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On the thermocapillary motion of partially engulfed compound drops

Published online by Cambridge University Press:  10 May 2009

L. ROSENFELD ,
O. M. LAVRENTEVA  and
A. NIR
L. ROSENFELD
Affiliation:
Chemical Engineering Department, Technion, Haifa 32000, Israel
O. M. LAVRENTEVA
Affiliation:
Chemical Engineering Department, Technion, Haifa 32000, Israel
A. NIR*
Affiliation:
Chemical Engineering Department, Technion, Haifa 32000, Israel
*
†Email address for correspondence: [email protected]
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Abstract

In this work the thermocapillary-induced motion of partially engulfed compound drops is considered. This phenomenon occurs in many natural and technological processes in which heat is exchanged between such hybrid drops and the medium around them through the interfaces. Two types of thermal fields and the resulting motions are studied; flow induced by an external temperature gradient and spontaneous thermocapillary motion. For the first flow type, it was found that, in general, the motion is induced in the direction of the temperature gradient. However, under certain physical conditions and drops' configuration a motion against the temperature gradient may be observed. In the second case, spontaneous thermocapillary motion, the compound drop moves due to surface tension gradients which result from the geometric non-uniformity of the system. Results are presented for several parameters such as configuration of the compound drop, viscosity, thermal conductivity ratio, the dependence of the various interfacial tensions on temperature and the volume ratio of the phases within the drop.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 626 , 10 May 2009 , pp. 263 - 289
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Berejnov, V., Leshansky, A. M., Lavrenteva, O. M. & Nir, A. 2002 Spontaneous thermocapillary interaction of drops: effect of surface deformation at nonzero capillary number. Phys. Fluids 14, 1326–1339.CrossRefGoogle Scholar
Bialik-Rosenfeld, L., Lavrenteva, O. M. & Nir, A. 2007 Spontaneous thermocapillary drops interaction: the effect of a surface reaction. AIChE J. 53, 2783–2794.CrossRefGoogle Scholar
Borhan, A., Haj-Hariri, H. & Nadim, A. 1992 Effect of surfactants on the thermocapillary migration of a concentric compound drop. J. Colloid Interface Sci. 149, 553–560.CrossRefGoogle Scholar
Dammel, F. & Beer, H. 2003 Heat transfer from a continuous liquid to an evaporating drop: a numerical analysis. Intl J. Thermal Sci. 42, 677–686.CrossRefGoogle Scholar
Feuillebois, F. 1989 Thermocapillary migration of two equal bubbles parallel to their line of centers. J. Colloid Interface Sci. 131, 267–274.CrossRefGoogle Scholar
Golovin, A. A., Nir, A. & Pismen, L. M. 1995 Spontaneous motion of two droplets caused by mass transfer. Ind. Engng Chem. Res. 34, 3278–3288.CrossRefGoogle Scholar
Haj-Hariri, H., Nadim, A. & Borhan, A. 1993 Reciprocal theorem for concentric compound drops in arbitrary Stokes flows. J. Fluid Mech. 252, 265–277.CrossRefGoogle Scholar
Hashimoto, H. & Kawano, S. 1990 A study on encapsulated liquid drop formation in liquid–liquid–gas systems (fundamental mechanisms of encapsulated drop formation). JSME Intl J. Ser. II 33 (4), 729–735.Google Scholar
Johnson, R. E., & Sadhal, S. S. 1985 Fluid mechanics of compound multiphase drops and bubbles. Annu. Rev. Fluid Mech. 17, 286–320.CrossRefGoogle Scholar
Lavrenteva, O. M., Leshansky, A. M., Berejnov, V. & Nir, A. 2002 Spontaneous thermocapillary interaction of drops, bubbles and particles in viscous fluid driven by capillary inhomogeneties. Ind. Engng Chem. Res. 41, 357–366.CrossRefGoogle Scholar
Lavrenteva, O. M., Leshansky, A. M. & Nir, A. 1999 Spontaneous thermocapillary interaction of drops, bubbles and particles: unsteady convective effects at low Péclet numbers. Phys. Fluids 11, 1768–1782.CrossRefGoogle Scholar
Lavrenteva, O. M. & Nir, A. 2001 Spontaneous thermocapillary interaction of drops and bubbles: unsteady convective effects at high Péclet numbers. Phys. Fluids 13, 368–381.CrossRefGoogle Scholar
Lebedev, N. N. 1965 Special Functions and Their Applications. Prentice-Hall.CrossRefGoogle Scholar
Loewenberg, M. & Davis, R. H. 1993 a Near-contact thermocapillary migration of a non-conducting, viscous drop normal to a planar interface. J. Colloid Interface Sci 160, 265–274.CrossRefGoogle Scholar
Loewenberg, M. & Davis, R. H. 1993 b Near-contact thermocapillary motion of two non-conducting drops. J. Fluid Mech 256, 107–131.CrossRefGoogle Scholar
Lyell, M. J. & Carpenter, M. J. 1993 The effect of residual contamination on Marangoni convection in a spherical liquid system. Appl. Sci. Res. 14, 639–662.CrossRefGoogle Scholar
Mercier, J. L., da Cunha, F. M., Teixeria, J. C. & Scofield, M. P. 1974 Influence of enveloping water layer on the rise of air bubbles in Newtonian fluid. J. Appl. Mech. 96, 29–34.CrossRefGoogle Scholar
Mori, Y. H. 1978 Configurations of gas–liquid two phase bubbles in immiscible liquid media. Int. J. Multiphase Flow 4, 383–396.CrossRefGoogle Scholar
Mori, Y. H., Komotori, K., Higeta, K. & Inada, J. 1977 Rising behavior of air bubbles in superposed liquid layers. Can. J. Chem. Engng 55, 9–12.CrossRefGoogle Scholar
Morton, D. S., Subramanian, R. S. & Balasubramaniam, R. 1990 The migration of a compound drop due to thermocapillarity. Phys. Fluids A 2, 2119–2133.CrossRefGoogle Scholar
Oguz, H. N. 1987 Fluid dynamics of compound multiphase drops and bubbles. Ph.D. thesis, University of Southern California.Google Scholar
Payne, L. E. & Pell, W. H. 1960 The Stokes flow problem for a class of axially symmetric bodies. J. Fluid Mech. 7, 529–549.CrossRefGoogle Scholar
Rosenfeld, L., Lavrenteva, O. M. & Nir, A. 2008 Thermocapillary motion of hybrid drops. Phys. Fluids 20 (7), 072102.CrossRefGoogle Scholar
Sadhal, S. S. 1983 A note on the thermocapillary migration of a bubble normal to a plane surface. J. Colloid Interface Sci. 95, 283–285.CrossRefGoogle Scholar
Sideman, S. & Taitel, Y. 1964 Direct contact heat transfer with change of phase: evaporation of drops in an immiscible liquid medium. Intl J. Heat Mass Transfer 7, 1273–1289.CrossRefGoogle Scholar
Sneddon, I. N. 1972 The Use of Integral Transforms. McGraw-Hill.Google Scholar
Stone, H., & Leal, G. 1990 Breakup of concentric double emulsion droplets in linear flow. J. Fluid Mech. 211, 123–156.CrossRefGoogle Scholar
Subramanian, R. S. & Balasubramaniam, R. 2001 The Motion of Bubbles and Drops in Reduced Gravity. Cambridge University Press.Google Scholar
Tochitani, Y., Mori, Y. H. & Komotori, K. 1977 a Vaporizing of single drops in an immiscible liquid. Part I. Forms and motions of vaporizing drops. Thermo Fluid Dyn 10, 51–59.Google Scholar
Tochitani, Y., Nakagawa, T., Mori, Y. H. & Komotori, K. 1977 b Vaporizing of single drops in an immiscible liquid. Part II. Heat transfer characteristics. Thermo Fluid Dyn 10, 71–79.Google Scholar
Torza, S. & Mason, S. G. 1970 Three-phase interactions in shear and electrical fields. J. Colloid Interface Sci. 33, 67–83.CrossRefGoogle Scholar
Tsemakh, D., Lavrenteva, O. M. & Nir, A. 2004 On the locomotion of a drop induced by the internal secretion of surfactant. Intl J. Multiphase Flow 30, 1337–1367.CrossRefGoogle Scholar
Vuong, S. T. & Sadhal, S. S. 1989 a Growth and translation of a liquid–vapor compound drop in a second liquid. Part 1. Fluid mechanics. J. Fluid Mech 209, 617–637.CrossRefGoogle Scholar
Vuong, S. T. & Sadhal, S. S. 1989 b Growth and translation of a liquid–vapor compound drop in a second liquid. Part 2. Heat transfer. J. Fluid Mech 209, 639–660.CrossRefGoogle Scholar
Young, N. O., Goldstein, J. S. & Block, M. J. 1959 The motion of gas bubbles in a vertical temperature gradient. J. Fluid Mech. 6, 350–364.CrossRefGoogle Scholar
Zabarankin, M. 2007 Asymmetric three-dimensional Stokes flows about two fused equal spheres. Proc. R. Soc. A 463, 2329–2349.CrossRefGoogle Scholar