The Flow of Layered Liquid Crystals in a Thin Wedge With Dislocations

Abstract

The velocity, displacement, and stress field of layered liquid crystals with dislocations in a lubricating gap are investigated numerically. Galerkin’s weighted residual finite element method is employed to solve a set of five highly nonlinear coupled differential equations in terms of two spatial coordinates. In addition to the usual continuity and momentum equations, equations are required for a body force term governing permeation through the layers and elastic displacement of the layers. The last equation contains a fourth derivative term which gives rise to dislocations and numerical complications. The results show a strong increase in load relative to an equivalent viscous lubricant. The load increase depends strongly on the magnitude of a permeation parameter.