PARTICLE CHARGING AT LOW PRESSURES
261
charging at atmospheric pressure. However, no low-pressure charging
data are available. The purpose of our present studies is to obtain ex-
perimental particle-charging data at the low pressures encountered in
operating electrostatic-precipitator aerosol samplers at high altitudes.
Electrical particle-charging theories have been summarized ina
recent book by White,’ who also showed that the electrical charge
imparted to particles can be calculated from the following two equations if certain simplifying assumptions regarding the particle-charging
mechanism are made:
np
=(1+2
(
K—1\
Ed?P
7 NeZit
i
re m NeZ;t +1
ne Sep in (1+SE)
aNe2
1
(1)
a
where n,= number of elementary units of charge on particle, dimenSionless
= dielectric constant of particle, dimensionless
E = intensity of applied electric field, statvolts/cm
dp = particle diameter, cm
e = elementary unit of charge = 4.803 x 107 esu
N = ion concentration, number of ions/cm?
Z; = electric mobility of ions, cm?/sec-statvolt
= charging time, sec
= Boltzmann’s constant
= mean speed of ions, cm/sec
= absolute temperature, °K
Equation 1 represents the so-called “field-charging process” in
which the ions are assumed to be driven onto the particles along the
electric-field lines. The effect of ion diffusion is neglected. Equation 2
is for the diffusion-charging process where it is assumedthat the
charging is due to the random thermal motion of the ions in the absence
of
an
applied electric field. In both equations, the mean free path
of the ions is assumed to be small compared to the diameter of
the particles. These equations have been found to be reasonably ac-
curate in predicting the particle charge if the experimental data are
obtained under such conditions that the assumptions made in deriving
these equations are nearly satisfied. However, in many charging
processes where both the field and diffusion mechanisms of particle
charging are of equal importance or where submicron particles are
involved whose diameters are of the same order of magnitude as the
mean free path of the ions, these equations are knownto predictincorrect particle charges. Attempts to solve the particle-charging
equations more rigorously by means of numerical methods and com-