# Yield stress fluid behavior of foam in porous media

## TL;DR

This study investigates foam flow in porous media, revealing a shear-thinning yield stress fluid behavior with high effective viscosity at low capillary numbers, influenced by pressure thresholds and flow heterogeneity.

## Contribution

It provides the first detailed local analysis linking foam rheology to pressure thresholds and flow heterogeneity in porous media.

## Key findings

- Effective viscosity reaches thousands of times water's viscosity at low capillary numbers.
- Flow heterogeneity increases with gas flow rate but does not fully explain shear thinning.
- Pressure thresholds account for the observed foam rheology and yield stress behavior.

## Abstract

We report a local analysis of the flow of foams in two dimensional heterogeneous model porous media. Pressure measurements are combined with direct observation in order to determine simultaneously the effective viscosity and the fraction of trapped gas. Experiments are conducted in the low-quality regime, in a large range of capillary numbers and relative gas flow rates. The effective viscosity is very high (up to a few thousands times that of water) at low capillary numbers and rheology can be described by a decreasing power-law function of the capillary number of exponent ranging from -1 to -0.75. The flow is heterogeneous and the fraction of preferential paths increases with relative gas flow rate. However, increase in fraction of preferential paths remains very limited for increasing capillary number, thus failing to account for the strongly shear thinning behavior observed. Additional experiments motivated by this finding, carried out in a straight channel of varying cross-section, show a deviation from Bretherton law at low capillary numbers in this geometry with the bubble train behaving as a shear-thinning yield stress fluid. The pressure threshold evidenced accounts quantitatively for the effective viscosity data in the micromodel, indicating that it is the main mechanism underlying the measured foam rheology.