A general boundary condition for liquid flow at solid surfaces

Abstract

Modelling fluid flows past a surface is a general problem in science and engineering, and requires some assumption about the nature of the fluid motion (the boundary condition) at the solid interface. One of the simplest boundary conditions is the no-slip condition1,2, which dictates that a liquid element adjacent to the surface assumes the velocity of the surface. Although this condition has been remarkably successful in reproducing the characteristics of many types of flow, there exist situations in which it leads to singular or unrealistic behaviour—for example, the spreading of a liquid on a solid substrate3,4,5,6,7,8, corner flow9,10 and the extrusion of polymer melts from a capillary tube11,12,13. Numerous boundary conditions that allow for finite slip at the solid interface have been used to rectify these difficulties4,5,11,13,14. But these phenomenological models fail to provide a universal picture of the momentum transport that occurs at liquid/solid interfaces. Here we present results from molecular dynamics simulations of newtonian liquids under shear which indicate that there exists a general nonlinear relationship between the amount of slip and the local shear rate at a solid surface. The boundary condition is controlled by the extent to which the liquid ‘feels’ corrugations in the surface energy of the solid (owing in the present case to the atomic close-packing). Our generalized boundary condition allows us to relate the degree of slip to the underlying static properties and dynamic interactions of the walls and the fluid.