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

In operation, migration velocity also depends strongly on factors such as accuracy of
electrode alignment, uniformity and smoothness of gas flow through the precipitator, rap-
ping of the electrodes, and the size and electrical stability of the rectifier sets. Migration
velocity can be estimated from a pilot-scale or an existing ESP system by using known
values for the collection plate surface area, volumetric gas flow rate, and particulate
collection efficiency in the Deutsch–Anderson equation.

Example 6
Find the migration velocity for an existing electrostatic precipitator, which the collection
3
2
plate area is 110 m , gas flow rate is 2.5 m /s, and collection efficiency is 99.5%.
Solution
3
Given: η = 99.5%, Q = 2.5 m /s, and A = 110 m 2
− (
η= − exp wA Q )
1
0 995 = 1 − exp − ( 100 / ) 2 5]
.
[ w
.
−
ln
w = (1 0.995 )(25. ) (110 ) = 012. m s (or 12 cm s)
3.2. Particulate Resistivity
Particulate resistivity, a measure of a particle’s resistance to electrical conduction, is
a fundamental indicator of migration velocity of the particles. Resistivity is of extreme
importance not only because it varies widely but also because it strongly influences the
collection efficiency of the precipitator. It could influence the electrostatic charges exerted
on the particles as well as the re-entrainment of collected particles from the collecting
plates. Once collected, the particles would release their charges to the collecting plates
depending on the particulate resistivity. The transfer of electrostatic charges completes
the electrical circuit, produces current flow, and allows maintenance of voltage drop
between the discharge and collecting electrodes.
The resistivity of a material can be determined experimentally by establishing a
current flow through a slab of the material. It is of importance to make resistivity
measurements of freshly collected particles in actual gas stream. In general, the mea-
surements should be made in the field rather than in the laboratory. Resistivities measured
in the laboratory on the same particles can be 100–1000 times greater than field resis-
tivities (23). The resistivity is defined as the resistance times the cross-sectional area
normal to the current flow divided by the path length (7):

Ra Va
p= = (44)
l il
where p is the particulate resistivity, R is the particulate resistance, a is the cross-sectional
area normal to the current flow, l is the path length in the direction of current flow, V is
the potential, and i is the current.
The resistivity of materials generally ranges from 10 −3 to 10 14 Ω-cm, whereas the
7
best range of the resistivity for particle collection in an ESP is 10 –10 10 Ω-cm. In gen-
eral, ESP design and operation are difficult for particulate resistivities above 10 11 Ω-cm.