Peristaltic transport of a biofluid in a pipe of elliptic cross section

Peristaltic transport of two fluids occupying the peripheral layer and the core in an elliptic tube is investigated in elliptic cylindrical co-ordinate system, under long wavelength and low Reynolds number approximations. The effect of peripheral-layer viscosity on the flow rate and the frictional force for a slightly elliptic tube is discussed. The limiting results for the one-fluid model are obtained for different eccentricities of the undisturbed tube cross sections with the same area. As a result of non-uniformity of the peristaltic wave, two different amplitude ratios are defined and the time-averaged flux and mechanical efficiency are studied for different eccentricities. It is observed that the time-averaged flux is not affected significantly by the pressure drop when the eccentricity is large. For the peristaltic waves with same area variation, the pumping seems to improve with the eccentricity.