Hydrogels are crosslinked polymer networks swollen with an aqueous solvent, and play central roles in biomicrofluidic devices. In such applications, the gel is often in contact with a flowing fluid, thus setting up a fluid-hydrogel two-phase system. We treat the hydrogel as a poroelastic material consisting of a Saint Venant-Kirchhoff polymer network and a Newtonian solvent. First, we propose boundary conditions on the interface between the gel and a pure solvent fluid phase. Then we develop a variational formulation that incorporates these conditions and satisfies a dissipative energy law. Tracking the gel-fluid interface by an arbitrary Lagrangian-Eulerian method, we solve the equations using finite elements. The method is applied to several flow problems, including hydrogel in 1D shear and compression and the deformation of a hydrogel particle in planar extension. The numerical results show excellent agreement with theoretical predictions.

* Collaborative work with Pengtao Yue (Virginia Tech) and Yuan-Nan Young (NJIT).
 

Li, L., Zhang, J., Xu, Z, Young, Y.-N., Feng, J. J. & Yue, P., An arbitrary Lagrangian-Eulerian method for simulating interfacial dynamics between a hydrogel and a fluid. J. Comput. Phys. 451, 110851 (2022)
Feng, J. J. & Young, Y.-N., Boundary conditions at a gel-fluid interface. Phys. Rev. Fluids 5, 124304 (2020)
 

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