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Electrostatistic Precipitation 167

will move to the collecting electrode in time t' = d/w, and the duct length for collection
efficiency of 100% is given by

=
L = vt' v  d 
 w  (35)
where L is in the direction of gas flow.
Example 3
Find the minimum length of a collecting electrode for a single-stage wire–plate-type pre-
cipitator with a 8-in. (0.2032-m) plate-to-plate spacing and an applied voltage of 600,000
V. Air velocity through the precipitator is 3 ft/s (0.9144 m/s) and the minimum particle
diameter is 1.0 µm.
Solution

Assume that E and E are the same; that is,
c p
,
E = E = 60 000 = 590 550 V m
,
c p
.
0 1016
2
Furthermore, let P =1, and µ for air at 25°C is 1.8 × 10 −5 N s/m . Thus, from Eq. (32),
w = ( 28 85. × 10 −12 )(0 5. × 10 −6 )(590 550, ) 2
3 × 1.8 × 10 −5
= 0.057 m s
which, after multiplying by the Cunningham correction factor, C=1.17, becomes
.
w = (0 057 )(1 17. ) = 0 0667. m s
Therefore, the length of electrode from Eq. (34) is

.
L = (0 9144 )(0 2032 2. / )(0 0667. ) = 1 4. m
Example 3 shows that 100% collection efficiency should result from a precipitator
about 1.4 m in length. This value may be representative of controlled laboratory condi-
tions. However, in practice, a precipitator for the conditions in Example 3 may well be
two to three times that length because the migration velocity w may, in practice, be two
or three times smaller than the idealized value given by Eq. (34). Such a discrepancy
arises because the migration velocity under realistic precipitator conditions is subject to
several factors such as uneven gas flow, re-entrainment of collected particles, and “effec-
tive” values of field intensity or space-charge density, which cannot be included in the
idealized theory. In engineering design, it is practical to use modified values of w that
are determined from actual field experience or are established by pilot-plant tests. The
theoretical equations therefore serve as a basis for analyzing field-precipitator perfor-
mance and for calculating a new design in which previous practical values for w exist.
The reader is referred to Tables 1 and 2 (Section 3.1) for typical values.
2.4.2. Particle Collection Efficiency
The particle collection efficiency of electrostatic precipitators was first developed
empirically by Evald Anderson in 1919 and then theoretically developed by W. Deutsch
in 1922. Thus, the collection efficiency equation of electrostatic precipitators is usually