Oscillatory thermocapillary convection in liquid bridges with highly deformed free surfaces: Experiments and energy-stability analysis

Physics of Fluids

Volumn 13, Issue 1, 2001, Pages 107-120

  Sumner, L B S ^a,d   Neitzel, G P ^a   Fontaine, J P ^b   Dell'Aversana, P ^c  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b IMRA Europe SAS   (France)

^c MARS srl   (Italy)

^d MERCER UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CAPILLARY FLOW; COMPUTER SIMULATION; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL TECHNIQUES; PRANDTL NUMBER; SURFACE TENSION; THERMAL GRADIENTS; VOLUME FRACTION;

LIQUID BRIDGES; THERMOCAPILLARY CONVECTION;

NATURAL CONVECTION;

CONVECTION; DEFORMATION; FLUID INTERFACE; OSCILLATING FLOW;

EID: 0034745736     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1329650     Document Type: Article

References (29)

1. S. H. Davis, "Thermocapillary instabilities," Annu. Rev. Fluid Mech. 19, 403 (1987).
2. M. F. Schatz and G. P. Neitzel, "Experiments on thermocapillary instabilities," Annu. Rev. Fluid Mech. 33, 93 (2001).
3. R. Monti, D. Castagnolo, P. Dell'Aversana, G. Desiderio, S. Moreno, and G. Evangelista, "An experimental and numerical analysis of thermocapillary flow of silicone oils in a micro-floating zone," Proceedings of the 43rd Cong. Int. Astro. Fed., Washington, DC, 1992 (unpublished).
4. W. R. Hu, J. Z. Shu, R. Zhou, and Z. M. Tang, "Influence of liquid bridge volume on the onset of oscillation in floating zone convection. I. Experiments," J. Cryst. Growth 142, 379 (1994).
5. J.-J. Xu and S. H. Davis, "Convective thermocapillary instabilities in liquid bridges," Phys. Fluids 27, 1102 (1984).
6. F. Preisser, D. Schwabe, and A. Scharmann, "Steady and oscillatory thermocapillary convection in liquid columns with free cylindrical surface," J. Fluid Mech. 126, 545 (1983).
7. 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 (1990).
8. G. P. Neitzel, C. C. Law, D. F. Jankowski, and H. D. Mittelmann, "Energy stability of thermocapillary convection in a model of the float-zone crystal-growth process. II. Nonaxisymmetric disturbances," Phys. Fluids A 3, 2841 (1991).
9. R. Velten, D. Schwabe, and A. Scharmann, "The periodic instability of thermocapillary convection in cylindrical liquid bridges," Phys. Fluids A 3, 267 (1991).
10. G. P. Neitzel, K.-T. Chang, D. F. Jankowski, and H. D. Mittelmann, "Linear-stability theory of thermocapillary convection in a model of the float-zone crystal-growth process," Phys. Fluids A 5, 108 (1993).
11. M. Levenstam and G. Amberg, "Hydrodynamical instabilities of thermocapillary flow in a half-zone," J. Fluid Mech. 297, 357 (1995).
12. M. Wanschura, V. M. Shevtsova, H. C. Kuhlmann, and H. J. Rath, "Convective instability mechanisms in thermocapillary liquid bridges," Phys. Fluids 7, 912 (1995).
13. J.-C. Chen and C.-F. Chu, "Numerical computation of fluid flow of floating-zone crystal growth of molybdenum," Int. J. Heat Mass Transf. 38, 1841 (1995).
14. J.-C. Chen and G.-H. Chin, "Linear stability analysis of thermocapillary convection in the floating zone," J. Cryst. Growth 154, 98 (1995).
15. V. M. Shevtsova and J.-C. Legros, "Oscillatory convective motion in deformed liquid bridges," Phys. Fluids 10, 1621 (1998).
16. V. M. Shevtsova, D. E. Melnikov, and J.-C. Legros, "Peculiarities of three-dimensional flow in liquid bridges at high Prandtl numbers," Comp. Fluid Dyn. (in press).
17. S. H. Davis and G. M. Homsy, "Energy-stability theory for free-surface problems: Buoyancy-thermocapillary layers," J. Fluid Mech. 98, 527 (1980).
18. L. B. S. Sumner, "Energy stability of thermocapillary convection in liquid bridges with a deformed free surface," Ph.D. thesis, Georgia Institute of Technology, 1998.
19. B.-I. Fu and S. Ostrach, "Numerical solution of thermocapillary flows in the floating zone," ASME PED 10, HTD 29 (1985).
20. FIDAP Version 7.0 Theory Manual (Fluid Dynamics International, Evanston, 1993).
21. J. R. Hyer, D. F. Jankowski, and G. P. Neitzel, "Thermocapillary convection in a model float zone," J. Thermophys. Heat Transfer 5, 577 (1991).
22. C. W. Lan and S. Kou, "Formulation for correcting optical distortions due to a transparent floating zone," J. Cryst. Growth 132, 471 (1993).
23. D. D. Joseph, Stability of Fluid Motions I, II (Springer, Berlin, 1976).
24. S. H. Davis and C. von Kerczek, "A reformulation of energy stability theory," Arch. Ration. Mech. Anal. 52, 112 (1973).
25. C. C. Paige and M. A. Saunders, "Solution of sparse indefinite systems of linear equations," SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 12, 617 (1975).
26. G. S. Charlson and R. L. Sani, "Thermoconvective instability in a bounded cylindrical fluid layer," Int. J. Heat Mass Transf. 13, 1479 (1970).
27. G. R. Hardin, R. L. Sani, D. Henry, and B. Roux, "Buoyancy-driven instability in a vertical cylinder: Binary fluids with Soret effect. I. General theory and stationary stability results," Int. J. Numer. Methods Fluids 10, 79 (1990).
28. M. Wanshura (private communication).
29. G. P. Neitzel, M. K. Smith, and M. J. Bolander, "Thermal instability with radiation by the method of energy," Int. J. Heat Mass Transf. 37, 2909 (1994).