PERISTALTIC TRANSPORT OF A COMPRESSIBLE VISCOUS LIQUID IN AN AXISYMMETRIC CYLINDRICAL PORE WITH SLIP AT THE WALLS

Department of Basic Engineering sciences, Faculty of Engineering,

Menofia University, Shebin El-Kom, Menofia, Egypt.

In real systems, there is always a certain amount of slip, which, however, is hard to detect

experimentally because of the required space resolution. In this paper, the motion of a

compressible viscous liquid with “slip” boundary condition is studied in an axisymmetric

cylindrical tube (pore) with traveling transversal waves. Like in peristaltic pumping, the

traveling transversal waves induce a net flow of the liquid inside the pore.

The viscosity as well as the compressibility of the liquid is taken into account. This problem

has numerous applications in various branches of science, including stimulation of fluid flow

in porous media under the effect of elastic waves and studies of blood flow dynamics in living

creatures. The Navier-Stokes equations for an axisymmetric cylindrical pore are solved by

means of a perturbation analysis, in which the ratio of the wave amplitude to the radius of the

pore is small parameter. In the second order approximation, a net flow induced by the

traveling wave is calculated for various values of the compressibility of the liquid, Reynolds

number and Knudsen number. The calculations disclose that the compressibility of the liquid

and Knudsen number of slip flow in presence of peristaltic transport have a strong influence

of the net flow rate. The effects of all parameters of the problem are numerically discussed

and graphically explained.