A Multi-Faceted Study of Nematic Order Reconstruction in Microfluidic Channels

TL;DR

This paper investigates the existence, structure, and dynamics of order reconstruction solutions in nematic flows within microfluidic channels, revealing conditions for their occurrence and detailed internal structures through analysis and simulations.

Contribution

It provides the first comprehensive analysis of nematic order reconstruction solutions in both passive and active microfluidic flows, including existence proofs and asymptotic characterizations.

Findings

OR solutions exist under specific boundary conditions in passive flows.

Unique nematic profiles are identified for boundary conditions that prevent OR solutions.

Numerical simulations confirm the universality of OR structures in various flow scenarios.

Abstract

We study order reconstruction (OR) solutions in the Beris-Edwards framework for nematodynamics, for both passive and active nematic flows in a microfluidic channel. OR solutions exhibit polydomains and domain walls, and as such, are of physical interest. We show that OR solutions exist for passive flows with constant velocity and pressure, but only for specific boundary conditions. We prove the existence of unique, symmetric and non-singular nematic profiles, for boundary conditions that do not allow for OR solutions. We compute asymptotic expansions for OR-type solutions for passive flows with non-constant velocity and pressure, and active flows, which shed light into the internal structure of domain walls. The asymptotics are complemented by extensive numerical studies that demonstrate the universality of OR-type structures in static and dynamic scenarios.