Core-annular flow through a horizontal pipe: hydrodynamic counterbalancing of buoyancy force on core

A theoretical investigation has been made of core-annular flow: the flow of a high-viscosity liquid
core surrounded by a low-viscosity liquid annular layer through a horizontal pipe. Special attention
is paid to the question of how the buoyancy force on the core, caused by a density difference
between the core and the annular layer, is counterbalanced. From earlier studies it is known that at
the interface between the annular layer and the core waves are present that move with respect to the
pipe wall. In the present study the core is assumed to consist of a solid center surrounded by a
high-viscosity liquid layer. Using hydrodynamic lubrication theory taking into account the flow in
the low-viscosity liquid annular layer and in the high-viscosity liquid core layer the development
of the interfacial waves is calculated. They generate pressure variations in the core layer and annular
layer that can cause a net force on the core. Steady eccentric core-annular flow is found to be
possible.