Rheology of liquid foam flowing through porous media

Liquid foams are widely used in porous media, like soils. Recent studies have explored foam flow in two- and three-dimensional porous media, but the effects of confinement on foam rheology remain poorly understood. We investigated foam flow through granular packing with stable bubble sizes and reduced compressibility across different liquid fractions. Our analysis shows that confined foam flow cannot be directly extrapolated from bulk foam properties. The apparent yield stress of confined foam increases with the degree of confinement, governed by the bubble-to-grain size ratio. This increase can be significant, especially for foams with high liquid content. The increase aligns with a smooth transition between yield stress values of bulk foams and those under strong confinement. This suggests that the geometric effect of bubbles passing through small constrictions is not significant. Instead, liquid redistribution within pore spaces at grain surfaces and contact areas is crucial. This effect is modeled and agrees with our data and literature. Finally, stopping bubble coarsening is shown to be essential to accurately understand foam rheology in porous media.