A variational analysis of nematic axisymmetric films: the covariant derivative case

TL;DR

This paper provides a comprehensive variational analysis of a model for nematic axisymmetric films, focusing on the covariant derivative case, specifically applied to revolution surfaces between coaxial rings.

Contribution

It offers the first detailed variational analysis of Giomi's nematic surface model with covariant derivatives for axisymmetric geometries.

Findings

Characterization of equilibrium shapes of nematic films

Comparison between covariant and surface gradient models

Insights into stability of axisymmetric nematic configurations

Abstract

Nematic surfaces are thin fluid structures, ideally two-dimensional, endowed with an in-plane nematic order. In 2012, two variational models have been introduced by Giomi [11] and by Napoli and Vergori [29,28]. Both penalize the area of the surface and the gradient of the director: in [11] the covariant derivative of the director is considered, while [28] deals with the surface gradient. In this paper, a complete variational analysis of the model proposed by Giomi is performed for revolution surfaces spanning two coaxial rings.