The Linear Stability of a Core Annular Flow in a Corrugated Tube

Abstract

A two-fluid core-annular flow (CAF) consists of two immiscible fluids flowing cocurrently in a tube or pore, where one (the annular) fluid wets the tube wall and surrounds the other (core) fluid. Core annular flows are widely studied and employed as a useful model to analyze a number of technologies and problems of scientific interest such as oil recovery. The interfacial stability, however, can significantly affect the efficiency of the recovery process. Clearly, it is important to understand the mechanism of instability in CAFs because it is often critical to either encourage or discourage the instability’s growth. Most investigations based on the perfect CAF (PCAF — perfect meaning co-axial and axisymmetric) through the idealized geometry of a cylindrical tube of uniform cross-section. The dominant effects on the linear stability problems for such CAFs are capillarity and viscosity stratification. Capillarity acts in two ways: it destabilizes the interfacial circumferential curvature and stabilizes the axial curvature of an interfacial deflection. The competition is such that disturbances with wavelengths shorter than the undisturbed interfacial circumference are stable and those longer are unstable. This feature of capillarity is independent of the base flow, and arises simply from the cylindrical geometry of the unperturbed fluid-fluid interface. Preziosi et al. (1989) investigated CAFs by numerically solving the full Orr-Sommerfeld equation. In lubricated pipelining m 1 A density difference is purely dispersive and dose not contribute to the stability to the leading order in e.