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Transient Marangoni convection induced by an isothermal sidewall of a rectangular liquid pool

Published online by Cambridge University Press:  04 October 2021

Enhui Chen  and
Feng Xu
Enhui Chen
Affiliation:
School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, PR China
Feng Xu*
Affiliation:
Beijing's Key Laboratory of Structural Wind Engineering and Urban Wind Environment, Beijing 100044, PR China
*
†Email address for correspondence: [email protected]
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Abstract

Transient Marangoni convection induced by an isothermal sidewall of a rectangular pool under a zero-gravity condition is studied using scaling analysis. Scaling analysis shows that there exist a number of flow regimes in each evolution scenario, depending on the Marangoni number, the Prandtl number and the aspect ratio. In a typical evolution scenario, a horizontal surface flow and a vertical flow adjacent to the sidewall may appear. Additionally, a number of scaling laws of the velocity and thickness of transient Marangoni convection are obtained. Further, numerical simulation is performed for validation of the selected scaling laws. There exits good agreement between the numerical results and the scaling predictions.

JFM classification

Convection: Marangoni convection Drops and Bubbles: Thermocapillarity
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 928 , 10 December 2021 , A6
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Batchlor, G.K. 2000 An Introduction to Fluid Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Birikh, R.V. 1966 Thermocapillary convection in a horizontal layer of liquid. J. Appl. Mech. Tech. Phys. 7, 43–44.CrossRefGoogle Scholar
Chan, C.L. & Chen, C.F. 2010 Effect of gravity on the stability of thermocapillary convection in a horizontal fluid layer. J. Fluid Mech. 647, 91–103.CrossRefGoogle Scholar
Chen, E. & Xu, F. 2021 Transient thermocapillary convection flows in a rectangular cavity with an evenly heated lateral wall. Phys. Fluids 33, 013602.CrossRefGoogle Scholar
Cowley, S.J. & Davis, S.H. 1983 Viscous thermocapillary convection at high Marangoni number. J. Fluid Mech. 135, 175–188.CrossRefGoogle Scholar
Doi, T. & Koster, J.N. 1993 Thermocapillary convection in two immiscible liquid layers with free surface. Phys. Fluids A 5, 1914–1927.CrossRefGoogle Scholar
de Gennes, P.G., Brochard Wyart, F. & Quéré, D. 2013 Capillarity and Wetting Phenomena: Drops, Bubbles, Pearls, Waves. Springer.Google Scholar
Gillon, P. & Homsy, M. 1996 Combined thermocapillary-buoyancy convection in a cavity: An experimental study. Phys. Fluids 8 (11), 2953–2963.CrossRefGoogle Scholar
Hamed, M. & Floryan, J.M. 2000 Marangoni convection. Part 2. A cavity subject to point heating. J. Fluid Mech. 405, 111–129.CrossRefGoogle Scholar
Hu, K.-X., He, M., Chen, Q.-S. & Liu, R. 2017 Linear stability of thermocapillary liquid layers of a shear-thinning fluid. Phys. Fluids 29, 073101.CrossRefGoogle Scholar
Hu, K.-X., Yan, C.-Y. & Chen, Q.-S. 2019 Instability of thermocapillary–buoyancy convection in droplet migration. Phys. Fluids 31, 122101.CrossRefGoogle Scholar
Jiang, H., Duan, L. & Kang, Q. 2017 A peculiar bifurcation transition route of thermocapillary convection in rectangular liquid layers. Exp. Therm. Fluid Sci. 88, 8–15.CrossRefGoogle Scholar
Jiang, Y., Nie, B. & Xu, F. 2019 Scaling laws of buoyant flows on a suddenly heated horizontal plate. Intl Commun. Heat Mass Transfer 105, 58–64.CrossRefGoogle Scholar
Jiang, Y., Nie, B., Zhao, Y., Carmeliet, J. & Xu, F. 2021 Scaling of buoyancy-driven flows on a horizontal plate subject to a ramp heating of a finite time. Intl J. Heat Mass Transfer 171, 121061.CrossRefGoogle Scholar
Kamotani, Y., Ostrach, S. & Pline, A. 1994 Analysis of velocity data taken in surface tension driven convection experiment in microgravity. Phys. Fluids 6, 3601–3609.CrossRefGoogle Scholar
Kang, Q., Duan, L., Zhang, L., Yin, Y., Yang, J. & Hu, W. 2016 Thermocapillary convection experiment facility of an open cylindrical annuli for sj-10 satellite. Microgravity Sci. Technol. 28, 123–132.CrossRefGoogle Scholar
Kang, Q., Wang, J., Duan, L., Su, Y., He, J., Wu, D. & Hu, W. 2019 The volume ratio effect on flow patterns and transition processes of thermocapillary convection. J. Fluid Mech. 868, 560–583.CrossRefGoogle Scholar
Kang, Q., Wu, D., Duan, L., Zhang, J., Zhou, B., Wang, J., Han, Z., Hu, L. & Hu, W. 2020 Space experimental study on wave modes under instability of thermocapillary convection in liquid bridges on tiangong-2. Phys. Fluids 32, 034107.Google Scholar
Kirdyashkin, A.G. 1984 Thermogravitational and thermocapillary flows in a horizontal liquid layer under the conditions of a horizontal temperature gradient. Intl J. Heat Mass Transfer 27, 1205–1218.CrossRefGoogle Scholar
Kowal, K.N., Davis, S.H. & Voorhees, P.W. 2018 Thermocapillary instabilities in a horizontal liquid layer under partial basal slip. J. Fluid Mech. 855, 839–859.CrossRefGoogle Scholar
Legros, J.C., Limbourg-Fontaine, M.C. & Petre, G. 1984 Influence of a surface tension minimum as a function of temperature on the Marangoni convection. Acta Astronaut. 11, 143–147.CrossRefGoogle Scholar
Liu, Q.S., Roux, B. & Velarde, M.G. 1998 Thermocapillary convection in two-layer systems. Intl J. Heat Mass Transfer 41, 1499–1511.CrossRefGoogle Scholar
Masoudi, S. & Kuhlmann, H.C. 2017 Axisymmetric buoyant–thermocapillary flow in sessile and hanging droplets. J. Fluid Mech. 826, 1066–1095.CrossRefGoogle Scholar
Ostrach, S. 1982 Low-gravity fluid flows. Annu. Rev. Fluid Mech. 14, 313–345.CrossRefGoogle Scholar
Patne, R., Agnon, Y. & Oron, A. 2020 Thermocapillary instabilities in a liquid layer subjected to an oblique temperature gradient: effect of a prescribed normal temperature gradient at the substrate. Phys. Fluids 32, 112109.CrossRefGoogle Scholar
Patne, R., Agnon, Y. & Oron, A. 2021 Thermocapillary instabilities in a liquid layer subjected to an oblique temperature gradient. J. Fluid Mech. 906, A12.CrossRefGoogle Scholar
Patterson, J. & Imberger, J. 1980 Unsteady natural convection in a rectangular cavity. J. Fluid Mech. 100, 65–86.CrossRefGoogle Scholar
Pearson, J.R.A. 1958 On convection cells induced by surface tension. J. Fluid Mech. 4, 489–500.CrossRefGoogle Scholar
Peltier, L.J. & Biringen, S. 1993 Time-dependent thermocapillary convection in a rectangular cavity: numerical results for a moderate prandtl number fluid. J. Fluid Mech. 257, 339–357.CrossRefGoogle Scholar
Pimputkar, S.M. & Ostrach, S. 1980 Transient thermocapillary flow in thin liquid layers. Phys. Fluids 23, 1281–1285.CrossRefGoogle Scholar
Popinet, S. 2018 Numerical models of surface tension. Annu. Rev. Fluid Mech. 50, 49–75.CrossRefGoogle Scholar
Salgado Sánchez, P., Ezquerro, J.M., Fernández, J. & Rodríguez, J. 2020 Thermocapillary effects during the melting of phase change materials in microgravity: heat transport enhancement. Intl J. Heat Mass Transfer 163, 120478.CrossRefGoogle Scholar
Salgado Sánchez, P., Ezquerro, J.M., Fernández, J. & Rodríguez, J. 2021 Thermocapillary effects during the melting of phase-change materials in microgravity: steady and oscillatory flow regimes. J. Fluid Mech. 908, A20.CrossRefGoogle Scholar
Schwabe, D. & Metzger, J. 1989 Coupling and separation of buoyant and thermocapillary convection. J. Cryst. Growth 97, 23–33.CrossRefGoogle Scholar
Schwabe, D. & Scharmann, A. 1981 The magnitude of thermocapillary convection in larger melt volumes. Adv. Space Res. 1, 13–16.CrossRefGoogle Scholar
Sen, A.K. 1986 Thermocapillary convection in a rectangular cavity with a deformable interface. Phys. Fluids 29, 3881–3883.CrossRefGoogle Scholar
Sen, A.K. & Davis, S.H. 1982 Steady thermocapillary flows in two-dimensional slots. J. Fluid Mech. 121, 163–186.CrossRefGoogle Scholar
Shieh, C.Y. & Yang, W.-J. 1987 Transient thermocapillary flow in rectangular tanks with phase change. Intl J. Heat Mass Transfer 30, 843–854.CrossRefGoogle Scholar
Shmyrov, A.V., Mizev, A.I., Demin, V.A., Petukhov, M.I. & Bratsun, D.A. 2019 Phase transitions on partially contaminated surface under the influence of thermocapillary flow. J. Fluid Mech. 877, 495–533.CrossRefGoogle Scholar
Smith, M.K. & Davis, S.H. 1983 Instabilities of dynamic thermocapillary liquid layers. Part 1. Convective instabilities. J. Fluid Mech. 132, 119–144.CrossRefGoogle Scholar
Strani, M., Piva, R. & Graziani, G. 1983 Thermocapillary convection in a rectangular cavity: asymptotic theory and numerical simulation. J. Fluid Mech. 130, 347–376.CrossRefGoogle Scholar
Tryggvason, G., Scardovelli, R. & Zaleski, S. 2011 Direct Numerical Simulations of Gas–Liquid Multiphase Flows. Cambridge University Press.Google Scholar
Villers, D. & Platten, J.K. 1985 Marangoni convection in systems presenting a minimum in surface tension. Phys. Chem. Hydrodyn. 6, 435–451.Google Scholar
Villers, D. & Platten, J.K. 1987 Separation of Marangoni convection from gravitational convection in earth experiments. Phys. Chem. Hydrodyn. 8, 173–183.Google Scholar
Villers, D. & Platten, J.K. 1990 Influence of interfacial tension gradients on thermal convection in two superposed immiscible liquid layers. Appl. Sci. Res. 47, 177–191.CrossRefGoogle Scholar
Villers, D. & Platten, J.K. 1992 Coupled buoyancy and Marangoni convection in acetone: experiments and comparison with numerical simulations. J. Fluid Mech. 234, 487–510.CrossRefGoogle Scholar
Wang, X., Xu, F. & Zhai, H. 2018 An experimental study of a starting plume on a mountain. Intl Commun. Heat Mass Transfer 97, 1–8.CrossRefGoogle Scholar
Wei, P.S., Liu, H.J. & Lin, C.L. 2012 Scaling weld or melt pool shape induced by thermocapillary convection. Intl J. Heat Mass Transfer 55, 2328–2337.CrossRefGoogle Scholar
Xu, F., Patterson, J.C. & Lei, C. 2009 Transient natural convection flows around a thin fin on the sidewall of a differentially heated cavity. J. Fluid Mech. 639, 261–290.CrossRefGoogle Scholar
Yoo, J., Nam, J. & Ahn, K.H. 2019 Thermocapillary flows on heated substrates with sinusoidal topography. J. Fluid Mech. 859, 992–1021.CrossRefGoogle Scholar
Zeng, Z., Mizuseki, H., Simamura, K., Fukuda, T., Higashino, K. & Kawazoe, Y. 2001 Three-dimensional oscillatory thermocapillary convection in liquid bridge under microgravity. Intl J. Heat Mass Transfer 44, 3765–3774.CrossRefGoogle Scholar
Zhang, S., Duan, L. & Kang, Q. 2016 Experimental research on thermocapillary migration of drops by using digital holographic interferometry. Exp. Fluids 57, 113.CrossRefGoogle Scholar