Mean-Field Convective Phase Separation under Thermal Gradients

TL;DR

This paper introduces a dynamical mean-field model explaining how temperature gradients induce convective phase separation and pattern formation in systems with attractive particles, supported by stability analysis and numerical simulations.

Contribution

It provides the first theoretical framework for understanding convective phase separation under thermal gradients using a mean-field approach.

Findings

Transition to periodic patterns driven by unstable modes

Convective currents are robust and appear regardless of initial conditions

Model predictions align with numerical simulations and phase diagram

Abstract

Nonequilibrium conditions fundamentally change how systems undergo phase separation. In systems with temperature gradients, attractive particles have been shown to form periodic patterns and steady convective currents, but a clear theoretical explanation for this behavior is still missing. Here, we present a dynamical mean-field model that describes the mechanism behind this convective phase separation. Using linear stability analysis, we show that the transition from a uniform state to a periodic pattern is driven by the emergence of a dominant unstable mode. Numerical simulations confirm the predicted phase diagram and demonstrate that these convective currents are a robust feature of the steady state, appearing regardless of the initial conditions. These results provide a direct approach for understanding how temperature gradients drive the formation of steady-state convective patterns.