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Stability of surfactant-laden core–annular flow and rod–annular flow to non-axisymmetric modes

Published online by Cambridge University Press:  28 January 2013

M. G. Blyth  and
Andrew P. Bassom
M. G. Blyth*
Affiliation:
School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK
Andrew P. Bassom
Affiliation:
School of Mathematics & Statistics, The University of Western Australia, Crawley 6009, Australia
*
†Email address for correspondence: [email protected]
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Abstract

The linear stability of core–annular fluid arrangements are considered in which two concentric viscous fluid layers occupy the annular region within a straight pipe with a solid rod mounted on its axis when the interface between the fluids is coated with an insoluble surfactant. The linear stability of this arrangement is studied in two scenarios: one for core–annular flow in the absence of the rod and the second for rod–annular flow when the rod moves parallel to itself along the pipe axis at a prescribed velocity. In the latter case the effect of convective motion on a quiescent fluid configuration is also considered. For both flows the emphasis is placed on non-axisymmetric modes; in particular their impact on the recent stabilization to axisymmetric modes at zero Reynolds number discovered by Bassom, Blyth and Papageorgiou (J. Fluid. Mech., vol. 704, 2012, pp. 333–359) is assessed. It is found that in general non-axisymmetric disturbances do not undermine this stabilization, but under certain conditions the flow may be linearly stable to axisymmetric disturbances but linearly unstable to non-axisymmetric disturbances.

JFM classification

Interfacial Flows (free surface): Interfacial Flows (free surface) Multiphase and Particle-laden Flows: Multiphase and Particle-laden Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 716 , 10 February 2013 , R13
Copyright
©2013 Cambridge University Press

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