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Linear instability of two-fluid Taylor–Couette flow in the presence of surfactant

Published online by Cambridge University Press:  24 March 2010

JIE PENG  and
KE-QIN ZHU
JIE PENG*
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
KE-QIN ZHU
Affiliation:
Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
*
†Email address for correspondence: [email protected]
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Abstract

The effect of an insoluble surfactant on the centrifugal and shear instability of a pair of radially stratified immiscible liquids in the annular gap between concentric two-fluid Taylor–Couette flow is investigated by a normal-mode linear analysis and complementary energy analysis. The interface is assumed to be concentric with the cylinders. The gravitational effects are ignored. Influences of density and viscosity stratification, surface tension, surfactant concentration distribution and Taylor–Couette shearing are considered comprehensively. The instability characteristics due to competition and interaction between various physical instability mechanisms are of principal concern. Neutral curves with upper and lower branches in the Reynolds number (Re1)/axial wavenumber (k) plane are obtained. A window of parameters is identified in which the flow is linearly stable. The Marangoni traction force caused by the gradient of surfactant concentration stabilizes the axisymmetric perturbations but initiates an instability corresponding to non-axisymmetric modes in the presence of basic Couette shearing flow. Co-rotation of the outer cylinder has a stabilizing effect in expanding the stable region, which dwindles in the counter-rotation situation.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 651 , 25 May 2010 , pp. 357 - 385
Copyright
Copyright © Cambridge University Press 2010

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