equation neglects the adhesion
problem (18). In a two-stage precipitator in which the electrical force reverses and tends
to pull the particle off, adhesive forces can still hold the particle. Adhesion is essential
in the collection of the lower-receptivity particle. Also, it is of importance in the trans-
fer of the particle from the collecting electrodes to the hopper. The effective transfer of
particles to the hopper is mainly dependent on the function of chunks or agglomeration
of particle, which can effectively fall with a minimum re-entrainment.
Adhesion resulting from differences in contact potential appears to be effective for par-
ticles of a few micrometers or less, but ineffective for large particles. More basic research
on the adhesive behavior is required in parallel with precipitator performance tests so
that proper rapping mechanisms can be designed to balance the various effects on changes
in the adhesive behavior.
2.4.3. Particle Re-entrainment
Once captured in an electrostatic precipitator, particles remain captured only in the
case of liquid droplets. Dry, solid particles are only lightly held onto the collecting elec-
trode and can be easily dislodged and re-entrained into the gas stream. Re-entrainment
may occur as a result of (1) low particle resistivity, (2) erosion of the particle from
collecting electrodes, and (3) rapping.
The dominant force holding particles on the collecting surface results from the flow
of current through the particles; if the particle resistivity is too low, not enough charge is
retained by the particle. In this case, the negative charge may leak off the particle, which,
in turn, acquires a positive charge from the collecting electrode and is forcefully accel-
erated away from that electrode. Large fly ash particles and carbon black particles
exhibit low resistivity. In the case of fly ash, the re-entrainment problem can be reduced
by using high-efficiency cyclones preceding the electrostatic precipitator. Carbon black
particles are too small to be separated by cyclones; nevertheless, the electrostatic precip-
itator helps to agglomerate the carbon particles into coarser particles, which then can be
removed by cyclones that follow the electrostatic precipitator.