STABILITY ANALYSIS OF THE GENERALIZED WASHBURN EQUATION

Abstract

Washburn’s equation describes the flow of a viscous incompressible fluid through a narrow vertical cylindrical pipe. It is a simplified version of the Navier-Stokes equations. If the vertical pipe has circular cross section of constant radius, equilibrium height of the fluid is asymptotically stable. In this study, it is shown that in the case of slowly varying cross section equilibrium height remains asymptotically stable, but critical value of the pa- rameter depends on the shape of the pipe. The model and its stability analysis generalize existing results, based upon lubrication theory approach, by inclusion of inertial term.