PARTICLE CHARGING AT LOW PRESSURES«
APPENDIX
.
279
oat
DERIVATION OF EQUATIONS FOR CALCULATING FRACTION,
i
os
.
OF CHARGED PARTICLES
. ®
oe
ar
The number of ions striking a unit surface area in the time interval,
dt, is, according to kinetic! theory, 1, N¢d& where N is tlg:don density
and c is the mean speed ofthe ips. If the diameter of a nevbsel particle
is dp, then the probability that this particle will be struck by an ion in
the time interval dt and thus becomecharged is ‘4 Ne 7 d% dt. If there
are N, such neutral particles at time,.t, then the folkewing«mumber
dNp = —Np {4 Ne 7d a
ihe
wo %,
ok
Pe
ee
aac
é a dt dt
ae
?
1s oe
Hence
fog
would be struck by ions during the tim@interval dt:
(A.1)
This equation can be integrated wal,
“yespect to un With the
initial condition that Np = Npg att = 0, the following equatioriis obtained:
Np = Npy exp (—'4 1 dpeNb)
“ie
en
Tr
*
Es
a€
(A.2)
Since the number of particles that becomé “charged iat, , the
fraction, f, of particles that become chargeciyttimeOmES
0 to te
=tis
2
(Nt). =
4
1 dae
then
= 1— exp [—Nt/(Nt),] oo
Equations A.5 and A.4 are plotted in Figs. 9 and 10, respectively.
REFERENCES
1, G. W. Hewitt, The Charging of Small Particles for Electrostatic Precipitation, Trans. Am. Inst. Elec. Engrs., 7611; 300 (1957).
2. G. W. Penney and R. D. Lynch, Measurements of Charge Imparted to Fine
Particles by a Corona Discharge, Trans. Am. Inst. Elec. Engrs., 761: 294~
299 (1957).