Flow-induced compaction of soft poroelastic materials

Fluid flows through poroelastic materials can result in solid deformation driven by the distribution of viscous shear stresses. The porosity and permeability of the solid matrix is altered spatially through a non-trivial coupling to the fluid flow. This behaviour is studied experimentally by examining fluid flow through a packing of soft hydrogel spheres driven by an imposed pressure head. The pressure head is varied, and, for each pressure, the steady-state mass flux and solid deformation are measured. For large pressure gradients, the fluid flow is found to decrease the permeability in such a way as to produce a flux that is independent of the applied pressure gradient. Measurements of the internal deformation, obtained by particle tracking, show that the medium compacts non-uniformly, with the porosity being lower at the outlet compared to the inlet. Intriguingly, we find a reproducible hysteresis of the poroelastic deformation between increasing and decreasing increments of the applied pressure head. The experimental results are compared to a simple one-dimensional model that accounts for non-linear elasticity of the solid and non-constant permeability.