On the Contact Line Dynamics of Three Phase Fluids

Date: Thu 15th Aug 2024

Abstract

Recent advances in cell-sized microparticle manufacture leverage liquid-liquid phase separation to enable cheap and rapid single-cell analysis. To better understand and optimise these methods, we investigate a model of phase separation in ternary polymer solutions. The model is a three-phase generalisation of the classical Cahn-Hilliard equation and corresponds to a singularly perturbed constrained gradient flow. Initially mixed systems minimise free energy by spontaneously separating into almost pure bulk regions bordered by narrow interfacial boundary layers between them. The key to understanding this system is to quantify the physically relevant limit of vanishing interfacial thickness. While the two-phase case is well-understood, the possibility of three-phase contact lines introduces significant complications. We combine three techniques to pursue this analysis to arbitrary asymptotic order:

1. Physically meaningful and geometrically elegant coordinate systems adapted to each subproblem;

2. A comprehensive symbolic algebra system for performing and validating the analysis;

3. Little-known identities for complete analytic solutions to the codimension-1 spectral subproblem.

After summarising the techniques and results, I will discuss the algorithms needed for accurate numerical validation of these models, touch on further issues arising for nonconstant mobilities, fluid flow, and three-dimensional systems, and conclude with implications for improved microfluidic manufacture of complex microparticles.