Abstract
Floating zone technique is a crucible-free process for growth of high quality single crystals. Unstable thermocapillary convection is a typical phenomenon during the process under microgravity. Therefore, it is very important to investigate the instability of thermocapillary convection in liquid bridges with deformable free-surface under microgravity. In this works, the Volume of Fluid (VOF) method is employed to track the free-surface movement. The results are presented as the behavior of flow structure and temperature distribution of the molten zone. The impact of Marangoni number (Ma) is also investigated on free-surface deformation as well as the instability of thermocapillary convection. The free-surface exhibits a noticeable axisymmetric (but it is non-centrosymmetric) and elliptical shape along the circumferential direction. This specific surface shape presents a typical narrow ‘neck-shaped’ structure with convex at two ends of the zone and concave at the mid-plane along the axial direction. At both θ = 0° and θ = 90°, the deformation ratio ξ increases rapidly with Ma at first, and then increases slowly. Moreover, the hydrothermal wave number m and the instability of thermocapillary convection increase with Ma.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Zeng, Z., Mizuseki, H., Shimamura, K., Higashino, K., Fukuda, T., and Kawazoe, Y., (2001), Marangoni convection in model of floating zone under microgravity, Journal of crystal growth, Vol. 229, No.1, pp. 601–604.
Melnikov, D. E., Shevtsova, V. M., and Legros, J. C., (2005), Route to aperiodicity followed by high Prandtlnumber liquid bridge. 1-g case, Acta astronautica, Vol. 56, No. 6, pp. 601–611.
Zeng, Z., Mizuseki, H., Shimamura, K., Fukuda, T., Kawazoe, Y., and Higashino, K., (2002), Usefulness of experiments with model fluid for thermocapillary convection—effect of Prandtl number on two-dimensional thermocapillary convection, Journal of crystal growth, Vol. 234, No. 1, pp. 272–278.
Minakuchi, H., Takagi, Y., Okano, Y., Gima, S., and Dost, S., (2014), The relative contributions of thermo-solutal Marangoni convections on flow patterns in a liquid bridge, Journal of Crystal Growth, Vol. 385, pp. 61–65.
Lappa, M., Savino, R., and Monti, R., (2001), Threedimensional numerical simulation of Marangoni instabilities in liquid bridges: influence of geometrical aspect ratio, International journal for numerical methods in fluids, Vol. 36, No. 1, pp. 53–90.
Lappa, M., (2005), Analysis of flow instabilities in convex and concave floating zones heated by an equatorial ring under microgravity conditions, Computers & fluids, Vol. 34, No. 6, pp. 743–770.
Lyubimova, T. P., and Skuridyn, R. V., (2014), The influence of vibrations on the stability of thermocapillary flow in liquid zone, International Journal of Heat and Mass Transfer, Vol. 69, pp. 191–202.
Gaponenko, Y., Glockner, S., Mialdun, A., and Shevtsova, V., (2011), Study of a liquid bridge subjected to interface shear stresses, Acta astronautica, Vol. 69, No. 3, pp. 119–126.
Gaponenko, Y., Mialdun, A., and Shevtsova, V., (2012), Shear driven two-phase flows in vertical cylindrical duct, International journal of multiphase flow, Vol. 39, pp. 205–215.
Tiwari, S., and Nishino, K., (2007), Numerical study to investigate the effect of partition block and ambient air temperature on interfacial heat transfer in liquid bridges of high Prandtl number fluid, Journal of crystal growth, Vol. 300, No. 2, pp. 486–496.
Xun, B., Li, K., Hu, W. R., and Imaishi, N., (2011), Effect of interfacial heat exchange on thermocapillary flow in a cylindrical liquid bridge in microgravity, International Journal of Heat and Mass Transfer, Vol. 54, No. 9, pp. 1698–1705.
Melnikov, D. E., and Shevtsova, V. M., (2014), The effect of ambient temperature on the stability of thermocapillary flow in liquid column, International Journal of Heat and Mass Transfer, Vol. 74, pp. 185–195.
Kamotani, Y., Ostrach, S., and Vargas, M., (1984), Oscillatory thermocapillary convection in a simulated floating-zone configuration, Journal of Crystal Growth, Vol. 66, No. 1, pp. 83–90.
Kuhlmann, H. C., & Nienhüser, C. (2002). Dynamic freesurface deformations in thermocapillary liquid bridges. Fluid dynamics research, 31(2), 103–127.
Sim, B. C., Kim, W. S., and Zebib, A., (2004), Dynamic free-surface deformations in axisymmetric liquid bridges, Advances in Space Research, Vol. 34, No. 7, pp. 1627–1634.
Shevtsova, V., Mialdun, A., Ferrera, C., Ermakov, M., Cabezas, M. G., and Montanero, J. M., (2008), Subcritical and oscillatory dynamic surface deformations in noncylindrical liquid bridges, FDMP: Fluid Dynamics & Materials Processing, Vol. 4, No. 1, pp. 43–54.
Liang, R., and Kawaji, M., (2009), Surface oscillation of a liquid bridge induced by single and multiple vibrations, Microgravity Science and Technology, Vol. 21, No. 1, pp. 31–37.
Ahmed, I., Masud, J., Nigar, M., and Khan, A. M., (2010), Effect of First Vibration Mode on Sub-Critical Thermocapillary Convection in Floating Zone Liquid Bridge, AIAA-2010-637, 48th AIAA Aerospace Sciences Meeting, Anaheim, USA, pp. 4–7.
Zhou, X. M., and Huang, H. L., (2010), Numerical simulation of steady thermocapillary convection in a two-layer system using level set method, Microgravity Science and Technology, Vol. 22, No.2, pp. 223–232.
Zhou, X. M., and Huai, X. L., (2015), Free Surface Deformation of Thermo-Solutocapillary Convection in Axisymmetric Liquid Bridge, Microgravity Science and Technology, Vol. 27, No. 1, pp. 39–47.
Dold, P., Cröll, A., Lichtensteiger, M., Kaiser, T., and Benz, K. W., (2001), Floating zone growth of silicon in magnetic fields: IV. Rotating magnetic fields, Journal of crystal growth, Vol. 231, No.1, pp. 95–106.
Author information
Authors and Affiliations
Additional information
This work is supported by National Natural Science Foundation of China (Grant Number 51276089)
Rights and permissions
About this article
Cite this article
Zhang, Y., Huang, HL., Zhou, XM. et al. Effect of Marangoni number on thermocapillary convection and free-surface deformation in liquid bridges. J. Therm. Sci. 25, 178–187 (2016). https://doi.org/10.1007/s11630-016-0849-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11630-016-0849-8