Peristaltic Transport of a Newtonian Fluid in an Asymmetric Channel with Wall Slip: Influence of Waveform Shapes

This study investigates the effects of wall slip and various waveforms on the peristaltic transport of a Newtonian fluid in a two-dimensional asymmetric channel. Channel asymmetry is generated by imposing peristaltic wave trains of different amplitudes and phase differences on the upper and lower channel walls. The mathematical formulation is developed under the assumptions of long wavelength and low Reynolds number. Exact analytical solutions for the stream function, axial velocity, and pressure gradient are obtained. Numerical computations are performed to analyze pumping characteristics, frictional forces, trapping, and reflux phenomena. Results show that increasing the permeability parameter reduces pumping against pressure rise, axial velocity, pressure gradient, trapped bolus size, and reflux layer thickness. For sufficiently large permeability, symmetry of the trapped bolus is lost. Under certain conditions, closed streamlines form, resulting in trapped boluses moving with the wave speed. A comparative analysis of four waveforms—triangular, sinusoidal, trapezoidal, and square—indicates that the square waveform yields the highest volumetric flux.