Influence of geometry heterogeneity on Liesegang patterns in rocks

Abstract

In far-from-equilibrium chemical systems, self-organizing diffusion-reaction processes can give rise to complex patterns. Such self-organizing patterns are commonly found in diverse rocks, emerging as periodic stripes, rings, and various polygons. While these patterns are well documented, the drivers of their diversity and the mechanisms behind pattern selection remain unclear. This study investigates how geometric heterogeneity influences the formation of Liesegang patterns in natural geological materials such as Zebra rocks, pyrite ores, and orbicular granites. Using numerical simulations based on phase-field modeling, we replicate various Liesegang pattern morphologies observed in nature, such as circular, triangular, and interacting bands, and analyze their dependence on initial geometry and boundary conditions. We demonstrate that the spatial distribution of reactive fluids and the shape of nucleation zones play critical roles in determining the final pattern morphology. Our results provide insight into the self-organization processes in geochemical systems and offer a predictive framework for understanding rhythmic mineral banding in rocks.