Transport Phenomena in Ionized Gases - Fundamentals of Ionized Gases - page 213

For the classical character of movement of atomic particles, the elastic cross sec-
tions are expressed through the interaction potential between colliding particles.
Correspondingly, kinetic coefficients of gases are expressed through the interaction
potential of particles. In particular, if the interaction potential U ( R )variessharply
with a change of distance R between colliding particles, the diffusion coefficient is
expressed through the interaction potential between a test particle and gas atom
by [27-30]

3 p T
8 p 2

U ( R 0 )
T

D D , D 2.25 . (4.60)

NR 0

πμ

This formula assumes repulsion between colliding particles when the connection
between the diffusion cross section and a sharply varied interaction potential of
particles is given by (2.15). In the same manner, one can express the thermal con-
ductivity coefficients of a gas through the repulsion interaction

potential of atomic particles [27-30]:

and viscosity η

75 p T
64 p π

5 p T m
16 p π

U ( R 2 )
T

D , η D , D 0.83 . (4.61)

mR 2 R 2

Note that the classical character of collision of atomic particles requires that large
collision momenta l give the main contribution to the collision cross sections, that
is, l is a

typical collision impact parameter, and v is a typical collision velocity. Let us make
the estimation for collision of two nitrogen molecules at temperature T

D μ v / „ 1, where μ is the reduced mass of colliding particles,

D

300 K

D p 8 T /(

D

when the average velocity of relative motion of molecules is v T πμ )

D p σ

10 4 cm/s. Taking a typical collision impact parameter as

6.7 ,where

the gas-kinetic cross section for collision of two nitrogen molecules in thermal
collisions is

g / π

σ D 39 Å 2 [34], we find D 3.5 Å. From this we have for a typical g

collision momentum l D μ v / „D 31, which justifies application of the classical

theory in this case.
Below we represent the values of kinetic coefficients for simple gases. Table 4.2
contains the self-diffusion coefficients at the normal number density of atoms or
molecules, N 10 19 cm 3 , which corresponds to normal gas conditions D 2.687

( T D 273 K, p D 1 atm). It is convenient to approximate the temperature depen-

Ta b l e 4 . 2 The diffusion coefficients of atoms or molecules in the parent gas expressed in

square centimeters per second and reduced to the normal number density [31].

D

D (cm 2 /s) D (cm 2 /s) D (cm 2 /s)

Gas Gas Gas

He 1.6 H 2 1.3 H 2 O . 8

Ne 0.45 N 2 0.18 CO 2 0.096

Ar 0.16 O 2 0.18 NH 3 0.25

Kr 0.084 CO 0.18 CH 4 0.20

Xe 0.048