The undulation instability in layered systems under shear flow - a simple model

We propose a generalization to the usual hydrodynamic description of smectic A liquid crystals: The layer normal and the director are assumed to be coupled elastically to each other in such a way that they are parallel in equilibrium. If a sample with the layers parallel to the plates is sheared, our generalization leads in first order to a flow alignment of the director in the flow direction without perturbing the layers. Due to this tilt of the director the layers have a tendency to reduce their thickness. A linear stability analysis shows that the layers accommodate this tendency above a critical shear rate by developing undulations with a wave vector parallel to the vorticity direction of the shear flow.