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Abstract--There is extensive literature on the stability of parallel two-phase flow, both in the context of liquid-liquid as well as gas-liquid flow. Aimed at making this literature more transparent, this paper presents a classification scheme for the various instabilities arising in parallel two-phase flow..To achieve such a classification, the equation governing the rate of change of the kinetic energy of the disturbances is evaluated for relevant values of the physical parameters. This shows the existence of five different ways of energy transfer from the primary to the disturbed flow, which have their origin in density stratification, velocity profile curvature, viscosity stratification or shear effects. Each class is discussed on the basis of references covering the developments over the last 35 years. © 1997 Elsevier Science Ltd.

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.

Transient disturbance growth in parallel two-phase flow is studied. When the disturbance growth is measured in terms of the kinetic energy norm, which is commonly used for single-phase flow, the disturbance growth function does not converge as the number of eigenmodes used in the computation increases. A solution to this problem is presented in the form of a norm that also includes the potential energy of the disturbed interface. This solution is used to examine the two-phase flow experiment by Kao and Park.