Peristaltic Flow of Two-Layered Fluids in an Elastic Tube

摘要

To analyze the flow of physiological fluids through elastic biological systems such as small blood vessels, peristaltic transport of immiscible incompressible fluids in a circular elastic tube is studied under long-wavelength and low Reynolds number assumptions. In the proposed two-layered model, core region is assumed to be governed by Jeffrey model, whereas the peripheral region is described by Newtonian model. Analytical expressions have been obtained for velocity, flux and pressure rise between two fluids. The equation of the interface is determined as a sixth-degree equation with coefficient functions of non-Newtonian, elastic and peristaltic parameters. This may be treated as a generalization of the work of Rao and Usha (J. Fluid Mech. 298:271-285, 1995) including the effects of elasticity and the non-Newtonian parameters. It is observed that the pressure rise decreases with the increasing values of Jeffrey parameter and radius of the elastic tube. In the absence of peristalsis, when coefficient of viscosity tends to one, ratio of radii tends to one and Jeffrey parameter tends to zero, our results are in good agreement with the results of Rubinow and Keller (J. theor. Biol. 35:299-313, 1972) for the flow of single viscous fluid in an elastic tube.