Viscous-inviscid model for the linear stability of core-annular flow

In this paper the linear stability of two immiscible fluids of widely different kinematic viscosity and equal density flowing through a circular pipe is analysed. A viscous-inviscid model is used which offers a consistent zeroth-order approximation to the stability problem as long as the thickness of the ring flow, where the inviscid fluid is located, is large enough. In this way the laminar sublayer at the pipe wall does not interact with the fluid interface. A closed form expression for the complex dispersion relation due to an arbitrary wavelength perturbation is derived, which determines a stability criterion, and then simplified for large and short wavelength values.