(in collaboration with Pengtao Yue of Virginia Tech and Yuan-nan Young of NJIT)

Hydrogels are crosslinked polymer networks swollen with an aqueous solvent. For their softness and chemical compatibility with living cells, hydrogels are often used as carrier matrix for cell cultures, especially in organ-on-chip devices and in vitro disease models.

In most of these applications, hydrogels are deployed using flowing liquids, thus giving rise to a fluid-gel two-phase flow situations. Our first task is to develop a poroelastic formulation, with proper boundary conditions on the interface between a hydrogel and a solvent. Then we have developed a finite-element algorithm for computing two-phase flows involving a hydrogel surrounded by a clear fluid. 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 stretching:

More recently, we have used the above theoretical model to explore the mechanisms of albuminuria, a kidney disease that hinges on the permeability of the poroelastic glomerular basement membrane:

(Diagram showing how the permeability through the glomerular basement membrane (GBM) is key to renal function.)

We have also discovered an intriguing hysteresis in flow through a gel layer, used a pore-scale model to evaluate the interfacial permeability parameter, and generalized the above model to fully couple thermodynamically driven swelling and an external flow. In particular, incorporating swelling allows us to probe the function of gel-based actuators. For example, the movie below shows how a cylindrical gel post swells in a stream after a change in the fluid temperature:

(Arrows show velocity of liquid inside the swelling gel cylinder.)