Phase Separation Dynamics in a Concentration Gradient

TL;DR

This paper investigates the dynamics of phase separation in systems with initial concentration gradients, revealing different flux decay behaviors and providing a scaling framework supported by numerical validation.

Contribution

It introduces a detailed analysis of phase separation with non-uniform initial conditions, including flux scaling laws and the final equilibrium interface structure.

Findings

Flux decays as t^{-2/3} with bulk pattern formation.

Flux decays as t^{-1/2} with homogeneous bulk.

Scaling arguments accurately predict observed behaviors.

Abstract

Phase separation dynamics with an initially non-uniform concentration are studied. Critical and off-critical behavior is observed simultaneously. A mechanism for an expanding phase separated region is demonstrated and the time dependence of the concentration is determined. The final equilibrium state consists of a planar interface separating one phase from the other. The evolution to this state is characterized by an experimentally observable flux, $j$, crossing this interface. We find that $j \sim t^{-2/3}$ if patterns are formed in the bulk and $j \sim t^{-1/2}$ if the bulk remains homogeneous. The results are explained in terms of scaling arguments which are confirmed numerically. (postScript figures appended to end of lateX file).