Fluctuating Flow of a Viscoelastic Fluid in a Porous Channel

Abstract

The problem of flow of a viscoelastic fluid characterized by the well-known Rivlin-Ericksen constitutive equations is discussed, when such a fluid is driven by an unsteady pressure gradient in the region between two parallel porous plates. It is assumed that on one plate the fluid is injected with certain constant velocity and that it is sucked off at the other with the same velocity. The governing differential equations, which do not involve the cross-viscosity parameter, are solved using a pertubation scheme treating the viscoelastic parameter to be small. The behavior of instantaneous velocity profiles, and magnitude and the phase lag of mass flux, which depend on the injection Reynolds number, the frequency parameter, and the viscoelastic parameter are discussed for various values of these parameters. Some very interesting departures of these from the corresponding flow of classical viscous fluids are reported when one or both of the injection Reynolds number and frequency parameter are small or large.