Dynamics of Phase-Separated Interfaces in Inhomogenous and Driven Mixtures

TL;DR

This paper develops a model for the movement of phase-separated interfaces in mixtures with spatially varying properties, revealing how heterogeneities induce forces that influence droplet dynamics and migration.

Contribution

It introduces a new sharp interface model that accounts for inhomogeneous surface tension and demonstrates its application to thermophoretic droplet behavior.

Findings

Heterogeneities in surface tension create capillary forces driving interface motion.

Droplet deformation and transport depend on a balance of bulk and capillary forces.

Small thermophobic droplets can spontaneously migrate toward high-temperature regions.

Abstract

We derive effective equations of motion governing the dynamics of sharp interfaces in phase-separated binary mixtures driven by spatio-temporal modulations of their material properties. We demonstrate, in particular, that spatial heterogeneities in the surface tension induce an effective capillary force that drives the motion of interfaces, even in the absence of hydrodynamics. Applying our sharp interface model to quantify the dynamics of thermophoretic droplets, we find that their deformation and transport properties are controlled by a combination of bulk and capillary forces, whose relative strength depends on droplet size. Strikingly, we show that small thermophobic droplets -- composed of a material with a positive Soret coefficient -- can spontaneously migrate towards high-temperature regions as a result of capillary forces.