Viscous fingering in liquid crystals: Anisotropy and morphological transitions

TL;DR

This paper models viscous fingering in nematic liquid crystals considering anisotropic viscosities, revealing a transition between tip-splitting and side-branching that explains experimental reentrant behavior.

Contribution

It introduces a minimal anisotropic viscosity model for viscous fingering in liquid crystals and characterizes the morphological transition using phase-field simulations.

Findings

Identifies a transition between tip-splitting and side-branching based on anisotropy and surface tension.

Shows the anisotropy dependence explains experimental reentrant transitions.

Findings are consistent with previous experiments and solidification simulations.

Abstract

We show that a minimal model for viscous fingering with a nematic liquid crystal in which anisotropy is considered to enter through two different viscosities in two perpendicular directions can be mapped to a two-fold anisotropy in the surface tension. We numerically integrate the dynamics of the resulting problem with the phase-field approach to find and characterize a transition between tip-splitting and side-branching as a function of both anisotropy and dimensionless surface tension. This anisotropy dependence could explain the experimentally observed (reentrant) transition as temperature and applied pressure are varied. Our observations are also consistent with previous experimental evidence in viscous fingering within an etched cell and simulations of solidification.