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Shape oscillations of an oil drop rising in water: effect of surface contamination

Published online by Cambridge University Press:  30 May 2012

Nicolas Abi Chebel
Affiliation:
Institut de Mécanique des Fluides de Toulouse, CNRS & Université de Toulouse, 31400 Toulouse, France Laboratoire de Génie Chimique, CNRS & Université de Toulouse, France IFP – Energies Nouvelles, 92852 Rueil-Malmaison CEDEX, France Fédération de Recherche FERMAT, CNRS, Toulouse, 31400 Toulouse, France
Jiří Vejražka
Affiliation:
Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, 165 02 Prague 6-Suchdol, Czech Republic
Olivier Masbernat
Affiliation:
Laboratoire de Génie Chimique, CNRS & Université de Toulouse, France Fédération de Recherche FERMAT, CNRS, Toulouse, 31400 Toulouse, France
Frédéric Risso*
Affiliation:
Institut de Mécanique des Fluides de Toulouse, CNRS & Université de Toulouse, 31400 Toulouse, France Fédération de Recherche FERMAT, CNRS, Toulouse, 31400 Toulouse, France
*
Email address for correspondence: frederic.risso@imft.fr

Abstract

Inertial shape oscillations of heptane drops rising in water are investigated experimentally. Diameters from 0.59 to 3.52 mm are considered, corresponding to a regime where the rising motion should not affect shape oscillations for pure immiscible fluids. The interface, however, turns out to be contaminated. The drag coefficient is considerably increased compared to that of a clean drop due to the well-known Marangoni effect resulting from a gradient of surfactant concentration generated by the fluid motion along the interface. Thanks to the decomposition of the shape into spherical harmonics, the eigenfrequencies and the damping rates of oscillation modes , 3, 4 and 5 have been measured. Frequencies are not affected by contamination, while damping rates are increased by a considerable amount that depends neither on drop instantaneous velocity nor on diameter. This augmentation, however, depends on the mode number: it is maximum for mode two (multiplied by 2.4) and then relaxes towards the value of a clean drop as increases. A previous similar investigation of a drop attached to a capillary has not revealed such an increase of the damping rates, indicating that the coupling between rising motion and surface contamination is responsible for this effect.

Type
Papers
Copyright
Copyright © Cambridge University Press 2012

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References

1. Abi Chebel, N., Risso, F. & Masbernat, O. 2011 Inertial modes of a periodically forced buoyant drop attached to a capillary. Phys. Fluids 23, 102104.CrossRefGoogle Scholar
2. Basaran, O. A., Scott, T. C. & Byers, C. H. 1989 Drop oscillations in liquid–liquid systems. AIChE 35, 12631270.CrossRefGoogle Scholar
3. Cuenot, B., Magnaudet, J. & Spennato, B. 1997 Flow about a fluid sphere at low to moderate Reynolds numbers. J. Fluid Mech. 339, 2540.CrossRefGoogle Scholar
4. Duineveld, P. C. 1995 The rise of an ellipsoidal bubble in water at high Reynolds number. J. Fluid Mech. 292, 325332.CrossRefGoogle Scholar
5. Hu, S. & Kintner, R. C. 1955 The fall of single liquid drops through water. AIChE 1, 4248.CrossRefGoogle Scholar
6. Lu, H. & Apfel, R. E. 1990 Quadrupole oscillations of drops for studying interfacial properties. J. Colloid Interface Sci. 134, 245255.CrossRefGoogle Scholar
7. Lu, H. & Apfel, R. E. 1991 Shape oscillations of drops in the presence of surfactants. J. Fluid Mech. 222, 351368.CrossRefGoogle Scholar
8. Miller, C. A. & Scriven, L. E. 1968 The oscillations of a fluid droplet immersed in another fluid. J. Fluid Mech. 32, 417435.CrossRefGoogle Scholar
9. Oliver, D. L. R. & Chung, J. N. 1987 Flow about a fluid sphere at low to moderate Reynolds numbers. J. Fluid Mech. 177, 118.CrossRefGoogle Scholar
10. Prosperetti, A. 1980 Normal mode analysis for the oscillations of a viscous liquid drop in an immiscible liquid. J. Mécanique 19, 149182.Google Scholar
11. Rivkind, V. Y. & Ryskin, G. M. 1976 Flow structure in motion of a spherical drop in a fluid medium at intermediate Reynolds numbers. J. Fluid Dynam. 11, 512.CrossRefGoogle Scholar
12. Schiller, L. & Naumann, A. Z. 1933 Über die grundlegenden Berechnungen bei der Schwerkraftaufbereitung. Z. Vereines Deutscher Ingenieure 77, 318320.Google Scholar
13. Subramanyam, S. V. 1969 A note on the damping and oscillations of a fluid drop moving in another fluid. J. Fluid Mech. 37, 715725.CrossRefGoogle Scholar
14. Vejražka, J., Fujasova, M., Stanovsky, P., Ruzicka, M. C. & Drahos, J. 2008 Bubbling controlled by needle movement. Fluid Dyn. Res. 40, 521533.CrossRefGoogle Scholar
15. Wegener, M., Kraume, M. & Paschedag, A. R. 2010 Terminal and transient drop rise velocity of single toluene droplets in water. AIChE 56, 210.CrossRefGoogle Scholar
16. Zenit, R. & & Magnaudet, J. 2008 Path instability of rising spheroidal air bubbles: a shape-controlled process. Phys. Fluids 20, 061702.CrossRefGoogle Scholar