Nematic liquid crystals on curved surfaces - a thin film limit

TL;DR

This paper derives a surface Landau-de Gennes model for nematic liquid crystals on curved surfaces from a thin film limit, revealing decoupling of tensor components and preserving key properties, with numerical simulations illustrating elastic and geometric interactions.

Contribution

It introduces a novel surface Landau-de Gennes model obtained via a thin film limit, capturing the interplay of elasticity, bulk energy, and surface geometry.

Findings

Decoupling of normal and tangential Q-tensor components in the thin film limit.

Preservation of uniaxiality and phase space properties in the surface model.

Numerical simulations demonstrating coupling of elastic energy with surface geometry.

Abstract

We consider a thin film limit of a Landau-de Gennes Q-tensor model. In the limiting process we observe a continuous transition where the normal and tangential parts of the Q-tensor decouple and various intrinsic and extrinsic contributions emerge. Main properties of the thin film model, like uniaxiality and parameter phase space, are preserved in the limiting process. For the derived surface Landau-de Gennes model, we consider an L2-gradient flow. The resulting tensor-valued surface partial differential equation is numerically solved to demonstrate realizations of the tight coupling of elastic and bulk free energy with geometric properties.