A hydrodynamical model of nematic liquid crystal films with a general state of orientational order

TL;DR

This paper introduces a comprehensive hydrodynamical Q-tensor model for nematic liquid crystal films on surfaces, incorporating arbitrary orientations and flow dynamics, validated through numerical experiments.

Contribution

It presents a novel, thermodynamically consistent model coupling 2D flow with 3D Q-tensor dynamics on surfaces, allowing for arbitrary liquid crystal orientations.

Findings

Model allows for arbitrary orientation of liquid crystals.

Energy law is satisfied in the coupled system.

Numerical experiments demonstrate the model's capabilities.

Abstract

We develop a Q-tensor model of nematic liquid crystals occupying a stationary surface which represents a fluidic material film in space. In addition to the evolution due to Landau--de\,Gennes energy the model includes a tangent viscous incompressible flow along the surface. A thermodynamically consistent coupling of a two-dimensional flow and a three-dimensional Q-tensor dynamics is derived from the generalized Onsager principle following the Beris--Edwards system known in the flat case. The main novelty of the model is that it allows for a flow of an arbitrarily oriented liquid crystal so the Q-tensor is not anchored to the tangent plane of the surface, and also obeys an energy law. Several numerical experiments explore kinematical and dynamical properties of the novel model.