Peristaltic pumping in thin, non-axisymmetric, annular tubes

TL;DR

This study models and simulates three-dimensional peristaltic flow in non-axisymmetric annular tubes, revealing how ellipticity and eccentricity influence flow rates and azimuthal motions relevant to cerebrospinal fluid dynamics.

Contribution

It introduces a numerical simulation of peristaltic flow in non-axisymmetric annular geometries, extending previous axisymmetric models to more realistic brain-related structures.

Findings

Flow decreases with increased ellipticity and eccentricity.

Azimuthal pressure variations induce oscillatory azimuthal flows.

Shearing motions may enhance Taylor dispersion.

Abstract

Two-dimensional laminar flow of a viscous fluid induced by peristalsis due to a moving wall wave has been studied previously for a rectangular channel, a circular tube, and a concentric circular annulus. Here we study peristaltic flow in a non-axisymmetric annular tube, where the flow is three dimensional, with azimuthal motions. This geometry is motivated by experimental observations of cerebrospinal fluid flow along perivascular spaces (PVSs) surrounding arteries in the brain, which is at least partially driven by peristaltic pumping. These PVSs are well matched, in cross-section, by an adjustable model consisting of an inner circle (arterial wall) and an outer ellipse (outer edge of the PVS), not necessarily concentric. We use this model, which may have other applications, as a basis for numerical simulations of peristaltic flow. We use a finite-element scheme to compute the flow driven by a propagating sinusoidal radial displacement of the inner wall. Unlike peristaltic flow in a concentric circular annulus, the flow is fully three-dimensional, with streamlines wiggling in both the radial and axial directions. We examine the dependence of the flow on the elongation of the outer elliptical wall and on the eccentricity of the configuration. We find that time-averaged volumetric flow decreases with increasing ellipticity or eccentricity. Azimuthal pressure variations, caused by the wall wave, drive an oscillatory azimuthal flow in and out of the narrower gaps. The additional shearing motion in the azimuthal direction will enhance Taylor dispersion in these flows, an effect that might have practical applications.