Phase-field model of long-time glass-like relaxation in binary fluid mixtures

TL;DR

This paper introduces a novel phase-field model for binary fluids that captures glass-like behaviors such as long-term relaxation and aging, by enabling zero-cost interfaces and resulting in compact fluid configurations.

Contribution

The model uniquely allows interfaces with zero local cost while maintaining positive global surface tension, leading to the formation of compact fluid structures and linking free-energy landscape ruggedness to morphology.

Findings

Emergence of compact fluid configurations ('compactons') with finite support.

Numerical simulations support analytical predictions.

Model reproduces key signatures of glassy dynamics in binary fluids.

Abstract

We present a new phase-field model for binary fluids exhibiting typical signatures of self-glassiness, such as long-time relaxation, ageing and long-term dynamical arrest. The present model allows the cost of building an interface to become locally zero, while preserving global positivity of the overall surface tension. An important consequence of this property, which we prove analytically, is the emergence of compact configurations of fluid density. Owing to their finite-size support, these "compactons" can be arbitrarily superposed, thereby providing a direct link between the ruggedness of the free-energy landscape and morphological complexity in configurational space. The analytical picture is supported by numerical simulations of the proposed phase-field equation.