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Small amplitude shape oscillations of a spherical liquid drop with surface viscosity

Published online by Cambridge University Press:  27 April 2011

D. V. LYUBIMOV ,
V. V. KONOVALOV ,
T. P. LYUBIMOVA  and
I. EGRY
D. V. LYUBIMOV
Affiliation:
Theoretical Physics Department, Perm State University, Perm 614990, Russia
V. V. KONOVALOV
Affiliation:
Institute of Continuous Media Mechanics, Perm 614013, Russia
T. P. LYUBIMOVA*
Affiliation:
Institute of Continuous Media Mechanics, Perm 614013, Russia
I. EGRY
Affiliation:
Institut fuer Materialphysik im Weltraum, German Aerospace Center, DLR, 51170 Cologne, Germany
*
†Email address for correspondence: [email protected]
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Abstract

The analysis of surface oscillations of liquid drops allows measurements of the surface tension and viscosity of the liquid. For small oscillations of spherical drops with a free surface, classical formulae by Rayleigh and Lamb relate these quantities to the frequency and damping of the oscillations. In many cases, however, the drop's surface is covered by a surface film, typically an oxide layer or a surfactant, exhibiting a rheological behaviour different from the bulk fluid. It is the purpose of this paper to investigate how such surface properties influence the oscillation spectrum of a spherical drop. For small bulk shear viscosity, the cases of small, finite and large surface viscosities are discussed, and the onset of aperiodic motion as a function of the surface parameters is also derived.

JFM classification

Drops and Bubbles: Drops Waves/Free-surface Flows: Capillary waves Multiphase and Particle-laden Flows: Multiphase flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 677 , 25 June 2011 , pp. 204 - 217
Copyright
Copyright © Cambridge University Press 2011

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