Hydrogels are crosslinked polymer networks swollen with an aqueous solvent. As soft solids mechanically and chemically compatible with living cells, hydrogels are often used in microfluidic and organ-on-chip devices as carrier matrix for cell cultures.
In most of these applications, hydrogels are deployed using flowing liquids, thus giving rise to a fluid-gel two-phase flow situations. How does a hydrogel interact mechanically with a flowing fluid? How to use fluid dynamics to control the gel-fluid interface for optimal configurations? Such questions have inspired our research on the interfacial dynamics of hydrogels.
Our first task is to develop a theoretical formulation, with proper boundary conditions (BCs) on the interface between a hydrogel and a clear fluid. Adopting a poroelasticity model for the gel, we must supply additional BCs to specify the velocity jumps at the fluid-gel interface. This has been achieved by a thermodynamic argument of positive entropy production on the interface. Thus, we have proposed 3 different sets of BCs and compared their performance in a series of test problems. The results point to one particular set as the best.
Using the above theoretical formulation, we have developed a finite-element algorithm for computing two-phase flows involving a hydrogel surrounded by a clear fluid. Currently, the numerical tool is being applied to several problems of fundamental and applied interest, including the flow around a gel particle, interfacial dynamics in microfluidics, and intracellular dynamics.
As an example, the following plots show a gel particle being deformed by a biaxial extensional flow, with the formation of cusps at the two poles under strong stretch (more details here):
(Flow and pressure fields around a gel particle. For symmetry, only 1/4 of the particle is shown.)
(Subject to stronger flow, the gel particle develops sharp points at its north and south poles, where the solid network is stretched to a very low volume fraction.)