Vortex flow in free-standing smectic C films driven by elastic distortions

Abstract

The effects of coupling between director and flow dynamics are well-known in nematic liquid crystals, but such interactions are often disregarded in smectic materials. Experimental studies of the relaxation of distorted director fields in free-standing smectic C films suggest that a neglect of flow effects may lead to quantitative errors in the evaluation of material parameters and even to qualitative misinterpretations. A quantitative analysis of flow coupling in particularly simple experimental geometries is presented here. In thin planar films, the smectodynamic theory can be approximated by the two-dimensional Ericksen-Leslie equations of nematodynamics, comprising two elasticity and five viscosity coefficients. This represents one of the simplest hydrodynamic problems in anisotropic fluids in 2D. We solve the full coupled system of incompressible quasi Navier–Stokes and director torque balance equations numerically for circular films with and without topological defects in the film center. The coupled evolution of director and flow fields during the relaxation of initial distortions is analyzed, and consequences of the nonlinearity of the dynamic equations are discussed.