  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.
