Analytical study of slightly eccentric core–annular flow

An analytical study was conducted on the flow of a rigid core surrounded by an annular liquid layer through a horizontal tube. Special emphasis was placed on the question how the buoyancy force on the core, caused by a possible density difference between the core and the annular layer, is counterbalanced. The analysis was carried out under the following restrictions: Stokes flow (no inertia), gap between the core and tube wall small compared with the tube radius, and eccentricity small compared with the gap between the core and the tube wall. A perturbation calculation was carried out with the amplitude of the wave at the core–annular interface as small parameter. The restoring (levitation) force is due to the viscous force exerted by the azimuthal velocity components on the core.