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Non-isothermal bubble rise dynamics in a self-rewetting fluid: three-dimensional effects

Published online by Cambridge University Press:  08 November 2018

Mounika Balla ,
Manoj Kumar Tripathi ,
Kirti Chandra Sahu Open the ORCID record for Kirti Chandra Sahu [Opens in a new window] ,
George Karapetsas Open the ORCID record for George Karapetsas [Opens in a new window]  and
Omar K. Matar
Mounika Balla
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Sangareddy 502 285, Telangana, India
Manoj Kumar Tripathi
Affiliation:
Indian Institute of Science Education and Research, Bhopal 462 066, Madhya Pradesh, India
Kirti Chandra Sahu*
Affiliation:
Department of Chemical Engineering, Indian Institute of Technology Hyderabad, Sangareddy 502 285, Telangana, India
George Karapetsas
Affiliation:
Department of Chemical Engineering, Aristotle University of Thessaloniki, GR 54124, Thessaloniki, Greece
Omar K. Matar
Affiliation:
Department of Chemical Engineering, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: ksahu@iith.ac.in
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Abstract

The dynamics of a gas bubble in a square channel with a linearly increasing temperature at the walls in the vertical direction is investigated via three-dimensional numerical simulations. The channel contains a so-called ‘self-rewetting’ fluid whose surface tension exhibits a parabolic dependence on temperature with a well-defined minimum. The main objectives of the present study are to investigate the effect of Marangoni stresses on bubble rise in a self-rewetting fluid using a consistent model fully accounting for the tangential surface tension forces, and to highlight the effects of three-dimensionality on the bubble rise dynamics. In the case of isothermal and non-isothermal systems filled with a ‘linear’ fluid, the bubble moves in the upward direction in an almost vertical path. In contrast, strikingly different behaviours are observed when the channel is filled with a self-rewetting fluid. In this case, as the bubble crosses the location of minimum surface tension, the buoyancy-induced upward motion of the bubble is retarded by a thermocapillary-driven flow acting in the opposite direction, which in some situations, when thermocapillarity outweighs buoyancy, results in the migration of the bubble in the downward direction. In the later stages of this downward motion, as the bubble reaches the position of arrest, its vertical motion decelerates and the bubble encounters regions of horizontal temperature gradients, which ultimately lead to the bubble migration towards one of the channel walls. These phenomena are observed at sufficiently small Bond numbers (high surface tension). For stronger self-rewetting behaviour, the bubble undergoes spiralling motion. The mechanisms underlying these three-dimensional effects are elucidated by considering how the surface tension dependence on temperature affects the thermocapillary stresses in the flow. The effects of other dimensionless numbers, such as Reynolds and Froude numbers, are also investigated.

JFM classification

Drops and Bubbles: Bubble dynamics Multiphase and Particle-laden Flows: Multiphase flow Drops and Bubbles: Thermocapillarity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 858 , 10 January 2019 , pp. 689 - 713
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Copyright
© 2018 Cambridge University Press 

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References

Abe, Y., Iwasaki, A. & Tanaka, K. 2004 Microgravity experiments on phase change of self-rewetting fluids. Ann. N.Y. Acad. Sci. 1027, 269–285.Google Scholar
Ahmed, S. & Carey, V. P. 1999 Effects of surface orientation on the pool boiling heat transfer in water/2-propanol mixtures. Trans. ASME J. Heat Transfer 121, 80–88.Google Scholar
Balasubramaniam, R. 1998 Thermocapillary and buoyant bubble motion with variable viscosity. Intl J. Multiphase Flow 24 (4), 679–683.Google Scholar
Balasubramaniam, R. & Chai, A.-T. 1987 Thermocapillary migration of droplets: an exact solution for small Marangoni numbers. J. Colloid Interface Sci. 119 (2), 531–538.Google Scholar
Borcia, R. & Bestehorn, M. 2007 Phase-field simulations for drops and bubbles. Phys. Rev. E 75 (5), 056309.Google Scholar
Brackbill, J. U., Kothe, D. B. & Zemach, C. 1992 A continuum method for modeling surface tension. J. Comput. Phys. 100, 335–354.Google Scholar
Brady, P. T., Herrmann, M. & Lopez, J. M. 2011 Confined thermocapillary motion of a three-dimensional deformable drop. Phys. Fluids 23 (2), 022101.Google Scholar
Cano-Lozano, J. C., Tchoufag, J., Magnaudet, J. & Martínez-Bazán, C. 2016 A global stability approach to wake and path instabilities of nearly oblate spheroidal rising bubbles. Phys. Fluids 28 (1), 014102.Google Scholar
Chen, J., Dagan, Z. & Maldarelli, C. 1991 The axisymmetric thermocapillary motion of a fluid particle in a tube. J. Fluid Mech. 233, 405–437.Google Scholar
Chen, J. C. & Lee, Y. T. 1992 Effect of surface deformation on thermocapillary bubble migration. AIAA J. 30 (4), 993–998.Google Scholar
Haj-Hariri, H., Shi, Q. & Borhan, A. 1997 Thermocapillary motion of deformable drops at finite Reynolds and Marangoni numbers. Phys. Fluids 9 (4), 845–855.Google Scholar
Herrmann, M., Lopez, J. M., Brady, P. & Raessi, M. 2008a Thermocapillary motion of deformable drops and bubbles. In Proceedings of the Summer Program 2008, p. 155. Stanford University: Center for Turbulence Research.Google Scholar
Herrmann, M., Lopez, J. M., Brady, P. & Raessi, M. 2008b Thermocapillary motion of deformable drops and bubbles. In Proceedings of the Summer Program, p. 155. Stanford University: Center for Turbulence Research.Google Scholar
Karapetsas, G., Sahu, K. C., Sefiane, K. & Matar, O. K. 2014 Thermocapillary-driven motion of a sessile drop: effect of non-monotonic dependence of surface tension on temperature. Langmuir 30 (15), 4310–4321.Google Scholar
Keh, H. J., Chen, P. Y. & Chen, L. S. 2002 Thermocapillary motion of a fluid droplet parallel to two plane walls. Intl J. Multiphase Flow 28 (7), 1149–1175.Google Scholar
Limbourgfontaine, M. C., Petre, G. & Legros, J. C. 1986 Thermocapillary movements under at a minimum of surface tension. Naturwissenschaften 73, 360–362.Google Scholar
Liu, H., Valocchi, A. J., Zhang, Y. & Kang, Q. 2013 Phase-field-based lattice Boltzmann finite-difference model for simulating thermocapillary flows. Phys. Rev. E 87 (1), 013010.Google Scholar
Liu, H., Zhang, Y. & Valocchi, A. J. 2012 Modeling and simulation of thermocapillary flows using lattice Boltzmann method. J. Comput. Phys. 231 (12), 4433–4453.Google Scholar
Ma, C. & Bothe, D. 2011 Direct numerical simulation of thermocapillary flow based on the volume of fluid method. Intl J. Multiphase Flow 37 (9), 1045–1058.Google Scholar
Magnaudet, J. & Mougin, G. 2007 Wake instability of a fixed spheroidal bubble. J. Fluid Mech. 572, 311–337.Google Scholar
Mahesri, S., Haj-Hariri, H. & Borhan, A. 2014 Effect of interface deformability on thermocapillary motion of a drop in a tube. Heat Mass Transfer. 50 (3), 363–372.Google Scholar
McGillis, W. R. & Carey, V. P. 1996 On the role of Marangoni effects on the critical heat flux for pool boiling of binary mixtures. Trans. ASME J. Heat Transfer 118, 103–109.Google Scholar
Merritt, R. M., Morton, D. S. & Subramanian, R. S. 1993 Flow structures in bubble migration under the combined action of buoyancy and thermocapillarity. J. Colloid Interface Sci. 155 (1), 200–209.Google Scholar
Nahme, R. 1940 Beiträge zur hydrodynamischen theorie der lagerreibung. Ing.-Arch. 11, 191–209.Google Scholar
Nas, S. & Tryggvason, G. 2003 Thermocapillary interaction of two bubbles or drops. Intl J. Multiphase Flow 29 (7), 1117–1135.Google Scholar
Petre, G. & Azouni, M. A. 1984 Experimental evidence for the minimum of surface tension with temperature at aqueous alcohol solution air interfaces. J. Colloid Interface Sci. 98, 261–263.Google Scholar
Popinet, S. 2003 Gerris: a tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys. 190, 572–600.Google Scholar
Popinet, S. 2009 An accurate adaptive solver for surface-tension-driven interfacial flows. J. Comput. Phys. 228, 5838–5866.Google Scholar
Popinet, S. 2018 Numerical models of surface tension. Annu. Rev. Fluid Mech. 50, 49–75.Google Scholar
Savino, R., Cecere, A. & Paola, R. D. 2009 Surface tension driven flow in wickless heat pipes with self-rewetting fluids. Intl J. Heat Fluid Flow 30, 380–388.Google Scholar
Savino, R., Cecere, A., Vaerenbergh, S. V., Abe, Y., Pizzirusso, G., Tzevelecos, W., Mojahed, M. & Galand, Q. 2013 Some experimental progresses in the study of self-rewetting fluids for the SELENE experiment to be carried in the Thermal Platform 1 hardware. Acta Astron. 89, 179–188.Google Scholar
Seric, I., Afkhami, S. & Kondic, L. 2018 Direct numerical simulation of variable surface tension flows using a volume-of-fluid method. J. Comput. Phys. 352 (1), 615–636.Google Scholar
Sharaf, D. M., Premlata, A. R., Tripathi, M. K., Karri, B. & Sahu, K. C. 2017 Shapes and paths of an air bubble rising in quiescent liquids. Phys. Fluids 29 (12), 122104.Google Scholar
Subramanian, R. S. 1992 Transport Processes in Drops, Bubbles and Particles. Hemisphere.Google Scholar
Subramanian, R. S., Balasubramaniam, R. & Wozniak, G. 2002 Fluid mechanics of bubbles and drops. In Physics of Fluids in Microgravity (ed. Monti, R.), pp. 149–177. Taylor and Francis.Google Scholar
Suzuki, K., Nakano, M. & Itoh, M. 2005 Subcooled boiling of aqueous solution of alcohol. In Proceedings of the 6th KSME-JSME Joint Conference on Thermal and Fluid Engineering Conference, pp. 21–23. ASME International.Google Scholar
Tripathi, M. K. & Sahu, K. C. 2018 Motion of an air bubble under the action of thermocapillary and buoyancy forces. Comput. Fluids 177, 58–68.Google Scholar
Tripathi, M. K., Sahu, K. C. & Govindarajan, R. 2015a Dynamics of an initially spherical bubble rising in quiescent liquid. Nat. Commun. 6, 6268.Google Scholar
Tripathi, M. K., Sahu, K. C., Karapetsas, G. & Matar, O. K. 2015b Bubble rise dynamics in a viscoplastic material. J. Non-Newtonian Fluid Mech. 222, 217–226.Google Scholar
Tripathi, M. K., Sahu, K. C., Karapetsas, G., Sefiane, K. & Matar, O. K. 2015c Non-isothermal bubble rise: non-monotonic dependence of surface tension on temperature. J. Fluid Mech. 763, 82–108.Google Scholar
Villers, D. & Platten, J. K. 1988 Temperature dependence of the interfacial tension between water and long-chain alcohols. J. Phys. Chem. A 92 (14), 4023–4024.Google Scholar
Vochten, R. & Petre, G. 1973 Study of heat of reversible adsorption at air–solution interface 2. Experimental determination of heat of reversible adsorption of some alcohols. J. Colloid Interface Sci. 42, 320–327.Google Scholar
Welch, S. W. J. 1998 Transient thermocapillary migration of deformable bubbles. J. Colloid Interface Sci. 208 (2), 500–508.Google Scholar
Weymouth, G. D. & Yue, D. K.-P. 2010 Conservative volume-of-fluid method for free-surface simulations on cartesian-grids. J. Comput. Phys. 229, 2853–2865.Google Scholar
Wu, Z.-B. & Hu, W.-R. 2012 Thermocapillary migration of a planar droplet at moderate and large Marangoni numbers. Acta Mechanica 223 (3), 609–626.Google Scholar
Wu, Z.-B. & Hu, W.-R. 2013 Effects of Marangoni numbers on thermocapillary drop migration: constant for quasi-steady state? J. Math. Phys. 54 (2), 023102.Google Scholar
Yang, B. & Prosperetti, A. 2007 Linear stability of the flow past a spheroidal bubble. J. Fluid Mech. 582, 53–78.Google Scholar
Young, N. O., Goldstein, J. S. & Block, M. J. 1959 The motion of bubbles in a vertical temperature gradient. J. Fluid Mech. 6, 350–356.Google Scholar
Zenit, R. & Magnaudet, J. 2008 Path instability of rising spheroidal air bubbles: a shape-controlled process. Phys. Fluids 20, 061702.Google Scholar
Zhang, L., Subramanian, R. S. & Balasubramaniam, R. 2001 Motion of a drop in a vertical temperature gradient at small Marangoni number – the critical role of inertia. J. Fluid Mech. 448, 197–211.Google Scholar
Zhao, J.-F., Li, Z.-D., Li, H.-X. & Li, J. 2010 Thermocapillary migration of deformable bubbles at moderate to large Marangoni number in microgravity. Microgravity Sci. Technol. 22 (3), 295–303.Google Scholar