Peristaltic transport of a Williamson fluid in asymmetric channels with permeable walls

The peristaltic flow of a Williamson fluid in asymmetric channels with permeable walls is investigated. The channel asymmetry is produced by choosing a peristaltic wave train on the wall with different amplitudes and phases. The solutions for stream function, axial velocity and pressure gradient are obtained for small Weissenberg number, We, via a perturbation expansion about We, while an exact solution method is discussed for large values of We. The exact solutions become singular as We tends to zero; hence the separate perturbation solutions are essential. Also, numerical results are obtained using the perturbation technique for the pumping and trapping phenomena, and these are used to bring out the qualitative features of the solutions. It is noted that the size of the trapped bolus decreases and its symmetry disappears for large values of the permeability parameter. The effects of various wave forms (namely, sinusoidal, triangular, square and trapezoidal) on the fluid flow are discussed.