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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: lyubimov@psu.ru
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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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References

REFERENCES

Bardet, B. 2006 Lévitation Électromagnétique: Expériences terrestres et simulations numériques. PhD thesis, Institut National Polytechnique de Grenoble.Google Scholar
Belton, G. R. 1976 Langmuir adsorption, the Gibbs adsorption isotherm, and interfacial kinetics in liquid metal systems. Metall. Trans. 7B, 35–42.Google Scholar
Bratukhin, U. K. & Makarov, S. O. 1994 Interphase Convection. PSU Press, p. 121 (in Russian).Google Scholar
Chandrasekhar, S. 1959 The oscillations of a viscous liquid globe. Proc. Lond. Math. Soc. 9, 141–149.Google Scholar
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Clarendon, pp. 467–477.Google Scholar
Cummings, D. & Blackburn, D. 1991 Oscillations of magnetically levitated liquid droplets. J. Fluid Mech. 224, 395–416.Google Scholar
Earnshaw, J. 1998 Discussion on ‘Measurements of thermophysical properties of liquid metals relevant to Marangoni effects’ by I. Egry et al. Phil. Trans R. Soc. Lond. A 356, 845–856.Google Scholar
Egry, I., Lohöfer, G. & Jacobs, G. 1995 Surface tension of liquid metals: results frommeasurements on ground and in space. Phys. Rev. Lett. 75, 4043–4044.Google Scholar
Egry, I., Lohöfer, G., Seyhan, I., Schneider, S. & Feuerbacher, B. 1998 Viscosity of eutectic Pd78Cu6Si16 measured by the oscillating drop technique in microgravity. Appl. Phys. Lett. 73, 462–463.Google Scholar
Egry, I. & Schick, M. 2011 The viscosity of eutectic Pd–Si alloys – a case study. Intl J. Mat. Res. (submitted).CrossRefGoogle Scholar
Korn, G. A. & Korn, T. M. 1968 Mathematical Handbook for Scientists and Engineers. McGraw-Hill Book Company, p. 17.Google Scholar
Lamb, H. 1881 On the oscillations of a viscous spheroid. Proc. Lond. Math. Soc. 13, 51–66.CrossRefGoogle Scholar
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice-Hall, p. 255.Google Scholar
Lu, H. & Apfel, R. E. 1991 Shape oscillations of drops in the presence of surfactants. J. Fluid Mech. 222, 351–368.Google Scholar
Miller, C. A. & Scriven, L. E. 1968 The oscillations of a fluid droplet immersed in another fluid. J. Fluid Mech. 32, 417–435.Google Scholar
Mock, W. 2004 VDI-Nachrichten. Available at: http://www.vdi-nachrichten.com/artikel/Die-Industrie-entdeckt-den-Weltraum/18521/1.Google Scholar
Prosperetti, A. 1980 Normal-mode analysis for the oscillations of a viscous liquid drop in an immiscible liquid. J. Mécanique 19, 149–182.Google Scholar
Rayleigh, Lord 1879 The capillary phenomena of jets. Proc. R. Soc. 29, 71–97.Google Scholar
Reid, W. 1960 The Oscillations of a viscous liquid drop. Appl. Math. 18, 86–89.Google Scholar
Sauerland, S., Brooks, R., Egry, I. & Mills, K. 1993 In Containerless Processing: Techniques and Applications (ed. Hofmeister, W. & Schiffman, R.), TMS Warrendale, pp. 65–69.Google Scholar
Scriven, L. E. 1960 Dynamics of a fluid interface. Equations of motion for Newtonian surface fluids. Chem. Engng Sci. 12, 98–108.Google Scholar
Sparling, L. & Sedlak, J. 1989 Dynamic equilibrium fluctuations of fluid droplets. Phys. Rev. A 39, 1351–1364.Google Scholar
Stone, H. A. 1990 A simple derivation of the time dependent convective–diffusion equation for surfactant transport along a deforming interface. Phys. Rev. A 2, 111–112.Google Scholar
Suryanarayana, P. & Bayazitoglu, Y. 1991 Surface tension and viscosity from damped free oscillations of viscous droplets. Intl J. Thermophys. 12, 137–151.Google Scholar
Szyszkowski, B. von 1908 Experimentelle Studien über kapillare Eigenschaften der wässerigen Lösungen von Fettsäuren. Z. Phys. Chem. 64, 385–414.Google Scholar
Tian, Y., Holt, R. G. & Apfel, R. E. 1995 Investigations of liquid surface rheology of surfactant solutions by droplet shape oscillations: Theory. Phys. Fluid. 7, 2938–2949.Google Scholar
Tian, Y., Holt, R. G. & Apfel, R. E. 1997 Investigations of liquid surface rheology of surfactant solutions by droplet shape oscillations: Experiment. J. Colloid Interface Sci. 187, 1–10.CrossRefGoogle Scholar
Wunderlich, R. 2008 Surface tension and viscosity of industrial Ti-Alloys measured by the oscillating drop method on board parabolic flights. High Temp. Mat. Process 27, 401–412.Google Scholar