Electroconvection in two-dimensional liquid crystal films

Abstract

We have studied electrically driven convection in freely suspended films of smectic A liquid crystal. The layered molecular structure of the smectic A mesophase makes the film behave like a two-dimensional isotropic fluid, and well-controlled hydrodynamic flow has been achieved in films as thin as two molecular layers in thickness. When a d.c. voltage applied across the film exceeds a certain critical value Vc, a one-dimensional pattern of convective vortices develops. The critical pattern wavelength appears to be independent of film thickness, and the critical voltage is linear in film thickness for thin films. Measurements of the pattern amplitude indicate a supercritical bifurcation at convection onset, and the amplitude grows as a 1/2-power law with respect to the normalized control parameter ε. The correlation length of the pattern varies as ε⁻¹/², and the pattern's relaxation time varies as ε⁻¹. These results are in agreement with predictions from a Ginzburg-Landau amplitude equation. Measurements of the flow velocity show that the amplitude of the pattern is suppressed at the lateral boundaries. The range of wave numbers for stable convection has been obtained experimentally. Close to onset we find the width of the stable band is proportional to ε, consistent with predictions of the theory of boundary-induced wavelength selection. In addition to convection experiments, a set of electrohydrodynamic equations is presented for understanding the two-dimensional electroconvection. Theoretical analysis indicates the normalized control parameter to be V²/Vc² - 1, in agreement with the experimental observations. A hydrodynamic model is also proposed to describe the flow observed near the sidewalls below the onset of convection. The flow in this model is caused by the electrohydrodynamic shear-stress interaction which originates from an interfacial charge density distribution at the lateral boundary.