Temporal Evolution of Flow in Pore-Networks: From Homogenization to Instability

TL;DR

This paper investigates how flow networks in porous media evolve over time, revealing conditions under which flow homogenizes or develops channels, and identifies a phase transition driven by erosion dynamics.

Contribution

It introduces a pore-network model that captures the transition between uniform flow and channel formation based on erosion laws, providing quantitative criteria for predicting network behavior.

Findings

Flow can become uniform or channelized depending on erosion law.

A phase transition between homogenization and instability is identified.

Quantitative criteria predict the network's evolution.

Abstract

We study the dynamics of flow-networks in porous media using a pore-network model. First, we consider a class of erosion dynamics assuming a constitutive law depending on flow rate, local velocities, or shear stress at the walls. We show that depending on the erosion law, the flow may become uniform and homogenized or become unstable and develop channels. By defining an order parameter capturing these different behaviors we show that a phase transition occurs depending on the erosion dynamics. Using a simple model, we identify quantitative criteria to distinguish these regimes and correctly predict the fate of the network, and discuss the experimental relevance of our result.