Shear flow dynamics in the Beris-Edwards model of nematic liquid crystals

TL;DR

This paper analyzes the shear flow dynamics of nematic liquid crystals within the Beris-Edwards model, highlighting differences between co-rotational and non-co-rotational cases and comparing with other models.

Contribution

It provides a detailed analysis of flow effects on nematic liquid crystal dynamics in the Beris-Edwards model, distinguishing between co-rotational and non-co-rotational regimes.

Findings

Gradient dynamics in co-rotational case up to periodic rotation

Identification of short and long time regimes in non-co-rotational case

Comparison with other liquid crystal models

Abstract

We consider the Beris-Edwards model describing nematic liquid crystal dynamics and restrict to a shear flow and spatially homogeneous situation. We analyze the dynamics focusing on the effect of the flow. We show that in the co-rotational case one has gradient dynamics, up to a periodic eigenframe rotation, while in the non-co-rotational case we identify the short and long time regime of the dynamics. We express these in terms of the physical variables and compare with the predictions of other models of liquid crystal dynamics.