Liesegang patterns interpreted as a chemo-hydromechanical instability

Abstract

Patterns in nature form through bifurcations triggered by Multiphysics feedbacks that involve chemical, hydraulic, mechanical, and thermal pro-cesses. A generic approach has been developed based on a nonlocal reac-tion-diffusion equation where patterns grow as a result of travelling dissi-pative waves. Here we present a simplified analysis on the formation of vastly different patterns (e.g., Liesegang stripes and dendritic precipitation) in Solnhofen limestone that are traditionally interpreted to result from the same group of chemical precipitation reactions. The transition from stripes to dendritic growth in the same formation suggests a commonality that is not yet captured or understood by the classical chemical feedback models. We propose that mechanical processes drive the patterns. The objective of this study is therefore to identify a set of characteristic diffusion coeffi-cients and reaction processes that generate pressure waves which can en-compass chemical and hydromechanical feedback process driving the selec-tion between the two-types of instabilities.