Formation of Liesegang Patterns

TL;DR

This paper explains the formation of Liesegang patterns through spinodal decomposition behind moving reaction fronts, aligning theoretical predictions with experimental observations of band spacing and width.

Contribution

It critically examines the assumptions of the spinodal decomposition model and demonstrates how it naturally accounts for the width law in Liesegang patterns.

Findings

The model reproduces the geometric sequence of band positions.

The spacing coefficient p agrees with the Matalon-Packter law.

The width law w_n ~ x_n emerges naturally from the theory.

Abstract

It has been recently shown that precipitation bands characteristic of Liesegang patterns emerge from spinodal decomposition of reaction products in the wake of moving reaction fronts. This mechanism explains the geometric sequence of band positions x_n ~ Q(1+p)^n and, furthermore, it yields a spacing coefficient, p, that is in agreement with the experimentally observed Matalon-Packter law. Here I examine the assumptions underlying this theory and discuss the choice of input parameters that leads to experimentally observable patterns. I also show that the so called width law relating the position and the width of the bands w_n ~ x_n follows naturally from this theory.