Shear viscosity and normal pressure differences in the scope of the extended Kirkwood-Smoluchowski equation.

Abstract

The potential contribution to the viscosity in liquids is calculated from the pair-correlation function, which may be obtained by solving the extended Kirkwood-Smoluchowski (KS) equation. A secondary boundary condition near the hard core (r=${1}^{+}$) for the excess pair probability current density in the relative pair space is derived rigorously and applied to the extended KS equation. The intermolecular potential consists of hard core plus arbitrary soft tail. The viscosity coefficients calculated in this work prove to be essentially functions of the square root of the shear rate rather than functions of the shear rate itself. We give the explicit representation for the viscosity coefficients in the case of hard spheres. The shear thinning of the shear viscosity is recovered. The viscosity of the normal pressure difference 1/2(${\mathit{p}}_{\mathit{x}\mathit{x}}$-${\mathit{p}}_{\mathit{y}\mathit{y}}$) is found to be positive. The normal pressure difference of the second kind 1/2[${\mathit{p}}_{\mathit{z}\mathit{z}}$-1/2(${\mathit{p}}_{\mathit{x}\mathit{x}}$+${\mathit{p}}_{\mathit{y}\mathit{y}}$)] vanishes in the first-order perturbation calculation with respect to the deformation.