Note on the hydrodynamic description of thin nematic films: strong anchoring model

TL;DR

This paper clarifies the hydrodynamic modeling of thin nematic liquid crystal films with strong anchoring, reconciling different approaches and showing elastic energy's stabilizing effect.

Contribution

It provides a rigorous derivation of the long-wave model for nematic films, unifying conflicting models and confirming elastic energy's stabilizing role.

Findings

Elastic energy always stabilizes the film.

The derived model aligns with thermodynamic gradient dynamics.

The paper clarifies the role of elastic energy in film evolution.

Abstract

We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal in the limit of strong anchoring at the free surface and at the substrate. We rigorously clarify how the elastic energy enters the evolution equation for the film thickness in order to provide a solid basis for further investigation: several conflicting models exist in the literature that predict qualitatively different behaviour. We consolidate the various approaches and show that the long-wave model derived through an asymptotic expansion of the full nemato-hydrodynamic equations with consistent boundary conditions agrees with the model one obtains by employing a thermodynamically motivated gradient dynamics formulation based on an underlying free energy functional. As a result, we find that in the case of strong anchoring the elastic distortion energy is always stabilising. To support the discussion in the main part of the paper, an appendix gives the full derivation of the evolution equation for the film thickness via asymptotic expansion.