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Thanks to their softness, biocompatibility, porosity, and ready availability, hydrogels are commonly used in microfluidic assays and organ-on-chip devices as a matrix for cells. They not only provide a supporting scaffold for the differentiating cells and the developing organoids, but also serve as the medium for transmitting oxygen, nutrients, various chemical factors, and mechanical stimuli to the cells. From a bioengineering viewpoint, the transmission of forces from fluid perfusion to the cells through the hydrogel is critical to the proper function and development of the cell colony. In this paper, we develop a poroelastic model to represent the fluid flow through a hydrogel containing a biological cell modeled as a hyperelastic inclusion. In geometries representing shear and normal flows that occur frequently in microfluidic experiments, we use finite-element simulations to examine how the perfusion engenders interstitial flow in the gel and displaces and deforms the embedded cell. The results show that pressure is the most important stress component in moving and deforming the cell, and the model predicts the velocity in the gel and stress transmitted to the cell that is comparable to in vitro and in vivo data. This work provides a computational tool to design the geometry and flow conditions to achieve optimal flow and stress fields inside the hydrogels and around the cell. 

When a hydrogel layer is compressed by a fluid flow normal to it, the flow rate may exhibit hysteresis when the imposed pressure drop varies, and we may observe bistability between a relaxed and a compressed state for the hydrogel. 

Two aspects of hydrogel mechanics have been studied separately in the past. The first is the swelling and deswelling of gels in a quiescent solvent bath triggered by an environmental stimulus such as a change in temperature or pH, and the second is the solvent flow around and into a gel domain, driven by an external pressure gradient or moving boundary. The former neglects convection due to external flow, whereas the latter neglects solvent diffusion driven by a gradient in chemical potential. Motivated by engineering and biomedical applications where both aspects coexist and potentially interact with each other, this work presents a poroelasticity model that integrates these two aspects into a single framework, and demonstrates how the coupling between the two gives rise to novel physics in relatively simple one-dimensional and two-dimensional flows. 

Boundary conditions between a porous solid and a fluid has been a long-standing problem in modeling porous media. For deformable poroelastic materials such as hydrogels, the question is further complicated by the elastic stress from the solid network. Recently, an interfacial permeability condition has been developed from the principle of positive energy dissipation on the hydrogel–fluid interface. Although this boundary condition has been used in flow computations and yielded reasonable predictions, it contains an interfacial permeability g as a phenomenological parameter. In this work, we use porescale models of flow into a periodic array of solid cylinders or parallel holes to determine g as a function of the pore size and porosity. This provides a means to evaluate the interfacial permeability for a wide range of poroelastic materials, including hydrogels, foams and biological tissues, to enable realistic flow simulations.