Flow of yield stress fluid in a percolating network

TL;DR

This paper investigates how a yield-stress fluid flows through a porous network with randomly distributed pore sizes, highlighting the critical behavior at the percolation threshold and the influence of the network's backbone on flow properties.

Contribution

It introduces a model combining yield-stress fluid dynamics with percolation theory, revealing how flow characteristics depend on network connectivity and pore size distribution.

Findings

Flow above the percolation threshold is deterministic with quantifiable fluctuations.

At the percolation threshold, flow properties become non-self-averaging.

Scaling at the threshold is governed solely by the critical percolation backbone.

Abstract

We study the flow of a Bingham yield-stress fluid in a pore network model where the throats have radii drawn from a uniform distribution. We consider the case in which a fraction of the largest radii is blocked. The fluid can flow only through the percolating cluster that exists when the fraction is above the percolation threshold. Two distinct flow regimes are identified: above the percolation threshold the flow curve can be characterized by deterministic values of the critical pressure drop, permeability, and other observables, with subleading fluctuations that we quantify. At the percolation threshold these quantities become non-self-averaging, and their scaling is governed exclusively by the critical percolation backbone, independent of the specific realization of the radii.