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Thermocapillary flow with evaporation and condensation at low gravity. Part 1. Non-deforming surface

Published online by Cambridge University Press:  26 April 2006

G. R. Schmidt
Affiliation:
Propulsion Laboratory, NASA Marshall Space Flight Center, Huntsville, AL 35812, USA
T. J. Chung
Affiliation:
Department of Mechanical Engineering, University of Alabama in Huntsville, Huntsville, AL 35899, USA
A. Nadarajah
Affiliation:
Department of Chemical Engineering, University of Alabama in Huntsville, Huntsville, AL 35899, USA

Abstract

The problem of steady motion and thermal behaviour of a volatile, wetting liquid in an open cavity under low gravity is defined and examined. The domain geometrically approximates a two-phase pore of liquid on a wicking structure surface, and consists of a 1 to 102 μu wide rectangular cavity bounded by a saturated vapour and liquid reservoir on its upper and lower surfaces, respectively. Thermal non-equilibrium and convection are established by symmetrically superheating or subcooling the pore boundaries by ∼ 1 K relative to the vapour. Numerical analyses show that although thermocapillary flow competes with interfacial phase change in dictating the circulation and flow structure, it tends to reinforce the convective effects of evaporation and condensation on surface temperature and heat transport. In addition, highly wetting fluids with curved menisci are characterized by greater circulation intensities and dynamic pressure gradients than a flat surface. The magnitude of these gradients suggests that the fixed menisci shapes assumed in this study are unrealistic, and that the influence of convection on surface morphology should be considered.

Type
Research Article
Copyright
© 1995 Cambridge University Press

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References

Bergman, T. L. & Keller, J. R. 1988 Combined buoyancy, surface tension flow in liquid metals. Numer. Heat Transfer 13, 4963.Google Scholar
Bergman, T. L. & Ramadhyani, S. 1986 Combined buoyancy- and thermocapillary-driven convection in open square cavities. Numer. Heat Transfer 9, 441451.Google Scholar
Burelbach, J. P., Bankoff, S. G. & Davis, S. H. 1988 Nonlinear stability of evaporating/condensing liquid films. J. Fluid Mech. 195, 463494.Google Scholar
Carpenter, B. & Homsy, G. M. 1989 Combined buoyant-thermocapillary flow in a cavity. J. Fluid Mech. 207, 121132.Google Scholar
Chen, H., Oshima, K. & Hinada, M. 1989 Numerical analysis of thermocapillary and evaporating flows at low Bond Number. In Proc. Symp. on Mechanics of Space Flight, Sagamihara, Japan, Nov. 24-25 1988, pp. 3953. Japan Inst. Space Astro. Sci.
Cuvelier, C. & Driessen, J. M. 1986 Thermocapillary free boundaries in crystal growth. J. Fluid Mech. 169, 126.Google Scholar
Duranceau, J. L. & Brown, R. A. 1989 Finite element analysis of melt convection and interface morphology in earthbound and microgravity floating zones. In Drops and Bubbles, 3rd Intl Colloq. Monterey. CA, 1988 (ed. T. G. Wang), pp. 133134. AIP.
Fu, B.-I. & Ostrach, S. 1983 Numerical solutions of thermocapillary flows in floating zones. In Transport Phenomena in Materials Processing, pp. 19. ASME.
Hadid, H. & Roux, B. 1992 Buoyancy- and thermocapillary-driven flows in differentially heated cavities for low Prandtl number fluids. J. Fluid Mech. 235, 136.Google Scholar
Hyer, J., Jankowski, D. & Neitzel, G. 1991 Thermocapillary convection in a model float zone. AIAA J. Thermo. Heat Transfer 5, 577582.Google Scholar
Jue, T. C., Ramaswamy, B. & Akin, J. E. 1991 Computation of thermocapillary and buoyancy affected cavity flow using semi-implicit FEM. Numer. Meth. Therm. Probs. 7 1, 402412.Google Scholar
Kamotani, Y. & Platt, J. 1992 Effect of free surface shape on combined thermocapillary and natural convection. AIAA J. Thermo. Heat Transfer 6, 721726.Google Scholar
Kobayashi, N. 1988 Steady convection caused by the temperature inhomogeneity in a cylindrical floating zone. Japan J. Appl. Phys. 27, 2024.Google Scholar
Lan, C. W. & Kou, S. 1991 Heat transfer, fluid flow and interface shapes in floating zone crystal growth. J. Cryst. Growth 108, 351366.Google Scholar
Mirzamoghadam, A. & Catton, I. 1988 A physical model of the evaporating meniscus. Trans. ASME C: J. Heat Transfer 110, 201207.Google Scholar
Ostrach, S. & Kamotani, Y. 1992 Recent developments in oscillatory thermocapillary flows. In Proc. AIAA/IKI Microgravity Science Symp., pp. 2532. AIAA.
Palmer, H. J. 1976 The hydrodynamic stability of rapidly evaporating liquids at reduced pressure. J. Fluid Mech. 75, 487511.Google Scholar
Patankar, S. V. 1980 Numerical Heat Transfer and Fluid Flow. Hemisphere.
Potash, M. & Wayner, P. 1972 Evaporation from a two-dimensional extended meniscus. Intl J. Heat Mass Transfer 15, 18511863.Google Scholar
Renk, F. J. & Wayner, P. C. 1979 An evaporating ethanol meniscus - Part II: Analytical studies. Trans. ASME C: J. Heat Transfer 101, 5962.Google Scholar
Schmidt, G. R. 1993 Thermocapillary flow with evaporation and condensation and its effect on liquid retention in low-g fluid acquisition devices. PhD dissertation, The University of Alabama in Huntsville.
Schmidt, G. R., Chung, T. J. & Nadarajah, A. 1995 Thermocapillary flow with evaporation and condensation at low gravity. Part 2. Deformable surface. J. Fluid Mech. 294, 349366.Google Scholar
Sen, A. K. 1986 Thermocapillary convection in a rectangular cavity with a deformable interface. Phys. Fluids 29, 38813883.Google Scholar
Sen, A. K. & Davis, S. H. 1982 Steady thermocapillary flows in two-dimensional slots. J. Fluid Mech. 121, 163186.Google Scholar
Shen, Y., Neitzel, P., Jankowski, D. & Mittelmann, H. 1990 Energy stability of thermocapillary convection in a model of the float-zone, crystal growth process. J. Fluid Mech. 217, 639660.Google Scholar
Strani, M., Piva, R. & Graziani, G. 1983 Thermocapillary convection in a rectangular cavity: asymptotic theory and numerical simulation. J. Fluid Mech. 130, 347376.Google Scholar
Swanson, L. W. & Herdt, G. C. 1992 Model of the evaporating meniscus in a capillary tube. Trans. ASME C: J. Heat Transfer 114, 434441.Google Scholar
Swanson, L. W. & Peterson, G. P. 1994 Evaporating extended meniscus in a V-shaped channel. AIAA J. Thermo. Heat Transfer 8, 172180.Google Scholar
Werhle, V. & Voulelikas, G. 1985 Evaporation from a two-dimensional meniscus. AIAA J. 23, 309313.Google Scholar
Zebib, A., Homsy, G. M. & Meiburg, E. 1985 High Marangoni number convection in a square cavity. Phys. Fluids 28, 34673476.Google Scholar