Abstract
It has been established that, in the case where a standing surface wave acts on a thermocapillary-convection flow in a cylindrical volume, there arises an oscillating-convection zone between the laminar and turbulent regimes of flow. It is shown that the boundary between these regimes is determined by the amplitude δ and the number of periods n of the standing wave and is practically independent of the Marangoni number and the oscillation frequency of this wave. At n = 2, in the range 0.004 < δ < 0.006, the parameters of the fluid cease to oscillate. The mechanisms by which the thermocapillary convection in closed volumes loses its stability are discussed.
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References
J. R. A. Pearson, On convection cells induced by surface tension, J. Fluid Mech., 4, Pt. 5, 489–500 (1958).
C. V. Sterling and L. E. Scriven, Interfacial turbulence: hydrodynamic instability and the Marangoni effect, AIChE J., 5, No. 4, 514–523 (1959).
L. E. Scriven and C. V. Sterling, On cellular convection driven by surface-tension gradients: effects of mean surface tension and surface viscosity, J. Fluid Mech., 19, pt. 3, 321–340 (1964).
D. A. Nield, Surface tension and buoyancy effects in cellular convection, J. Fluid Mech., 19, Pt. 3, 341–352 (1964).
M. K. Smith and S. H. Davis, Instabilities of dynamic thermocapillary liquid layers, Fluid Mech., 132, Pt. 1, Convective instabilities, 119–144; Pt. 2, Surface-wave instabilities, 145–162 (1983).
J.-J. Xu and S. H. Davis, Instability of capillary jets with thermocapillarity, J. Fluid Mech., 161, Pt. 1, 1–25 (1985).
J. Serrin, On the stability of viscous fluid methods, Arch. Rat. Mech. Analysis, 3, No. 1, 1–13 (1959).
S. H. Davis and C. A. Kerczek, Reformation of energy stability theory, Arch. Rat. Mech. Anal., 52, No. 1, 112–117 (1973).
S. H. Davis and G. M. Homsy, Energy stability theory for free-surface problems: buoyancy-thermocapillary layers, J. Fluid Mech., 98, Pt. 3, 527–553 (1980).
Y. Shen, G. P. Neitzel, D. F. Jankowski, and H. D. Mittelmann, Energy stability of thermocapillary convection in a model of the float-zone crystal-growth process, J. Fluid Mech., 217, 639–660 (1990).
F. Preisser, D. Schwabe, and A. Scharmann, Steady and oscillatory thermocapillary convection in liquid columns with free cylindrical surface, J. Fluid Mech., 126, 545–567 (1983).
D. Rivas, High-Reynolds-number thermocapillary flows in shallow enclosures, Phys. Fluids A: Fluid Dyn., 3, No. 2, 280–291 (1991).
Z. H. Cao, X. T. You, Z. M. Tang, and W. R. Hu, Experimental investigation of thermocapillary convection in half floating zone, Adv. Space Res., 11, No. 7, 229–232 (1991).
A. I. Feonychev and I. S. Kalachinskaya, Influence of variable accelerations on the growth of crystals by the method of a floating zone aboard space vehicles, Kosm. Issled., 39, No. 4, 400–406 (2001).
A. I. Feonychev, Inertial-capillary surface waves and their influence on crystal growth in zero gravity, Inzh.-Fiz. Zh., 77, No. 2, 83–92 (2004).
V. I. Pokhilko, On Solution of Navier-Stokes Equations for a Cubic Cavity, Preprint No. 11 of the Institute of Mathematical Modeling, Russian Academy of Sciences, Moscow (1994).
A. I. Feonychev, Use of the eigenfrequency of a convective cell for determining the frequency characteristics of the oscillation thermal gravitational and thermocapillary convections in closed volumes, Inzh.-Fiz. Zh., 77, No. 5, 105–112 (2004).
A. I. Feonychev and N. V. Bondareva, Action of a rotating magnetic field on the stability of a convection and the crystal growth in zero gravity and on the ground, Inzh.-Fiz. Zh., 77, No. 4, 50–61 (2004).
A. I. Feonychev, I. S. Kalachinskaya, and V. I. Pokhilko, Deformation of fluid column by action of axial vibration and some aspects of high-rate thermocapillary convection, in: Proc. Third Microgravity Fluid Physics Conf., 13–15 June 1996, Cleveland, Ohio, USA; NASA Conference Publication 3338 1996, pp. 493–498.
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Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 80, No. 5, pp. 108–115, September–October, 2007.
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Feonychev, A.I. Stability of thermocapillary convection and regimes of a fluid flow acted upon by a standing surface wave. J Eng Phys Thermophy 80, 961–969 (2007). https://doi.org/10.1007/s10891-007-0128-3
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DOI: https://doi.org/10.1007/s10891-007-0128-3