Q-tensor model for electrokinetics in nematic liquid crystals

TL;DR

This paper develops a tensor-based mathematical model for electrokinetics in nematic liquid crystals, extending previous theories to include disclinations and biaxiality, and demonstrates its application through electro-osmotic flow simulations.

Contribution

It introduces a second-rank tensor model for nematic electrolytes, capturing complex defect structures and anisotropies, advancing the theoretical framework beyond director-based models.

Findings

Electro-osmotic flows depend strongly on director configurations.

Space charge separation occurs even with isotropic permittivity and conductivity.

The model aligns with known induced-charge electro-osmotic effects.

Abstract

We use a variational principle to derive a mathematical model for a nematic electrolyte in which the liquid crystalline component is described in terms of a second-rank order tensor. The model extends the previously developed director-based theory and accounts for presence of disclinations and possible biaxiality. We verify the model by considering a simple but illustrative example of liquid crystal-enabled electro-osmotic flow (LCEO) around a stationary dielectric spherical particle placed at the center of a large cylindrical container filled with a nematic electrolyte. Assuming homeotropic anchoring of the nematic on the surface of the particle and uniform distribution of the director on the surface of the container, we consider two configurations with a disclination equatorial ring and with a hyperbolic hedgehog, respectively. The computed electro-osmotic flows show a strong dependence on the director configurations and on the anisotropies of dielectric permittivity and electric conductivity of the nematic characteristic of liquid crystal-enabled electrokinetics. Further, the simulations demonstrate space charge separation around the dielectric sphere, even in the case of isotropic permittivity and conductivity. This is in agreement with the induced-charge electro-osmotic effect described for isotropic electrolytes surrounding dielectric spheres.