Shear flow in smectic A liquid crystals

This paper considers the onset of a shear-induced instability in a sample of smectic A liquid crystal. Unlike many previous models, the usual director n need not necessarily coincide with the local smectic layer normal a; the traditional Oseen constraint ([Formula: see text]) is not imposed when flow is present. A recent dynamic theory for smectic A (Stewart 2007 Contin. Mech. Thermodyn. 18 343-60) will be used to examine a stationary instability in a simple 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 the velocity. 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 the associated smectic layer undulations. Despite some critical phenomena being largely unaffected by any coupling to the flow, it will be shown that the influence of some material parameters, especially the smectic layer compression constant B(0) and the coupling constant B(1), upon the critical shear rate and critical tilt angle can be greatly affected by flow.