Solution landscapes of ferronematics in microfluidic channels

TL;DR

This paper explores the complex solution landscapes of ferronematics in microfluidic channels, revealing how system parameters influence multistability and the emergence of intricate domain structures, with implications for experimental design.

Contribution

It introduces a detailed analysis of solution landscapes for ferronematics, highlighting the role of domain size and coupling in creating multistable states and complex polydomain configurations.

Findings

Increasing domain size and coupling lead to new solutions.

Ferronematic polydomains are prevalent and significant.

Order reconstruction solutions are complex and key to landscape connectivity.

Abstract

We investigate solution landscapes for ferronematics i.e., a dilute suspension of magnetic nano-particles in a nematic liquid crystal host, in a reduced one-dimensional setting relevant for microfluidic problems. Solution landscapes show how critical points of an energy functional connect to one another on the energy landscape, hence revealing potential mechanism by which multistable systems may switch between different stable states. By varying model parameters, we show that increasing domain size and increasing nemato-magnetic coupling have the same impact on the solution landscape, in that both result in new emergent solutions. Hence, this presents multiple avenues for experimental realisation of multistable ferronematic systems with desired properties. We also show the prevalence, and therefore importance, of ferronematic polydomains, which present themselves as what we call order reconstruction (OR) solutions. These ferronematic OR solutions possess a great deal of complexity in terms of the location and multiplicity of domain walls, and also play a key role in the connectivity of stable states for the solution landscapes considered.