The role of advection in phase-separating binary liquids

TL;DR

This paper investigates how advection influences phase separation in binary liquids using the advective Cahn-Hilliard model, combining analytical and numerical methods to explore flow effects and particle formation.

Contribution

It introduces a comprehensive analysis of advection's role in phase separation, including the feedback mechanisms and singular solutions in related models.

Findings

Advection significantly affects phase separation dynamics.

Emergence of singular solutions interpreted as magnetic particle formation.

Classification of particle interactions using dynamical systems.

Abstract

Using the advective Cahn-Hilliard equation as a model, we illuminate the role of advection in phase-separating binary liquids. The advecting velocity is either prescribed, or is determined by an evolution equation that accounts for the feedback of concentration gradients into the flow. Here, we focus on passive advection by a chaotic flow, and coupled Navier-Stokes Cahn-Hilliard flow in a thin geometry. Our approach is based on a combination of functional-analytic techniques, and numerical analysis. Additionally, we compare and contrast the Cahn-Hilliard equation with other models of aggregation; this leads us to investigate the orientational Holm-Putkaradze model. We demonstrate the emergence of singular solutions in this system, which we interpret as the formation of magnetic particles. Using elementary dynamical systems arguments, we classify the interactions of these particles.