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.