Layered Systems Under Shear Flow

Abstract

We discuss and review a generalization of the usual hydrodynamic description of smectic A liquid crystals motivated by the experimentally observed shear-induced destabilization and reorientation of smectic A like systems. We include both the smectic layering (via the layer displacement u and the layer normal $\hat{p}$) and the director $\hat{n}$ of the underlying nematic order in our macroscopic hydrodynamic description and allow both directions to differ in non equilibrium situations. In a homeotropically aligned sample the nematic director couples to an applied simple shear, whereas the smectic layering stays unchanged. This difference leads to a finite (but usually small) angle between $\hat{n}$ and $\hat{p}$, which we find to be equivalent to an effective dilatation of the layers. This effective dilatation leads, above a certain threshold, to an undulation instability of the layers with a wave vector parallel to the vorticity direction of the shear flow. We include the couplings of the velocity field with the order parameters for orientational and positional order and show how the order parameters interact with the undulation instability. We explore the influence of the magnitude of various material parameters on the instability. Comparing our results to available experimental results and molecular dynamic simulations, we find good qualitative agreement for the first instability. In addition, we discuss pathways to higher instabilities leading to the formation of onions (multilamellar vesicles) via cylindrical structures and/or the break-up of layers via large amplitude undulations.