On nematic electrolytes

TL;DR

This paper models the complex electrokinetics of nematic electrolytes through coupled nonlinear PDEs, proving existence, uniqueness, and equilibrium properties using maximal regularity theory.

Contribution

It introduces a comprehensive mathematical framework for nematic electrolytes, coupling ion transport, electrostatics, fluid dynamics, and liquid crystal behavior, with rigorous analytical results.

Findings

Proved existence and uniqueness of strong solutions.

Established criteria for global solutions.

Characterized equilibrium states.

Abstract

We study a system of nonlinear partial differential equations modeling the electrokinetics of a nematic electrolyte material consisting of various ion species suspended in a nematic liquid crystal within a bounded domain in two or three dimensions. The system couples a Nernst-Planck model for ion concentrations with the Poisson equation for the electrostatic potential, a Navier-Stokes equation for the fluid solvent, and the Ericksen-Leslie equations with general Leslie stress for nematic liquid crystals. We consider the case of isotropic elasticity for the liquid crystal and impose a unit-length constraint on the director field. The no-flux condition for the electrochemical potential leads to a nonlinear (and nonlocal) boundary condition for the ion concentrations. Using the theory of maximal regularity, we prove existence and uniqueness of strong solutions, provide criteria for global existence, and characterize the set of equilibria.