Kinetic theory and molecular dynamics simulations of microscopic flows

Abstract

This study aims at the understanding of the viscosity distributions near a solid wall in microscopic pores. The pair-correlation function is derived from the density distribution function, which in itself is obtained from molecular dynamics simulations. The revised Enskog equation for the shear flow of strongly inhomogeneous hard-sphere fluids is solved by the Chapman–Enskog method and the viscosity coefficients are obtained by keeping all the high-order derivatives of the density and pair-correlation functions. The molecular dynamics method is used in order to simulate the Couette flow of a Lennard-Jones fluid in a micropore, with weak or strong wall–fluid interactions. Under the weak interaction, slip is observed near the wall and the fluid in the contact layer exhibits higher viscosity than the fluid in other regions. Under the strong interaction, a layer of fluid always adhered to the wall is observed. A low viscosity valley often exists next to the high viscosity region, where apparently the flow commences. It is observed that the molecular dynamics simulations predict higher viscosity than the kinetic theory of the hard-sphere model, as it is expected. However, the distributions obtained from both methods are in qualitative agreement. The present study suggests that, provided the bulk viscosity and appropriate boundary conditions are used, the Navier–Stokes equations are valid at a distance of two to three molecular layers from the wall.