A model liquid crystal cell in an RC circuit

TL;DR

This paper models a nematic liquid crystal cell as a variable capacitor in an RC circuit, coupling director and charge dynamics to analyze system behavior and equilibrium states.

Contribution

It introduces a coupled dynamical system for director and charge dynamics derived from energy expressions, highlighting effects of different time scales.

Findings

Quantified effects of varying time scales in the system

Developed a dynamical model coupling director and charge dynamics

Provided numerical illustrations of system behavior

Abstract

A nematic liquid-crystal cell subject to an electric field created by electrodes held at constant potential is modeled as a variable capacitor in an RC circuit. The state of the system is characterized in terms of the director field in the cell and the charge on the electrodes. A dynamical system is developed that couples director dynamics in the cell (with no fluid flow) and charge dynamics in the circuit. The dynamical equations are derived from expressions for the total potential energy of the system and a dissipation involving a single rotational viscosity for the director plus Joule heating associated with current in the circuit. An effort is made to quantify effects, in particular the widely differing time scales for the processes involved, and numerical illustrations are given. The exercise illuminates aspects of the modeling of equilibrium states of such a system.