Shear flow in smectic A liquid crystals

Abstract

This paper considers the onset of a shear-induced instability in a sample ofsmectic A liquid crystal. Unlike many previous models, the usual directorn need not necessarily coincide with the local smectic layer normala; the traditional Oseen constraint () is not imposed when flow is present. A recent dynamic theory for smectic A (Stewart 2007Contin. Mech. Thermodyn. 18 343–60) will be used to examine a stationary instability in asimple model when the director reorientation and smectic layer distortions are, firstly,assumed not to be coupled to the velocity and, secondly, are supposed coupled to thevelocity. A critical shear rate at which the onset of the instability occurs will be identified,together with an accompanying critical director tilt angle and critical wavenumber for theassociated smectic layer undulations. Despite some critical phenomena beinglargely unaffected by any coupling to the flow, it will be shown that the influenceof some material parameters, especially the smectic layer compression constantB0 and the couplingconstant B1, upon the critical shear rate and critical tilt angle can be greatly affected byflow.