# Binary Diffusion Coefficients for Gases

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Binary diffusion coefficients at low to moderate pressures (such that the ideal gas behavior is valid) can be predicted with reasonable accuracy (to within about 5% of experimental data) from the kinetic theory of gases using results from the Chapman–Enskog theory based on the Lennard–Jones (6-12) potential [1].

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Contributed by: Brian G. Higgins and Housam Binous (February 2013)

Open content licensed under CC BY-NC-SA

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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].

Reference

[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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