Peristaltic transport of a power-law fluid in a porous tube

Abstract

Peristaltic transport of a power-law fluid in an axisymmetric porous tube is studied under long wavelength and low Reynolds number assumptions. The slip boundary conditions given by Beavers–Joseph and Saffman type are considered in obtaining solutions for the flow and resulting pumping characteristics are compared. Trapping and reflux phenomena are discussed for various parameters of interest governing the flow like Da Darcy number, α Beavers–Joseph constant and n the fluid behavior index. The novel feature arising in pumping due to a straight section dominated (SSD) wave form other than sinusoidal wave is discussed. The time mean flow becomes negative in free pumping for a shear thickening fluid or shear thinning fluid for an expansion or contraction SSD wave, respectively. The pressure rise increases for the increasing of Da against which the peristalsis acts as a pump and decreases for an increase in α . Peristalsis works as a pump against a greater pressure rise for a shear thickening fluid and the opposite happens for a shear thinning fluid, compared with Newtonian fluid. The trapped bolus volume for sinusoidal wave is observed to decrease as the fluid behavior index decreases from shear thickening to shear thinning fluid, whereas it increases for increasing Darcy number. The rheological property of the fluid, wave shape and porous nature of the wall play an important role in peristaltic transport and may be useful in understanding transport of chyme in small intestines.