PARTICLE CHARGING AT LOW PRESSURES
269
where np is the number of elementary units of charge on particle, 7 is
the viscosity of air, in poises, and C is Cunningham’s correction to
Stokes’ law (dimensionless).!?
The charge spectrometer was designed so that several independent
procedures could be used to determine the particle charge. These
procedures have been described in detail in Ref. 14. The present
procedure of placing electron-microscope grids at intervals along the
center rod of the charge spectrometer for particle collection and for
charge measurement is the most direct and reliable procedure since
it
allows
the particle size to be directly measured from electron
micrographs. The procedure has the further advantage of permitting
the determination of particle-charging data over a decade range of
particle sizes from a single run by using a polydisperse aerosol.
However, the procedure is tedious since a large numberof particles
must be sized from the electron micrographs to obtain a good statistical average. Sample electron micrographs are shown in Fig. 5. The
magnification of the electron microscope was established directly each
time the microscope was used by means of a carbon replica of a dif-
fraction grating of 54,864 lines per inch. The nominal magnification of
the electron microscope was not used.
EXPERIMENTAL RESULTS
The measured charge on particles of various sizes is presented in
Figs. 6 to 8 for particles charged inan electric field of 240 volts/cm at
0.01 atm. The results were obtained from electron micrographs similar
to those presented in Fig. 5.
Figure 6 shows the results of two tests
in which different ion
densities, N, and different charging times, t, were used. However, the
product Nt was the same for the two tests. The close agreement between the results of these two tests indicates that the particle charge
is primarily a function of the product Nt, if other conditions remain
constant, and is independent of the individual values of N and t occurring
in the product. This is to be expected from both Eqs. 1 and 2 and has
been shown by Hewitt! to be true for charging at atmospheric pressure.
Also included in Fig. 6 are two theoretical curves calculated from Eqs.
1 and 2 for conducting particles (i.e., K = ©), The measured charge is
seen to be much higher than the charges predicted by Eqs. 1 and 2.
Figures 7 and 8 show the effect of varying the Nt product on the
particle charge and particle mobility. The increase in particle charge
and particle mobility with increasing Nt shows that these particles can
be charged to higher levels by using higher Nt values. The relations
between the particle charge and the particle size in Fig. 7 are linear
on the log—log plot. This indicates that these relations can be represented by an equation of the form