Nonaxisymmetric waves in core-annular flow with a small viscosity ratio

Abstract

The ‘‘core-annular’’ mode of two-fluid pipeline flow can be an attractive method for the transportation of viscous crude oil. In core-annular flow a thin water film surrounds the oil core and acts as a lubricant. Waves on the oil/water interface play an essential role in the balance of forces on the lighter oil core. The theoretical description of these interfacial waves is the subject of this paper. To predict whether or not a transition of a flat to a wavy interface will occur, the stability of the undisturbed interface is analyzed. The differential equations governing the growth of interfacial disturbances are solved by using matched asymptotic expansions, with the ratio of the viscosities of water and oil (μwater≊10−4μoil) as a small parameter. The stability analysis shows that nonaxisymmetric modes are important, because the growth rates of nonaxisymmetric and axisymmetric modes are approximately the same. This supplements the current picture on the formation of interfacial waves in core-annular flow.