Modeling and Simulation of Hydrogel Interfacial Dynamics

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. Using a recently proposed model, we treat the hydrogel as a poroelastic material consisting of a Saint Venant-Kirchhoff polymer network and a Newtonian solvent, and numerically study the motion and deformation of gel drops suspended in viscous flows. We develop a variational formulation that elegantly takes care of the complex matching conditions on the gel-fluid interface and further satisfies a dissipative energy law. The gel-fluid interface is tracked by an arbitrary Lagrangian-Eulerian method. All the equations are solved in a unified finite-element framework using the open-source deal.II library. The numerical results for different problems, including the compressive response of hydrogel in 1D flow, the deformation of hydrogel under shear, and the deformation of a hydrogel particle under planar extensional flow, show very good agreement with theoretical predictions.