Calculation of equilibrium and transport properties using modified hard-core potential models

Abstract

We present in this paper a new method of modifying hard-core potentials to correctly predict the equilibrium and non-equilibrium properties of real fluids at low densities (specifically when ρ ⩽ B/ C where ρ is density, and B and C are the second and third virial coefficients) only by one set of potential parameters. Because the molecular diameter becomes smaller when temperature increases, we introduced a new expression for the variation of molecular diameter with temperature that incorporates this effect. The temperature dependence of the diameter was used in both Sutherland (ST) and square-well (SW) potential models to modify the second virial coefficient. Then we have shown that the experimental second virial coefficient fits into the modified Sutherland (MST) and modified square-well (MSW) quite well for the entire temperature range for which experimental data are reported, including the inversion temperature. Such fittings give the parameters of the modified potential models, which are used to calculate the non-equilibrium properties of He, Ne, N 2, O 2, CO, and NO, including viscosity, thermal conductivity, and self-diffusion coefficients. In comparison with experimental data, such modifications of the potential models give much better results than those obtained from the original ST and SW models, especially at high temperatures at which the deviations are reduced significantly. Therefore, there is no need to use two sets of potential parameters; one for the equilibrium and another for the non-equilibrium properties of real fluids, if we use the modified hard-core potential models.