KINETIC THEORY OF FLOW IN STRONGLY INHOMOGENEOUS FLUIDS

Abstract

Enskog's kinetic theory of dense hard sphere fluids, modified to allow long-ranged attractive interactions in a mean field sense, is solved for the case of slow flow in strongly inhomogeneous fluids, such as fluids near solid surfaces or liquid-vapor interfaces. In the equilibrium limit the theory yields the exact Yvon-Born-Green equation for the density distribution. In the slow flow limit the viscosity is a tensorial functional of the density distribution. Expressions for the velocity profile are derived for plane laminar and Couette flows. The density dependence of the transport coefficients is smoothed once through the angle averaging of the binary collisions of the Enskog theory. In the planar flows the velocity profile obeys a second order differential equation with variable coefficients and so the density dependence is further muted by two successive spatial integrations. The result leads one to expect the velocity profile to depend relatively weakly on density variations. This conclusion is in agreement with recently available computer simulations of flow in micropores. Another conclusion of the work is that one cannot introduce a flow or pore size independent effective viscosity to describe flow in micropores.