Stationary core-annular flow through a horizontal pipe

This is the authors' abstract. We don't add key points for this paper.

A theoretical investigation has been made of core-annular flow: the flow of a high-viscosity liquid core surrounded by a low-viscosity annular liquid layer through a horizontal pipe. Special attention is paid to the question how the buoyancy force on the core, caused by a possible density difference between the core and the annular layer, is counterbalanced. From earlier studies it is known that at the core surface ripples are present that have the shape of "bamboo" waves or "snake" waves. They generate pressure variations and secondary flows in the annular layer that can cause a net hydrodynamic force on the core. Using hydrodynamic-lubrication theory (assuming the core to be rigid) it has been shown that for snake waves the lubrication force can counterbalance the buoyancy force. For bamboo waves that is not the case.