Low Reynolds number pumping near an elastic half space

TL;DR

This study examines how wave-like boundary motions near an elastic half space influence low Reynolds number fluid flow, revealing different flow directions for transverse and longitudinal waves and aligning with cerebrospinal fluid data.

Contribution

It introduces a model analyzing the impact of prescribed wave motions on fluid flow near elastic boundaries, highlighting differences between transverse and longitudinal waves.

Findings

Transverse waves produce net forward flow and uniform elastic oscillations.

Longitudinal waves generate net backward flow with nonuniform elastic motion.

Model results agree with cerebrospinal fluid velocity measurements.

Abstract

Previous studies on peristalsis, the pumping of fluid along a channel by wave-like displacements of the channel walls, have shown that the elastic properties of the channel and the peristaltic wave shape can influence the flow rate. Motivated by the oscillatory flow of cerebrospinal fluid along compliant perivascular spaces, we consider a prescribed wave motion of a single boundary which pumps fluid at small Reynolds number near an elastic half space. We investigate the relationship between flow rate and elastic deformation as a function of the fluid and solid properties. We consider transverse and longitudinal motion of the driving peristaltic wave. We find that a transverse peristaltic wave produces net forward flow and induces elastic motion in which all material points oscillate uniformly. Conversely, a longitudinal peristaltic wave produces a net backward flow and drives elastic motion which is nonuniform in the elastic solid. We use dimensional values relevant to the flow of cerebrospinal fluid and find agreement with in vivo velocity data.