An asymptotic theory for the linear stability of a core-annular flow in the thin annular limit

Document Type

Article

Publication Date

1-1-1992

Abstract

We study the linear stability of a vertical, perfectly concentric, core—annular flow in the limit in which the gap is much thinner than the core radius. The analysis includes the effects of viscosity and density stratification, interfacial tension, gravity and pressure-driven forcing. In the limit of small annular thicknesses, several terms of the expression for the growth rate are found in order to identify and characterize the competing effects of the various physical mechanisms present. For the sets of parameters describing physical situations they allow immediate determination of which mechanisms dominate the stability. Comparisons between the asymptotic formula and available full numerical computations show excellent agreement for non-dimensional ratio of undisturbed annular thickness to core radius as large as 0.2. The expansion leads to new linear stability results (an expression for the growth rate in powers of the capillary number to the| power) for wetting layers in low-capillary-number liquid—liquid displacements. The expression includes both capillarity and viscosity stratification and agrees well with the experimental results of Aul & Olbrich (1990). Finally, we derive Kuramoto-Sivashinsky-type integro-differential equation for the later nonlinear stages of the interfacial dynamics, and discuss their solutions. © 1992, Cambridge University Press. All rights reserved.

Identifier

0026800078 (Scopus)

Publication Title

Journal of Fluid Mechanics

External Full Text Location

https://doi.org/10.1017/S0022112092002878

e-ISSN

14697645

ISSN

00221120

First Page

653

Last Page

677

Volume

243

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