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An arbitrary Lagrangian-Eulerian method for simulating interfacial dynamics between a hydrogel and a fluid. (English) Zbl 07517156

Summary: 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 [Y.-N. Young, Y. Mori and M. J. Miksis, “Slightly deformable Darcy drop in linear flows”, Phys. Rev. Fluids 4, No. 6, Article ID 063601, 25 p. (2019; doi:10.1103/PhysRevFluids.4.063601)], we treat the hydrogel as a poroelastic material consisting of a Saint Venant-Kirchhoff polymer network and a Newtonian viscous solvent, and develop a finite-element method for computing flows involving a fluid-hydrogel interface. The interface is tracked by using a fixed-mesh arbitrary Lagrangian-Eulerian method that maps the interface to a reference configuration. The interfacial deformation is coupled with the fluid and solid governing equations into a monolithic algorithm using the finite-element library deal.II. The code is validated against available analytical solutions in several non-trivial flow problems: one-dimensional compression of a gel layer by a uniform flow, two-layer shear flow, and the deformation of a Darcy gel particle in a planar extensional flow. In all cases, the numerical solutions are in excellent agreement with the analytical solutions. Numerical tests show second-order convergence with respect to mesh refinement, and first-order convergence with respect to time-step refinement.

MSC:

65Mxx Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
74Fxx Coupling of solid mechanics with other effects
76-XX Fluid mechanics

Software:

deal.ii; UMFPACK
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Full Text: DOI

References:

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