Fundamental Studies on the Bearman–Kirkwood Theory of Transport. I. The Diffusion Coefficient Ratio

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Abstract
Although the Bearman–Kirkwood theory of transport in binary mixtures was developed as a theory of the liquid state, it is formally possible to carry out calculations of the self‐diffusion coefficient ratio, D 1 / D 2 , at all densities at which radial distribution functions are available for a given intermolecular potential. These calculations can be used to check the internal consistency of the theory at any density. For, except at unit mole fraction of solvent, the theory provides three alternative expressions for D 1 / D 2 , which should agree when the theory is consistent. For Lennard‐Jones parameters of a model system corresponding to argon and krypton, explicit calculation shows that at each mole fraction and temperature, the three expressions disagree except at a density characteristic of a liquid or dense fluid. At the densities of consistency, D 1 / D 2 assumes a not unreasonable value and remains quite independent of temperature in agreement with available data on argon and krypton. At unit mole fraction, another consistency test is available which qualitatively justifies the application of the theory to so‐called “regular solutions” and quantitatively gives densities of consistency smoothly connected to those at other mole fractions.