An arbitrary Lagrangian-Eulerian method for simulating interfacial dynamics between a hydrogel and a fluid

Comparison of four boundary conditions for the fluid-hydrogel interface

“…Feng and Young [17] concluded that in order to discriminate among the BCs, one needs to compute flows in complex geometries or transient conditions, and with a prominent Brinkman stress. Partly for this purpose, we have recently developed a finite-element algorithm for computing fluid-hydrogel two-phase flows, using BC1 and BC2 as examples [18]. The numerical formalism can be easily adapted to BC3 and BCM (see Appendix A).…”

“…Based on these, we recommend BC2 for studying the fluid dynamics of a hydrogel interface with a surrounding fluid. A finite-element algorithm for computing fluid-hydrogel two-phase flows has recently appeared [18].…”

“…First, we have used a linearly elastic constitutive equation for the solid network, which holds in the limit of small strains. For more complex flows with large strains, hyperelastic models should be used, such as the Saint Venant-Kirchhoff model used by Li et al [18]. Then the solutions may show novel nonlinear features.…”

“…where µ s and λ s are the Lamé constants of the solid skeletal phase, and E = [∇u s + (∇u s ) T ]/2 is the linear strain tensor. Hyperelastic models can also be used, as in Li et al [18], but the linear model affords simplicity and ease of comparing the BCs in the current context. As the BCs will be expressed in terms of the stress tensors, a different constitutive equation for the solid network will not change the form of the BCs.…”

“…9(a). More details of the finite-element formulation and numerical validation can be found in Li et al [18]. A hydrogel particle with a circular undeformed shape is placed at the center of a planar extensional flow.…”