Environmental Engineering Reference
In-Depth Information
electron number density can be higher by several orders of magnitude, the electri-
cal method for energy input into a gas through electrons is more effective than gas
heating.
4.2
Transport Phenomena in Neutral Gases
4.2.1
Transport of Particles in Gases
Let us consider a weakly nonuniform gas when a thermodynamic parameter that
characterizes its state varies slowly in space. A flux occurs in this gas that tends
to equalize this thermodynamic parameter over the spatial region. Depending on
a certain slowly varied parameter, this flux determines a certain transport phe-
nomenon in a gas. The number density of atoms or molecules of each species
and the temperature and the mean velocity of atoms or molecules are parameters
that may vary. If some of these parameters vary in this region, appropriate fluxes
arise to equalize these parameters over the total volume of a gas or plasma. The
flux is small if a variation of the appropriate parameter is small on distances of the
order of the mean free path of atoms or molecules. Then a stationary state of the
system with fluxes exists, and such states are conserved during times much longer
than typical times between particle collisions. This corresponds to the criterion
λ
L
,
(4.24)
where
is the mean free path of particles in a collision and
L
is a typical size of
the gaseous system under consideration or the distance over which a parameter
varies noticeably. If this criterion is fulfilled, the system is in a stationary state to a
first approximation, and transport of particles, heat, or momentum occurs in the
second approximation in terms of an expansion over a small parameter according
to criterion (4.24). Various types of such transport will be considered below.
The coefficients of proportionality between fluxes and corresponding gradients
are called kinetic coefficients or transport coefficients. In particular, the diffusion
coefficient
D
is introduced as the proportionality factor for the relationship between
the particle flux
j
and the gradient of concentration
c
of a given species, or
j
D
λ
c
, (4.25)
where
N
is the total particle number density. If the concentration of a given
species
k
is low (
c
k
DN
r
1), that is, this species is an admixture to a gas, the flux of
particles of a given species can be written as
j
D
D
k
r
N
k
,
(4.26)
where
N
k
is the number density of particles of a given species.
The thermal conductivity coefficient
is defined as the proportionality factor for
the relationship between the heat flux
q
and the temperature gradient:
q
D
r
T
.
(4.27)
