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.