Dynamic instabilities caused by reaction-cross-diffusion waves in compacting porous media

Abstract

Patterns in nature are often interpreted as a product of reaction-diffusion processes which result in dissipative structures. Thermodynamic constraints allow prediction of the final state with the dynamic evolution of the micro-processes refrained. Here we introduce a new micro-physics based approach that allows us to discover a family of soliton-like excitation waves - coupling the micro-scale cross-constituent interactions to the large scale dynamic behaviour of the open system. These waves can appear in hydromechanically coupled porous media under external loads. They arise when mechanical forcing of the porous skeleton releases internal energy through a phase change, leading to tight coupling of the pressure in the solid matrix with the dissipation of the pore fluid pressure. In order to describe these complex multiscale interactions in a thermodynamic consistent framework, we consider a dual-continuum system, where the large-scale continuum properties of the matrix-fluid interaction are described by a reaction-self diffusion formulation, and the small-scale release of internal energy by a reaction-cross diffusion formulation that spells out the macroscale reaction and relaxes the adiabatic constraint on the local reaction term in the conventional reaction-diffusion formalism. Using this approach, we recover the familiar Turing bifurcations (e.g., rhythmic metamorphic banding), Hopf bifurcations (e.g., Episodic Tremor and Slip), and present the new excitation wave phenomenon. The parametric space is investigated numerically and compared to serpentinite deformation in subduction zones.