A Statistical Mechanical Theory of the Coefficients of Shear and Bulk Viscosity of Monatomic Liquids

Citation

Buff, Frank Paul (1949) A Statistical Mechanical Theory of the Coefficients of Shear and Bulk Viscosity of Monatomic Liquids. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/6vjk-v091. https://resolver.caltech.edu/CaltechTHESIS:06142025-203348846

Abstract

A detailed molecular theory of the coefficients of shear and bulk viscosity of monatomic liquids is developed on the basis of the general theory of transport processes proposed by Kirkwood. The coefficients are expressed explicitly in terms of the potential of intermolecular force and the perturbations in the pair number density produced by viscous fluid flow. These perturbations are obtained from the steady state solutions of an equation of forced diffusion, derived from the generalized Chandrasekhar equations determining the distribution functions of sets of one and two molecules. This procedure leads to a set of ordinary differential equations, which are solved in terms of the Whittaker confluent hypergeometric function by means of a reasonable analytic approximation to the experimental radial distribution function.

With the use of the Lennard-Jones potential and the approximate radial distribution function, calculations of the coefficients of shear and bulk viscosity of liquid argon at 89°K and 1.2 atm. have been carried out. The theory leads explicitly to ratios of the coefficients to the friction constant of the theory of Brownian motion. With an estimate of the friction constant, a value of the shear viscosity of liquid argon in moderately good agreement with experiment is obtained.

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