Non-Newtonian flow of a model liquid between concentric cylinders

Abstract

Computer simulations of fluids out of equilibrium indicate that even the simplest fluid is in principle non-Newtonian. In particular, the simulations can provide explicitly the pressure tensor as a function of shear rate at a given temperature and density. In this paper the steady state flow of a model soft sphere liquid between rotating vertical concentric cylinders is discussed from a microscopic standpoint, given the coefficients that characterize the pressure tensor. The equations of motion are solved numerically. It is found that the normal pressure differences lead to an enhanced depression of the free surface at the inner cylinder, in contrast to a climbing (Weissenberg effect) which is usually regarded as the consequence of such differences. Reasons for the behavior observed for the soft sphere system are discussed. A consequence of the analysis is that a unique and self-consistent solution of the equations of motion is obtained only if the effects of finite compressibility are included.