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Stability of miscible core–annular flows with viscosity stratification

Published online by Cambridge University Press:  14 November 2007

B. SELVAM ,
S. MERK ,
RAMA GOVINDARAJAN  and
E. MEIBURG
B. SELVAM
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
S. MERK
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
RAMA GOVINDARAJAN
Affiliation:
Engineering Mechanics Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore 560 064, India
E. MEIBURG*
Affiliation:
Department of Mechanical Engineering, University of California, Santa Barbara, CA 93106, USA
*
†Author to whom correspondence should be addressed.
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Abstract

The linear stability of variable viscosity, miscible core–annular flows is investigated. Consistent with pipe flow of a single fluid, the flow is stable at any Reynolds number when the magnitude of the viscosity ratio is less than a critical value. This is in contrast to the immiscible case without interfacial tension, which is unstable at any viscosity ratio. Beyond the critical value of the viscosity ratio, the flow can be unstable even when the more viscous fluid is in the core. This is in contrast to plane channel flows with finite interface thickness, which are always stabilized relative to single fluid flow when the less viscous fluid is in contact with the wall. If the more viscous fluid occupies the core, the axisymmetric mode usually dominates over the corkscrew mode. It is demonstrated that, for a less viscous core, the corkscrew mode is inviscidly unstable, whereas the axisymmetric mode is unstable for small Reynolds numbers at high Schmidt numbers. For the parameters under consideration, the switchover occurs at an intermediate Schmidt number of about 500. The occurrence of inviscid instability for the corkscrew mode is shown to be consistent with the Rayleigh criterion for pipe flows. In some parameter ranges, the miscible flow is seen to be more unstable than its immiscible counterpart, and the physical reasons for this behaviour are discussed.

A detailed parametric study shows that increasing the interface thickness has a uniformly stabilizing effect. The flow is least stable when the interface between the two fluids is located at approximately 0.6 times the tube radius. Unlike for channel flow, there is no sudden change in the stability with radial location of the interface. The instability originates mainly in the less viscous fluid, close to the interface.

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Type
Papers
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Journal of Fluid Mechanics , Volume 592 , 10 December 2007 , pp. 23 - 49
Copyright
Copyright © Cambridge University Press 2007

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