Cross-scale dynamic interactions in compacting porous media as a trigger to pattern formation

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 but the dynamic evolution of the microprocesses is hidden. We introduce a new microphysics-based approach that couples the microscale cross-constituent interactions to the large-scale dynamic behaviour, which leads to the discovery of a family of soliton-like excitation waves. These waves can appear in hydromechanically coupled porous media as a reaction to external stimuli. They arise, for instance, 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 dissipation 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.