9860

Binary Diffusion Coefficients for Gases

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].
In this Demonstration, you can select a pair of molecules from the pull-down menus and then use the sliders to select a temperature and pressure for the process. The binary diffusion coefficient for the selected gas pair is shown in a contour plot. You can also view the binary mixture parameters and the molecular parameters for the selected binary mixture.

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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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