An evaluation of density corrections for estimating diffusivities in liquids and liquid mixtures

Abstract

In this work we analyse the effect of density correction on the estimation of diffusion coefficients in liquids and liquid mixtures using the Carnahan-Starling (1969, J. Chem. Phys. 51, 635–636) pair correlation function and the correlation of Speedy (1987, Molec. Phys. 62, 509–515) and Harris (1992, Molec. Phys. 77, 1153–1167) which have been proposed as models of self-diffusion coefficient of hard-sphere fluids. The hard-sphere diameters of nine liquids were estimated by fitting the experimental self-diffusion coefficients with the smooth-hard-sphere theory and the estimated diameters were used for predicting diffusivities in 13 binary and eight ternary systems. This theory with the density- and temperature-dependent hard-sphere diameter obtained from the Weeks-Chandler-Andersen (Weeks et al., 1971, J. Chem. Phys. 54, 5237–5247) perturbation theory of liquids is shown to be an excellent approach for predicting diffusivities in liquids and liquid mixtures. The calculations involved nonideal mixtures as well as systems with high molecular asymmetry. The predicted diffusivities are in good agreement with the experimental data for the binary and also for the ternary systems. The present results are much better than the estimates of Guo and Kee (1991, Chem. Engng Sci. 46, 2133–2140) for the mutual diffusion coefficient at infinite dilution for any of the density correction methods. It seems, then, that the coupling parameter of the rough hard-sphere theory has no essential role for predicting diffusion coefficients, even for large molecules, if a suitable hard-sphere diameter is used. The methodology proposed here only makes use of pure component information and density of mixtures. The simple algebraic relations proposed are without any binary adjustable parameters and can be readily used for estimating diffusivities in multicomponent liquid mixtures.