  We apply the lubrication approximation to solve for the flow generated by a
peristaltic traveling wave in a finite, planar channel, and focus on channels
that are shorter than the wavelength. Cerebrospinal fluid (CSF) is hypothesized
to be peristaltically transported by arterial pulsations through the
perivascular spaces in the brain. Prior investigations with idealized models
have reached differing conclusions about the feasibility of this mechanism. One
notable distinction between studies is the choice of domain length, where
sub-wavelength domains are physiologically realistic. Here, we find that
sub-wavelength channels significantly modulate the mean value, phase, and
amplitude of flow rate for sinusoidal and arbitrary peristaltic waves. The
boundary conditions create an internal pressure gradient such that the
instantaneous flow rate varies along the length of the channel, and the
difference between the ends and the middle of the channel is more pronounced
for very short channels. This distribution in flow rate is not experimentally
observed in perivascular flows at the surface of the brain, and hence these
idealized peristaltic models, in the absence of more complete geometries or
boundary conditions, do not adequately represent perivascular flows.
