Electrohydrodynamic (EHD) Flow in a Smectic a Liquid Crystal

Abstract

In EHDs one studies a liquid flow induced by an electric field. The liquid must contain a sufficient amount of ions which interacts with the external field. If the electric field is below a certain threshold the liquid remains stable, but conducts an ionic current. Above the threshold for EHD instability (EHDI), a liquid flow pattern develops. EHDIs are found in isotropic liquids as well as LCs. The book of Blinov¹ is a good introduction to the field. Here, we consider the EHD flow in a Sm-A LC doped with ions. The material is confined between two glass plates which are coated with transparent electrode patterns. The plates are parallel to the x-y plane and the molecules are initially oriented with their long-axis perpendicular to the plates, i.e. parallel to the z-axis (homeotropic orientation). The appearance of a EHDI in a homeotropic Sm-A was predicted theoreticly in 1972² and investigated experimentally from 1977^3–8. The theory, is developed from the 1D Helfrich-Orsay model for a planar nematic LC (the molecular long-axis parallel to the plates limiting the sample), but takes into account some properties specific to the homeotropic Sm-A phase. The only velocity component in the 1D model is v_z(x) which is modulated with a half period equal to the sample thickness. Experiments on Sm-A, report a circular flow in the x-y plane. It is obvious that the 1D model is insufficient to explain the observed flow pattern. It should be noted however, that in these experiments we are dealing with the situation occurring slightly above the threshold, whereas the theory predicts the situation only below the threshold. Firstly, we review in a simple way, some aspects of the Sm-A phase which are relevant for the observations presented in the experimental part. At the end we briefly discuss the observations.