Low Reynolds number peristaltic pumping near a poroelastic half space

Low Reynolds number flow near a poroelastic interface can be found in biological and engineered systems. A particular medical interest is the flow of cerebrospinal fluid (CSF) through annular perivascular spaces between arteries and brain tissue. Vascular deformation from heartbeats has been hypothesized to induce directed CSF flow along these channels, functioning as a mechanism which clears neurodegenerative metabolic waste from surrounding extracellular tissue. We aim to characterize the effect of a nearby poroelastic solid on the overall efficiency of peristaltic pumping as well as find an optimum pumping frequency as a function of physical parameters. We develop a 2D Stokes flow model of peristaltically driven fluid motion near a poroelastic half space. In this geometry, the lower boundary is an infinite train of traveling waves which pump fluid along an open channel. The open fluid layer is bound above by a poroelastic half space, through which fluid can flow. Stresses at the fluid-porous interface produce elastic deformations within the solid. Consequently, porosity is not constant in time or space, leading to nonlinearities in the fluid-solid interactions. Velocities and deformations are thus solved numerically. We will present the scaling relationships between flow rate, peristaltic wave parameters, and poroelastic mechanics to identify the conditions of maximum and minimum CSF pumping, aiming to supplement recent theories of CSF flow in the brain.