A brief outline of the formulas used in the calculations is given below. The calculations are based on the Lennard–Jones (6-12) potential:
.
In the above expression,
is called the collision diameter (a measure of the diameter of the molecule), and
is the maximum energy of attraction between a pair of molecules. The resulting working equation from Chapman–Enskog kinetic theory for estimating the product of the mixture molar density with binary diffusion coefficient
is
,
where
is the molar density of the binary mixture,
(g/mol) is the molecular weight of species
, and
is the binary collision diameter, which is estimated from collision diameter parameters
using the following mixing rule:
.
The quantity
is called the collision integral for diffusion and is a function of the reduced temperature
, defined as
.
In this expression,
is the Boltzmann constant and
is the characteristic energy appearing in the Lennard–Jones potential for the binary pair estimated using the mixing rule
,
where the units of
are kelvins. For ideal gases, we can estimate
as
. The resulting binary diffusivity is then given by
,
where
is in atm. In these calculations, a correlation for
as a function of the reduced temperature
is computed from data (table E.2 in [1]). The molecular parameters for the individual species are taken from table E.1 in [1].
[1] R. B. Bird, W. E. Stewart, and E. N. Lightfoot,
Transport Phenomena, 2nd ed., New York: John Wiley & Sons, 2002.
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