Modelling spreading dynamics of liquid crystals in three spatial dimensions

TL;DR

This paper models the three-dimensional spreading dynamics of nematic liquid crystal droplets using a derived nonlinear PDE, analyzing elastic and anchoring effects through stability analysis and simulations.

Contribution

It introduces a new PDE-based framework for 3D liquid crystal droplet spreading, incorporating elastic distortion and anchoring variations.

Findings

Elastic distortion influences droplet stability.

Anchoring variations affect spreading behavior.

Simulations predict defect-induced spreading patterns.

Abstract

We study spreading dynamics of nematic liquid crystal droplets within the framework of the long-wave approximation. A fourth order nonlinear parabolic partial differential equation governing the free surface evolution is derived. The influence of elastic distortion energy and of imposed anchoring variations at the substrate are explored through linear stability analysis and scaling arguments, which yield useful insight and predictions for the behaviour of spreading droplets. This behaviour is captured by fully nonlinear time-dependent simulations of three dimensional droplets spreading in the presence of anchoring variations that model simple defects in the nematic orientation at the substrate.