Spatiotemporal complexity of electroconvection patterns in nematic liquid crystals

TL;DR

This paper explores the complex spatiotemporal patterns in electroconvection of nematic liquid crystals, combining theoretical modeling with experiments to understand secondary instabilities and pattern dynamics.

Contribution

It introduces coupled amplitude equations to accurately describe slow modulations and flow interactions in electroconvection patterns, validated by experiments.

Findings

Galerkin stability diagram matches amplitude equation predictions

Numerical simulations align well with experimental observations

Secondary instabilities lead to diverse complex patterns

Abstract

We investigate a number of complex patterns driven by the electro-convection instability in a planarly aligned layer of a nematic liquid crystal. They are traced back to various secondary instabilities of the ideal roll patterns bifurcating at onset of convection, whereby the basic nemato-hydrodynamic equations are solved by common Galerkin expansion methods. Alternatively these equations are systematically approximated by a set of coupled amplitude equations. They describe slow modulations of the convection roll amplitudes, which are coupled to a flow field component with finite vorticity perpendicular to the layer and to a quasi-homogeneous in-plane rotation of the director. It is demonstrated that the Galerkin stability diagram of the convection rolls is well reproduced by the corresponding one based on the amplitude equations. The main purpose of the paper is, however, to demonstrate that their direct numerical simulations match surprisingly well new experiments, which serves as a convincing test of our theoretical approach.