Solution landscapes in nematic microfluidics

TL;DR

This paper explores the static and dynamic solution landscapes of a simplified nematic flow model in microfluidics, revealing multiple equilibria, their stability, and how initial conditions and parameter changes influence final states.

Contribution

It provides a comprehensive numerical and analytical study of static equilibria, their classification, and the dynamic sensitivity in nematic microfluidic flows, including the effects of parameter variation and initial conditions.

Findings

Multiple static equilibria exist for different parameter pairs.

Solution landscapes change with pressure gradient and anchoring strength.

Time delays can influence the final steady state selection.

Abstract

We study the static equilibria of a simplified Leslie--Ericksen model for a unidirectional uniaxial nematic flow in a prototype microfluidic channel, as a function of the pressure gradient $\mathcal{G}$ and inverse anchoring strength, $\mathcal{B}$. We numerically find multiple static equilibria for admissible pairs $(\mathcal{G}, \mathcal{B})$ and classify them according to their winding numbers and stability. The case $\mathcal{G}=0$ is analytically tractable and we numerically study how the solution landscape is transformed as $\mathcal{G}$ increases. We study the one-dimensional dynamical model, the sensitivity of the dynamic solutions to initial conditions and the rate of change of $\mathcal{G}$ and $\mathcal{B}$. We provide a physically interesting example of how the time delay between the applications of $\mathcal{G}$ and $\mathcal{B}$ can determine the selection of the final steady state.