Stability analysis of fluid-fluid interfaces

Abstract

Two problems in pipe flow are discussed in which the stability of fluid–fluid interfaces plays an important role. A stability analysis for a simplified 2-D geometry is presented. In gas–liquid pipe flow different flow regimes occur. This is known to be related to the stability properties of the flow. We shall present a linear stability analysis of plane two-phase Poiseuille flow. Two different unstable modes can occur, corresponding to experimental findings for pipe flow. The first is a finite wavelength mode related to the transition to wavy flow via a Hopf bifurcation. The second unstable mode is an infinite wavelength mode, which may be related to the transition to slug flow. Core-annular flow can be used to transport very viscous crude oils. The crude oil is surrounded by a thin water film, which prevents the core from touching the wall. In the hydrodynamic force balance, waves on the interface play an important role. A linear stability analysis of plane Poiseuille-Couette flow can predict the wavelength in agreement with experimental results even far beyond the critical point. No non-linear analysis is available as yet.