Flow-driven branching in a frangible porous medium

TL;DR

This paper introduces a theoretical model for flow-driven branching in fragile porous media, demonstrating how fluid flow influences and shapes the formation of branched networks with potential applications in controlling such structures.

Contribution

It presents a simple multi-phase framework capturing the feedback between flow and permeability, revealing conditions for network splitting and coalescence in frangible porous materials.

Findings

Branched networks emerge from the model based on external flow geometry.

Flow-driven feedback influences network topology and evolution.

Conditions for network splitting and coalescence are identified.

Abstract

Channel formation and branching is widely seen in physical systems where movement of fluid through a porous structure causes the spatiotemporal evolution of the medium in response to the flow, in turn causing flow pathways to evolve. We provide a simple theoretical framework that embodies this feedback mechanism in a multi-phase model for flow through a fragile porous medium with a dynamic permeability. Numerical simulations of the model show the emergence of branched networks whose topology is determined by the geometry of external flow forcing. This allows us to delineate the conditions under which splitting and/or coalescing branched network formation is favored, with potential implications for both understanding and controlling branching in soft frangible media.