Abstract
Effects of Marangoni number, aspect ratio and gravity level on thermocapillary convection in a liquid layer is investigated numerically, in which the level set method is employed to capture free surface deformation. The computational results show that, with the increase of Marangoni number the free surface deformation is increased and it can lead to free surface rupture if the Marangoni number is large enough. The end walls has a damping effect on the free surface deformation, and as the aspect ratio (A =L/(0.5H)) decreases the deformability of free surface is reduced. The gravity can damp the free surface deformation, particularly as gravity level varies from 0.0001g 0 to g 0 the free surface deformability decreases steeply.
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Babu, V., Korpela, S.A.: Three-dimensional thermocapillary convection in a cavity. Comput. Fluids. 18, 229–238 (1990)
Brackbill, J.U., Kothe, D.B., Zemach, C.: A continuum method for modeling surface tension. J. Comput. Phys. 100(2), 335–354 (1992)
Carpenter, M., Homsy, G.M.: High Marangoni number convection in a square cavity. Part II. Phys. Fluids A 2, 137–149 (1990)
Gupta, N.R., Hossein, H.H., Borhan, A.: Thermocapillary flow in double-layer fluid structures: an effective single-layer model. J. Colloid Interface Sci. 293, 158–171 (2006)
Hamed, M., Floryan, J.M.: Marangoni convection. Part 1. A cavity with differentially heated sidewalls. J. Fluid Mech 405, 79–110 (2000)
Koster, J.N.: Early mission report on the four ESA facilities: biorack; bubble, drop and particle unit; critical point facility and advanced protein crystallization facility flown on the IML-2 spacelab mission. Microgr. News ESA 7, 2–7 (1994)
Lappa, M.: On the nature and structure of possible three-dimensional steady flows in closed and open parallelepipedic and cubical containers under different heating conditions and driving forces. Fluid Dyn. Mater. Proc. 1, 1–19 (2005)
Mundrane, M., Xu, J., Zebib, A.: Thermocapillary convection in a rectangular cavity with a deformable interface. Adv. Space Res. 16, 41–53 (1995)
Ni, M.J., Komori, S., Abdou, M.: A variable-density projection method for interfacial flows. Numer. Heat Tran. B 44, 553–574 (2003)
Peltier, L. J., Biringen, S.: Time-dependent thermocapillary convection in a rectangular cavity: numerical results for a moderate Prandtl number fluid. J. Fluid Mech. 257, 339–357 (1993)
SaB, V., Kuhlmann, H.C., Rath, H.J.: Investigation of three-dimensional thermocapillary convection in a cubic container by a multi-grid method. Int. J. Heat Mass Transfer. 39, 603– 613 (1996)
Saghir, M.Z., Abbaschian, R., Raman, R.: Numerical analysis of thermocapillary convection in axisymmetric liquid encapsulated InBi. J. Crys. Grow 169, 110–117 (1996)
Smith, M. K., Davis, S. H.: Instabilities of dynamic thermocapillary liquid layers. Part 1: Convective instabilities. J. Fluid Mech. 132, 119–144 (1983)
Strani, M., Piva, R., Graziani, G.: Thermocapillary convection in a rectangular cavity: asymptotic and numerical simulation. J. Fluid Mech. 130, 347–376 (1983)
Sussman, M., Smereka, P., Osher, S.: A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114, 146–159 (1994)
Tang, Z.M., Li, K., Hu, W.R.: Influence of free surface curvature of a liquid layer on the critical Marangoni convection. Int. J. Heat Mass Transfer. 51(21–22), 5102–5107 (2008)
Xu, J., Zebib, A.: Oscillatory two- and three-dimensional thermocapillary convection. J. Fluid Mech. 364, 187–209 (1998)
Xun, B., Li, K., Hu, W.R.: Instability of thermocapillary flow in liquid layers under microgravity. Sci. China Phys. Mech. Astron. 55(4), 684–692 (2012)
Zhou, X.M., Huang, H.L.: Numerical simulation of steady thermocapillary convection in a two-layer system using level set method. Microgravity Sci. Technol. 22, 223–232 (2010)
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This work was supported by National Natural Science Foundation of China (Grant No.501206165).
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Zhou, X., Huai, X. Numerical Investigation of Thermocapillary Convection in a Liquid Layer with Free Surface. Microgravity Sci. Technol. 25, 335–341 (2014). https://doi.org/10.1007/s12217-014-9361-5
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DOI: https://doi.org/10.1007/s12217-014-9361-5