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Thermocapillary migration and interaction of drops: two non-merging drops in an aligned arrangement

Published online by Cambridge University Press:  04 February 2015

Zhaohua Yin  and
Qiaohong Li
Zhaohua Yin*
Affiliation:
National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
Qiaohong Li
Affiliation:
National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China Educational Equipment R&D Center, Ministry of Education, Beijing, PR China
*
†Email address for correspondence: [email protected]
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Abstract

A numerical study on the interaction of two spherical drops in thermocapillary migration in microgravity is presented. Unequal drop sizes in the axisymmetric model lead to strong drop interaction if the leading drop is smaller. The effect of the ratio of the two drop radii, their initial distance apart, and non-dimensional numbers on the interaction is studied in the case of non-merging drops in detail. The Marangoni number adopted in this paper is fairly large (around 100) so as to reveal the phenomena of real flows. As a result, the heat wake behind the leading drop plays an important role in drop interaction, and obviously different final drop distances and transient migration processes are observed for various sets of non-dimensional numbers. The influence of drop deformation on drop interaction is also investigated for relatively large capillary number (up to 0.2). Finally, some simulations are performed to explain the phenomena of drop interaction in previous experiments, and some suggestions for future experiments are also provided.

JFM classification

Drops and Bubbles: Drops and Bubbles Multiphase and Particle-laden Flows: Multiphase flow Drops and Bubbles: Thermocapillarity
Type
Papers
Information
Journal of Fluid Mechanics , Volume 766 , 10 March 2015 , pp. 436 - 467
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Copyright
© 2015 Cambridge University Press 

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References

Anderson, J. 1985 Droplet interactions in thermocapillary motion. Intl J. Multiphase Flow 11, 813–824.Google Scholar
Balasubramaniam, R. & Chai, A. 1987 Thermocapillary migration of droplets – an exact solution for small Marangoni numbers. J. Colloid Interface Sci. 119, 531–538.Google Scholar
Balasubramanian, R., Lacy, C., Woniak, G. & Subramanian, R. 1996 Thermocapillary migration of bubbles and drops at moderate values of the Marangoni number in reduced gravity. Phys. Fluids 8, 872–880.Google Scholar
Balasubramanian, R. & Subramanian, R. 1999 Axisymmetric thermal wake interaction of two bubbles in a uniform temperature gradient at large Reynolds and Marangoni numbers. Phys. Fluids 11, 2856–2864.Google Scholar
Berejnov, V., Lavrenteva, O. M. & Nir, A. 2001 Interaction of two deformable viscous drops under external temperature gradient. J. Colloid Interface Sci. 242, 202–213.Google Scholar
Borcia, R. & Bestehorn, M. 2007 Phase-field simulations for drops and bubbles. Phys. Rev. E 75, 056309.Google Scholar
Brady, P., Herrmann, M. & Lopez, J. 2011 Confined thermocapillary motion of a three-dimensional deformable drop. Phys. Fluids 23, 022101.Google Scholar
Chang, L., Yin, Z. & Hu, W. 2011 Transient behavior of the thermocapillary migration of drops under the influence of deformation. Sci. Sin. 41, 960–968.Google Scholar
Chen, J. & Lee, T. 1992 Effect of surface deformation on thermocapillary bubble migration. AIAA J. 30, 993–998.Google Scholar
Choudhuri, D. & Raja Sekhar, G. 2013 Thermocapillary drift on a spherical drop in a viscous fluid. Phys. Fluids 25, 043104.Google 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
Frolovskaya, O., Nir, A. & Lavrenteva, O. M. 2006 Stationary regimes of axisymmetric thermal wake interaction of two buoyant drops at low Reynolds and high Peclet number. Phys. Fluids 18, 072103.CrossRefGoogle Scholar
Hadland, P., Balasubramaniam, R., Wozniak, G. & Subramanian, R. 1999 Thermocapillary migration of bubbles and drops at moderate to large Marangoni number and moderate Reynolds number in reduced gravity. Exp. Fluids 26, 240–248.CrossRefGoogle Scholar
Haj-Hariri, H., Nadim, A. & Borhan, A. 1990 Effect of inertia on the thermocapillary velocity of a drop. J. Colloid Interface Sci. 140, 277–286.CrossRefGoogle Scholar
Haj-Hariri, H., Shi, Q. & Borhan, A. 1997 Thermocapillary motion of deformable drops at finite Reynolds and Marangoni numbers. Phys. Fluids 9, 845–855.Google Scholar
Keh, H. & Chen, S. 1990 The axisymmetric thermocapillary motion of two fluid droplets. Intl J. Multiphase Flow 16, 515–527.CrossRefGoogle Scholar
Keh, H. & Chen, S. 1992 Droplet interactions in axisymmetric thermocapillary motion. J. Colloid Interface Sci. 151, 1–16.Google Scholar
Lappa, M. 2005 Assessment of VOF strategies for the analysis of Marangoni migration, collisional coagulation of droplets and thermal wake effects in metal alloys under microgravity conditions. Comput. Mater. Continua 2, 51–64.Google Scholar
Lavrenteva, O. M. & Nir, A. 2003 Axisymmetric thermal wake interaction of two drops in a gravity field at low Reynolds and high Peclet numbers. Phys. Fluids 15, 3006–3014.Google Scholar
Lee, T. & Keh, H. 2013 Axisymmetric thermocapillary migration of a fluid sphere in a spherical cavity. Intl J. Heat Mass Transfer 62, 772–781.Google Scholar
Leshansky, A. M. & Nir, A. 2001 Thermocapillary alignment of gas bubbles induced by convective transport. J. Colloid Interface Sci. 240, 544–551.Google Scholar
Li, Q.2013 Thermocapillary migration and interactions of two drops. Master’s thesis, Institute of Mechanics, Chinese Academy of Sciences.Google Scholar
Liu, H., Valocchi, A., Zhang, Y. & Kang, Q. 2013 Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows. Phys. Rev. E 87, 013010.Google Scholar
Liu, H., Zhang, Y. & Valocchi, A. 2012 Modeling and simulation of thermocapillary flows using lattice Boltzmann method. J. Comput. Phys. 231, 4433–4453.CrossRefGoogle Scholar
Loewenberg, M. & Davis, R. H. 1993 Near-contact thermocapillary motion of two non-conducting drops. J. Fluid Mech. 256, 107–131.Google Scholar
Meyyappan, M., Wilcox, W. R. & Subramanian, R. S. 1983 The slow axisymmetric motion of two bubbles in a thermal gradient. J. Colloid Interface Sci. 94, 243–257.CrossRefGoogle Scholar
Nas, S., Muradoglu, M. & Tryggvason, G. 2006 Pattern formation of drops in thermocapillary migration. Intl J. Heat Mass Transfer 49, 2265–2276.Google Scholar
Nas, S. & Tryggvason, G. 2003 Thermocapillary interaction of two bubbles or drops. Intl J. Multiphase Flow 29, 1117–1135.Google Scholar
Rother, M. A., Zinchenko, A. Z. & Davis, R. H. 2002 A three-dimensional boundary-integral algorithm for thermocapillary motion of deformable drops. J. Colloid Interface Sci. 245, 356–364.Google Scholar
Schedin, S. 2006 Digital holographic interferometry. J. Hologr. Speckle 3, 1–17.CrossRefGoogle Scholar
Stimson, M. & Jefferey, G. B. 1926 The motion of two spheres in a viscous fluid. Proc. R. Soc. Lond. A 111, 110–116.Google Scholar
Subramanian, R. & Balasubramaniam, R. 2001 The Motion of Bubbles and Drops in Reduced Gravity. Cambridge University Press.Google Scholar
Subramanian, R., Balasubramaniam, R. & Wozniak, G. 2002 Fluid mechanics of bubbles and drops. In Physics of Fluids in Microgravity (ed. Monti, R.), pp. 149–177. Taylor & Francis.Google Scholar
Sun, R. & Hu, W. 2002 The thermocapillary migrations of two bubbles in microgravity environment. J. Colloid Interface Sci. 255, 375–381.Google Scholar
Sun, R. & Hu, W. 2003 Planar thermocapillary migration of two bubbles in microgravity environment. Phys. Fluids 15, 3015–3027.Google Scholar
Treuner, M., Galindo, V., Gerbeth, G., Langbein, D. & Rath, H. J. 1996 Thermocapillary bubble migration at high Reynolds and Marangoni numbers under low gravity. J. Colloid Interface Sci. 179, 114–127.Google Scholar
Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S. & Jan, Y.-J. 2001 A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169, 708–759.Google Scholar
Welch, S. 1998 Transient thermocapillary migration of deformable bubbles. J. Colloid Interface Sci. 208, 500–508.Google Scholar
Wozniak, G., Balasubramaniam, R., Hadland, P. & Subramanian, R. S. 2001 Temperature fields in a liquid due to the thermocapillary motion of bubbles and drops. Exp. Fluids 31, 84–89.Google Scholar
Wu, Z. & Hu, W. 2013 Effects of Marangoni numbers on thermocapillary drop migration: constant for quasi-steady state? J. Math. Phys. 54, 023102.Google Scholar
Yin, Z., Chang, L., Hu, W. & Gao, P. 2011 Thermocapillary migration and interactions of two nondeformable droplets. Z. Angew. Math. Mech. 32, 761–773.Google Scholar
Yin, Z., Chang, L., Hu, W., Li, Q. & Wang, H. 2012 Numerical simulations on thermocapillary migrations of nondeformable droplets with large Marangoni numbers. Phys. Fluids 24, 092101.Google Scholar
Yin, Z., Gao, P., Hu, W. & Chang, L. 2008 Thermocapillary migration of nondeformable drops. Phys. Fluids 20, 082101.CrossRefGoogle Scholar
Young, N., Goldstein, J. & Block, M. 1959 The motion of bubbles in a vertical temperature gradient. J. Fluid Mech. 6, 350–356.Google Scholar
Zhang, X. G. & Davis, R. H. 1992 The collision rate of small drops undergoing thermocapillary migration. J. Colloid Interface Sci. 52, 548–561.Google Scholar
Zhao, J., Zhang, L., Li, Z. & Qin, W. 2011 Topological structure evolvement of flow and temperature fields in deformable drop Marangoni migration in microgravity. Intl J. Heat Mass Transfer 54, 4655–4663.CrossRefGoogle Scholar
Zhou, H. & Davis, R. 1996 Axisymmetric thermocapillary migration of two deformable viscous drops. J. Colloid Interface Sci. 181, 60–72.Google Scholar