Flow- and interface-driven compaction of a confined soft porous medium: When does friction matter?

The compaction of soft, porous media holds relevance for a host of problems in engineering, geoscience, and biology. Recent and classical studies have considered the compaction of sponges or hydrogel beads, among other model systems, confined in cylinders or Hele-Shaw cells with fluid-permeable boundaries at the outlet of the cell. A well-known qualitative feature of these systems is that, when compacted by a piston, the equilibrium state is homogeneously stressed along the axis, while flow-driven compaction results in a gradient in solid stress along the direction of flow due to the viscous pressure gradient within the pore space. In the latter scenario, solid stresses are greatest at the permeable outlet.

In this talk, we reveal the surprisingly prominent role friction can play in distorting these classical results. We perform experiments on water-saturated granular packings of hydrogel beads, which have extremely low friction coefficients, in a rectilinear Hele-Shaw cell. We find that, for piston-like compaction driven by the injection of a pressurised gas bubble, the compaction is strongly influenced by friction between the beads and the confining walls of the cell, resulting in solid stresses that are focused near the moving air-packing interface and screened further into the packing by friction. Accounting for frictional tangential stresses in a rigorous poromechanical model reveals that the frictional stress term is effectively amplified by a factor equal to the axial length of the packing divided by the depth of the cell. Hence, even very slippery porous media can exhibit friction-dominated compaction when strongly confined.

Consistent with previous studies of compaction in packings of hydrogel beads, we find a much weaker influence of frictional effects when compaction is driven by a background flow. We probe into the distinctions between flow- and piston-driven compaction using both experiments and modelling.