Banding instabilities in poroelastic media under flow-driven compaction

When cross-linked poroelastic media are subjected to a hydrostatic pressure difference, they compact, remaining fully swollen on their uppermost surface and becoming increasingly compressed with depth. A critical unexplored effect of cross-linking and resistance to shear deformation is investigated, which is not seen in classical models of poroelastic media treated as free elastic spheres, and resists the kind of compressive compaction that characterises these systems. Eventually, a steady-state profile dependent on osmotic, shear and transport properties is reached, supporting a uniform interstitial flow wherein the medium acts like a passive filter. In this paper, we show how these steady-state profiles are not necessarily stable, and propose a mechanism for the formation of instabilities, wherein some regions of the medium swell and others compact, forming distinctive horizontal or vertical banding patterns. In the latter case, these bands appear qualitatively to be higher-permeability conduits or channels, similar to wormholes or tunnels seen in granular media. It is possible to quantify the effect of changing the pressure head on the growth rate of instabilities and the separation lengthscale in this channelisation case, and how material properties like shear stiffness and dependence of permeability on porosity affect the dynamics of instability. Critically, it is shown that these instabilities are a fluid-mechanical effect, with an entirely new mechanism based on the porosity--permeability relationship and not on elastic effects. With an understanding of these mechanisms, we can derive insight into channelisation in poroelastic systems in geophysics, human biology and industry.