Environmental Engineering Reference
In-Depth Information
4.4.8
Electrophoresis
A weakly ionized gas can be used to achieve the separation of isotopes and ele-
ments in a mixture of gases, by making use of the different currents for different
types of charged atomic particles. As such an example, we consider electrophoresis
in a gas discharge plasma. This phenomenon corresponds to a partial separation
of the components of the system [103]. We take a gas in a cylindrical tube to consist
of two components, a buffer gas (e.g., helium) and an admixture of easily ionized
atoms (e.g., mercury, cadmium, zinc). The admixture atoms will give rise to an ion-
ic component because of the low ionization potential of these atoms. The number
densities of the components satisfy the inequalities N
N i ,where N is
the number density of the atoms of the buffer gas, N a is the number density of
admixture atoms, and N i is the number density of ions.
Because the ion current arises from the admixture ions, we have the balance
equation
N a
D dN a
dx C
w i N i
D
0
for the admixture, where D is the diffusion coefficient of the admixture atoms in
the buffer gas, w i is the ion drift velocity, and the x -axisisdirectedalongthetube
axis. Assuming the ion diffusion coefficient D i and the diffusion coefficient D in a
gas for admixture atoms to be the same order of magnitude D i
D ,andusingthe
( d ln N a / dx ) 1
Einstein relation (4.38) for a typical size L
D
responsible for the
gradient of the admixture number density, we find that
T
eEc i
L
,
and admixture atoms are located in a region of size L . In this expression, c i
D
N i / N a is the degree of ionization of the admixture, T is the temperature of atoms
or ions, and E is the electric field strength. If the size L is small compared with the
discharge tube length, the admixture gas is gathered near the cathode.
Under electrophoresis conditions, a discharge plasma is nonuniform, and the
glowing of this plasma due to radiation from the excited atoms of the admixture
is concentrated near the cathode; this is of importance for gas lasers [104]. Elec-
trophoresis is established for a time
L /( c i w ) after switching off the discharge.
In fact, in a region near the anode, the number density of admixture atoms and
ions decreases. An increase of the rate constant for ionization is required, so the
electric field strength in this region must be increased. Thus, electrophoresis can
change the parameters of a gas discharge.
τ
4.4.9
Recombination of Positive and Negative Ions in Gases
Theanalysisofmotionofionsinagasinanexternalelectricfieldallowsusto
describe the character of recombination of positive and negative ions in a dense
 
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