Islam M. EL-Desoky and A. A. Mousa
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.