Enslaved Phase-Separation Fronts and Liesegang Pattern Formation

TL;DR

This paper demonstrates that a diffusive phase-separation front can produce Liesegang-like patterns with predictable domain sizes, and identifies a critical speed below which only two domains form, verified through analytical and numerical methods.

Contribution

It introduces an analytical model for Liesegang pattern formation driven by an enslaved phase-separation front, including a critical speed threshold and numerical validation.

Findings

Pattern size and spacing match Liesegang patterns

Analytical form of the pattern for equal component composition

Existence of a critical front speed for pattern formation

Abstract

We show that an enslaved phase-separation front moving with diffusive speeds U = C T^(-1/2) can leave alternating domains of increasing size in their wake. We find the size and spacing of these domains is identical to Liesegang patterns. For equal composition of the components we are able to predict the exact form of the pattern analytically. We also show that there is a critical value for C below which only two domains are formed. Our analytical predictions are verified by numerical simulations using a lattice Boltzmann method.