A comparison of four boundary conditions for the fluid-hydrogel interface*

In adopting a poroelastic model for a hydrogel, one views its constituent fluid and solid phases as interpenetrating continua, thereby erasing the ``pore-scale" geometry. This gives rise to the need for additional boundary conditions (BCs) at the interface between a hydrogel and a clear fluid to supplement the momentum equations for the fluid and solid phases in the hydrogel. Using a thermodynamic argument on energy dissipation, we propose three sets of boundary conditions for the gel-fluid interface that link the normal and tangential velocity jumps across the interface to the normal and tangential stresses on either side of the interface. Using several flow problems---one-dimensional compression, two-layer Couette and Poiseuille shear flows, and deformation of a gel particle by a planar extension flow---as tests, we compare the predictions of these three BCs with that of a previously proposed BC. Some differences are stark and reveal flaws in certain BCs. Others are subtler and will require quantitative experimental data for validation. Based on these results, we recommend one set of BCs over the other three for computing the flow and deformation of hydrogels in contact with a clear fluid. In addition, we suggest benchmark experiments to validate the BCs and our recommendation.