INSTABILITY IN POISEUILLE FLOW IN A BIDISPERSE POROUS MEDIUM WITH RELATIVELY LARGE MACROPORES

Abstract

The hydrodynamic stability of an incompressible fluid flowing through a bidisperse porous medium is being investigated. The problem has been investigated when the Darcy theory is applied to micropores and the Brinkman theory is applied to macropores. This includes an incompressible fluid at isothermal conditions confined in an infinite channel with a constant pressure gradient throughout its length. The fluid moves laminarly along the pressure gradient, generating a parabolic velocity profile that is independent of time. Flow in a circular duct is shown to be stable to small disturbances for all Reynolds numbers, whereas flow in a plane-parallel channel is unstable if the Reynolds number exceeds a critical value, which depends on the problem parameters.