Couple-stresses in peristaltic transport of fluids

Abstract

Peristaltic pumping by a sinusoidal travelling wave in the walls of a two-dimensional channel filled with a viscous incompressible couple-stress fluid, is investigated theoretically. A perturbation solution is obtained, which satisfies the momentum equation for the case in which the amplitude ratio (wave amplitude:channel half width) is small. The results show that the mean axial velocity decreases with increasing couple-stress parameter eta . The phenomenon of reflux (mean flow reversal) is discussed. A reversal of velocity in the neighbourhood of the centre line occurs when the pressure gradient is greater than that of the critical reflux condition. It is found that the critical reflux pressure increases with the couple-stress parameter. Numerical results are reported for various values of the physical parameters of interest.