Viscosity of isotropic hard particle fluids

Abstract

A kinetic theory for the frequency-dependent shear viscosity η(ω) of isotropic fluids, composed of non-spherical hard convex bodies, is extended in two ways. First, the theory is reformulated to allow η(ω) to be expressed directly in terms of matrix elements involving the shear stress tensor rather than in terms of the transverse momentum correlation function. Second, relaxation of the antisymmetric component of the stress, due to coupling with spin angular momentum, is explicitly incorporated; this corrects an error in a previous version of the theory. The revised kinetic theory is compared with computer simulations for hard ellipsoids of revolution of axial ratio 2, 3, 5 and 10. Both the symmetric and antisymmetric contributions to η(ω) are well reproduced. Coupling with the collective molecular second-rank orientation tensor remains an important factor in determining the variation of η(ω) from high to low frequencies; the prediction of the magnitude of the associated dip in η(ω) is significantly improved. The new version of the theory is also more successful in predicting values of the zero-frequency shear viscosity η, the shear-orientation coupling parameter R, and the Stokes–Einstein (–Debye) products Dsη and Drη.