Vibrational Model of Heat Conduction in a Fluid of Hard Spheres

Abstract

Application of a vibrational model of heat transfer to a fluid made of hard spheres is discussed. The model was originally proposed to describe heat conduction in fluids with soft pairwise interactionsHere, it is shown that only minor modifications are required to apply the model in the opposite limit of hard sphere interactions. Good agreement with recent results from molecular dynamics simulation is documented in the moderately dense regime. Near the freezing point, however, the model overestimates the thermal conductivity coefficient (by ≃50%). The new approach is compared with other simple models for the thermal conductivity coefficients such as Bridgman’s expression and the Enskog formula. The value of the coefficient in the Bridgman’s expression, appropriate for the hard sphere fluid, is determined. A new expression for the dependence of the reduced thermal conductivity coefficient on the reduced excess entropy is proposed. The obtained results can be useful for rough estimates of the thermal conductivity coefficient of simple fluids with steep interactions when more accurate experimental results are not available.