A Soft Porous Media Monolayer Experiment for Exploring Deviations from Darcy's Law

Characterizing and predicting fluid transport through soft porous media is of great importance in many contexts, including hydrogeology, various industrial settings, and biology. Fluid flow through non-deformable porous media demonstrates a linear relationship between fluid flux and pressure gradient, as described by Darcy's law. In soft porous media, material deformation can lead to a variable, nonlinear relationship between fluid flux and pressure gradients such that Darcy's law is violated. In fact, recent studies have demonstrated hysteretic behavior, in which the flux through a porous domain for a particular applied pressure drop is lower when the pressure is decreasing compared to when it is increasing. In this work, fluid is driven through a porous monolayer of hydrogel particles for a broad range of porosities, and image analysis is employed to capture both solid phase deformation and fluid velocity. We will present preliminary results aimed at quantifying the functional relationship between pressure gradients and fluid flux in a soft porous medium. We aim to characterize hysteretic behavior and use the results to build flow models for exploring interstitial fluid transport in biological systems, which often exhibit periodic oscillations in pressure.