We derive a mathematical model of a nematic electrolyte based on the Ericksen-Leslie theory of liquid crystal flow. Our goal is to investigate the nonlinear electrokinetic effects that occur because the nematic matrix is anisotropic, in particular, transport of ions in a direction perpendicular to the electric field as well as quadratic dependence of the induced flow velocity on the electric field. The latter effect makes it possible to generate sustained flows in the nematic electrolyte that do not reverse their direction when the polarity of the applied electric field is reversed. From a practical perspective, this enables the design of AC-driven electrophoretic and electroosmotic devices. Our study of a special flow in a thin nematic film shows good qualitative agreement with laboratory experiments.
Bibliographical noteFunding Information:
The first author's work was supported by the NSF through grant DMS-1435372. The second author's work was supported by the NSF through grant DMS-1434969. The third author's work was supported by the NSF through grant DMS-1434185. The fourth author's work was supported by the NSF through grants DMS-1434734 and DMS-1418991
- Liquid crystals
- Variational principles