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Peristaltic motion of a Johnson-Segalman fluid in a planar channel

This paper is devoted to the
study of the two-dimensional flow of a Johnson-Segalman fluid in
a planar channel having walls that are transversely displaced by
an infinite, harmonic travelling wave of large wavelength. Both
analytical and numerical solutions are presented. The analysis
for the analytical solution is carried
 out for small Weissenberg
numbers. (A Weissenberg number is the ratio of the relaxation
time of the fluid to a characteristic time associated with the
flow.) Analytical solutions have been obtained for the stream
function from which the relations of the velocity and
the longitudinal pressure gradient have been derived. The
expression of the pressure rise over a wavelength has
also been determined. Numerical computations are performed and
compared to the perturbation analysis. Several limiting
situations with their implications can be examined from the
presented analysis.