Numerical Method of Lines for the Relaxational Dynamics of Nematic Liquid Crystals

TL;DR

This paper introduces an efficient numerical method based on the method of lines to solve the Landau-de Gennes equations, enabling accurate simulations of nematic liquid crystal dynamics.

Contribution

It presents a new computational scheme that is easy to implement and balances efficiency with accuracy for modeling nematic liquid crystal behavior.

Findings

Validated the de Gennes ansatz for the isotropic-nematic interface.

Demonstrated anisotropic droplet behavior in nucleation.

Confirmed dynamical scaling during coarsening.

Abstract

We propose an efficient numerical scheme, based on the method of lines, for solving the Landau-de Gennes equations describing the relaxational dynamics of nematic liquid crystals. Our method is computationally easy to implement, balancing requirements of efficiency and accuracy. We benchmark our method through the study of the following problems: the isotropic-nematic interface, growth of nematic droplets in the isotropic phase and the kinetics of coarsening following a quench into the nematic phase. Our results, obtained through solutions of the full coarse-grained equations of motion with no approximations, provide a stringent test of the de Gennes ansatz for the isotropic - nematic interface, illustrate the anisotropic character of droplets in the nucleation regime and validate dynamical scaling in the coarsening regime.