Theoretical and Experimental Study of Transient Squeezing Flow in a Thin Porous Gap

In this study, we report a novel theoretical and experimental approach to examine transient squeezing flow in a thin gap filled with highly porous media. This problem is inspired by such biological phenomena as the cerebral spinal fluid flow in the subarachnoid space. It is featured by low Reynolds number, low Strouhal number and low Brinkman number. Thus, convective fluid acceleration is negligible and the pressure response is governed by the local acceleration, the viscous force and the Darcy resistance. By using a Laplace transform method, we have analytically solved the problem, which shows that the flow starts with an inviscid limit and as time goes on, it reaches steady flow governed by the Brinkman equation. A novel experimental setup, containing a piston instrumented with a displacement sensor and a pressure transducer, was established to examine the validity of the theoretical solution. Excellent agreement between the theory and the experimental data was obtained, validating the theoretical approach. The study presented herein examining the fundamental mechanisms of transient fluid flow in a soft porous media will have a significant impact on biological and industrial applications.