Dynamics and flow effects in the Beris-Edwards system modelling nematic liquid crystals

TL;DR

This paper investigates how fluid flow influences the behavior of nematic liquid crystals by analyzing the Beris-Edwards model, focusing on eigenvalue preservation and defect formation at high Ericksen numbers.

Contribution

It provides new insights into the flow-induced dynamics of Q-tensors, particularly regarding eigenvalue constraints and defect emergence in the Beris-Edwards system.

Findings

Flow affects eigenvalue preservation of Q-tensors.

Defects dynamically emerge at high Ericksen numbers.

Flow modifies the stability and structure of liquid crystal configurations.

Abstract

We consider the Beris-Edwards system modelling incompressible liquid crystal flows of nematic type. This couples a Navier-Stokes system for the fluid velocity with a parabolic reaction-convection-diffusion equation for the Q-tensors describing the direction of liquid crystal molecules. In this paper, we study the effect that the flow has on the dynamics of the Q-tensors, by considering two fundamental aspects: the preservation of eigenvalue-range and the dynamical emergence of defects in the limit of high Ericksen number