Hystereses in one-dimensional 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. Since the pressure simultaneously drives the Darcy flow through the pores and compresses the gel, the flux-pressure relationship can become non-monotonic. Most interestingly, we discover two types of hysteresis when either the pressure drop or the flux is controlled, which are also confirmed by transient numerical simulations. The hystereses stem 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. Finally, we suggest experimental setups and conditions to seek such hystereses in real gels.