Hystereses in flow-induced compression of a poroelastic hydrogel

We investigate theoretically the one-dimensional compression of a hydrogel layer by a uniform fluid flow normal to the gel surface. The flow is driven by a pressure drop across the gel layer, which is modeled as a poroelastic medium. The novelty comes from considering, for the first time, the impact of interfacial permeability and compression. This leads to several new features for the flow and gel compression. As the pressure simultaneously drives the Darcy flow through the pores and compresses the gel, the flux-pressure relationship may become non-monotonic. Most interestingly, we discover two types of hysteresis when the pressure or the flux is controlled, which are also confirmed by transient numerical simulations. The first type of hysteresis stems from the interplay between the gel compression at the upstream interface and that in the bulk of the gel, and would not be predicted by models that ignore the interfacial compression. The second type hinges on strain-hardening in the gel that maintains a non-vanishing permeability at high pressure. Finally, we suggest experimental setups and conditions to seek such hystereses in real gels. When a hydrogel layer is compressed by a fluid flow normal to it, the flow rate may exhibit hysteresis when the imposed pressure drop varies, and we may observe bistability between a relaxed and a compressed state for the hydrogel.