Convective instabilities in nematics caused by an elliptical shear

Abstract

A nematic liquid crystal, oriented homeotropically (n//z) between two parallel plates (⟩ z) in relative motion x = x0 sin ωt on one plate, y = y0 cos ωt on the other one, exhibits a sequence of convective instabilities for increasing values of a dimensionless parameter N proportional to x0 y0 ω. Above a first critical number Nc1, parallel convection rolls establish through the sample. This article gives a systematic experimental description of this instability which was discussed first by Pieranski and Guyon and analysed in detail by Dubois-Violette and Rothen. For a higher critical number Nc2, the convective structure changes from rolls to a two dimensional periodic and stationary pattern. For even larger values of the parameter N, the two dimensional structure becomes non stationary and loses long range order symmetry. The melting of this structure is described; possible connection with the loss of ordering of two dimensional systems is suggested