The hydrodynamics of ferroelectric smectic C liquid crystals

A continuum model incorporating flow is developed as an extension to the work of Stewart and Momoniat who considered a mechanical soliton travelling through a sample of smectic C* liquid crystal. Here we study a wave front propagating through an infinite sample of ferroelectric liquid crystal in a planar geometry, under the influence of an inclined electric field of constant magnitude. We use the dynamic theory for smectic C liquid crystals of Leslie, Stewart and Nakagawa, appropriately extended to include the spontaneous polarisation and elastic energy terms encountered in smectic C* materials. We incorporate flow terms into our model giving a total of five dynamic equations. The resulting dynamic equations have infinitesimal perturbations imposed upon them. The perturbation equations are linearised and, by exploiting an exact solution in the case where the field is co-planar with the sample, a set of linear perturbation equations are developed. Simplifying assumptions lead to a pair of equations which, when suitable time decaying, spatially dependent perturbations are applied yield an eigenvalue problem. By employing a suitable numerical scheme we examine the resulting stability problem and use the results to identify critical electric field strengths below which we conjecture, travelling waves are not initiated. We also present a novel method for determining wave front profiles for a mechanical soliton in a planar sample of ferroelectric smectic C liquid crystal. We end by looking at numerical method for determining wave speeds in ferroelectric smectic C liquid crystals which employs discretised nonlinear Volterra integral equations of the second kind. The method is completely general in scope, and may in fact be used to tackle wave speed problems for any appropriate reaction-diffusion equation which admits travelling wave solutions.A continuum model incorporating flow is developed as an extension to the work of Stewart and Momoniat who considered a mechanical soliton travelling through a sample of smectic C* liquid crystal. Here we study a wave front propagating through an infinite sample of ferroelectric liquid crystal in a planar geometry, under the influence of an inclined electric field of constant magnitude. We use the dynamic theory for smectic C liquid crystals of Leslie, Stewart and Nakagawa, appropriately extended to include the spontaneous polarisation and elastic energy terms encountered in smectic C* materials. We incorporate flow terms into our model giving a total of five dynamic equations. The resulting dynamic equations have infinitesimal perturbations imposed upon them. The perturbation equations are linearised and, by exploiting an exact solution in the case where the field is co-planar with the sample, a set of linear perturbation equations are developed. Simplifying assumptions lead to a pair of equations which, when suitable time decaying, spatially dependent perturbations are applied yield an eigenvalue problem. By employing a suitable numerical scheme we examine the resulting stability problem and use the results to identify critical electric field strengths below which we conjecture, travelling waves are not initiated. We also present a novel method for determining wave front profiles for a mechanical soliton in a planar sample of ferroelectric smectic C liquid crystal. We end by looking at numerical method for determining wave speeds in ferroelectric smectic C liquid crystals which employs discretised nonlinear Volterra integral equations of the second kind. The method is completely general in scope, and may in fact be used to tackle wave speed problems for any appropriate reaction-diffusion equation which admits travelling wave solutions