Journal article

SHEAR-FLOW IN THE 2-BODY BOLTZMANN GAS .2. SMALL AND LARGE GAMMA-EXPANSION OF THE SHEAR VISCOSITY

GP MORRISS, DJ ISBISTER, BD HUGHES

JOURNAL OF STATISTICAL PHYSICS | PLENUM PUBL CORP | Published : 1986

Abstract

In two and three dimensions, the relaxation time Boltzmann equation can be solved analytically for the distribution function for a system of two hard particles subject to isothermal shear. The previous solutions of Morriss, and Ladd and Hoover are shown to be formally equivalent. The integral representation for the average of each of the elements of the pressure tensor in the steady state is obtained for both sllod and dolls tensor equations of motion. Rigorous equations are derived which relate the viscosity and the normal stress differences in these two methods. We obtain asymptotic expansions for each element of the pressure tensor for both small and large γ. For high shear rates, the vis..

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