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Linear stability of two-layer Couette flows

Published online by Cambridge University Press:  04 August 2017

Alireza Mohammadi Open the ORCID record for Alireza Mohammadi [Opens in a new window]  and
Alexander J. Smits
Alireza Mohammadi*
Affiliation:
Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA
Alexander J. Smits
Affiliation:
Mechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544, USA Mechanical and Aerospace Engineering, Monash University, Monash, VIC 3800, Australia
*
†Email address for correspondence: alirezam@princeton.edu
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Abstract

The stability of two-layer Couette flow is investigated under variations in viscosity ratio, thickness ratio, interfacial tension and density ratio. The effects of the base flow on eigenvalue spectra are explained. A new type of interfacial mode is discovered at low viscosity ratio with properties that are different from Yih’s original interfacial mode (Yih, J. Fluid Mech., vol. 27, 1967, pp. 337–352). No unstable Tollmien–Schlichting waves were found over the range of parameters considered in this work. The results for thin films with different thicknesses can be collapsed onto a single curve if the Reynolds number and wavenumber are suitably defined based on the parameters of the thin layer. Interfacial tension always has a stabilizing effect, but the effects of density ratio cannot be so easily generalized. Neutral stability curves for water–alkane and water–air systems are presented as an initial step towards better understanding the effects of flow stability on the longevity and performance of liquid-infused surfaces and superhydrophobic surfaces.

JFM classification

Waves/Free-surface Flows: Channel flow Instability: Instability Multiphase and Particle-laden Flows: Multiphase flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 826 , 10 September 2017 , pp. 128 - 157
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Copyright
© 2017 Cambridge University Press 

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