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Thermocapillary instability as a mechanism for film boiling collapse

Published online by Cambridge University Press:  03 August 2018

Eskil Aursand Open the ORCID record for Eskil Aursand [Opens in a new window] ,
Stephen H. Davis  and
Tor Ytrehus
Eskil Aursand*
Affiliation:
Department of Energy and Process Engineering, Norwegian University of Science and Technology (NTNU), Kolbjørn Hejes v. 1B, Trondheim N-7491, Norway Department of Engineering Sciences and Applied Mathematics, McCormick School of Engineering and Applied Science, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA
Stephen H. Davis
Affiliation:
Department of Engineering Sciences and Applied Mathematics, McCormick School of Engineering and Applied Science, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208, USA
Tor Ytrehus
Affiliation:
Department of Energy and Process Engineering, Norwegian University of Science and Technology (NTNU), Kolbjørn Hejes v. 1B, Trondheim N-7491, Norway
*
†Email address for correspondence: [email protected]
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Abstract

We construct a model to investigate the interfacial stability of film boiling, and discover that instability of very thin vapour films and subsequent large interface superheating is only possible if thermocapillary instabilities are present. The model concerns horizontal saturated film boiling, and includes novel features such as non-equilibrium evaporation based on kinetic theory, thermocapillary and vapour thrust stresses and van der Waals interactions. From linear stability analysis applied to this model, we are led to suggest that vapour film collapse depends on a balance between thermocapillary instabilities and vapour thrust stabilization. This yields a purely theoretical prediction of the Leidenfrost temperature. Given that the evaporation coefficient is in the range 0.7–1.0, this model is consistent with the average Leidenfrost temperature of every fluid for which data could be found. With an evaporation coefficient of 0.85, the model can predict the Leidenfrost point within 10 % error for every fluid, including cryogens and liquid metals where existing models and correlations fail.

JFM classification

Low-Reynolds-number flows: Lubrication theory Drops and Bubbles: Thermocapillarity Interfacial Flows (free surface): Thin films
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 852 , 10 October 2018 , pp. 283 - 312
Copyright
© 2018 Cambridge University Press 

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References

Agostini, B., Fabbri, M., Park, J. E., Wojtan, L., Thome, J. R. & Michel, B. 2007 State of the art of high heat flux cooling technologies. Heat Transfer Engng 28 (4), 258–281.Google Scholar
Auliano, M., Fernandino, M., Zhang, P. & Dorao, C. A. 2017 The Leidenfrost phenomenon on sub-micron tapered pillars. In ASME 2017 15th International Conference on Nanochannels, Microchannels, and Minichannels, pp. V001T08A003–V001T08A003. American Society of Mechanical Engineers.Google Scholar
Aursand, E. 2018 Inclination dependence of planar film boiling stability. Intl J. Multiphase Flow doi:10.1016/j.ijmultiphaseflow.2018.05.010.Google Scholar
Aursand, P., Gjennestad, M., Aursand, E., Hammer, M. & Wilhelmsen, Ø. 2017 The spinodal of single- and multi-component fluids and its role in the development of modern equations of state. Fluid Phase Equilib. 436, 98–112.Google Scholar
Baumeister, K. J. & Simon, F. F. 1973 Leidenfrost temperature: its correlation for liquid metals, cryogens, hydrocarbons, and water. Trans. ASME J. Heat Transfer 95, 166–173.Google Scholar
Berenson, P. J. 1961 Film-boiling heat transfer from a horizontal surface. Trans. ASME J. Heat Transfer 83 (3), 351–356.Google Scholar
Bernardin, J. D. & Mudawar, I. 1999 The Leidenfrost point: experimental study and assessment of existing models. Trans. ASME J. Heat Transfer 121 (4), 894–903.Google Scholar
Berthoud, G. 2000 Vapor explosions. Annu. Rev. Fluid Mech. 32 (1), 573–611.Google Scholar
Burelbach, J. P., Bankoff, S. G. & Davis, S. H. 1988 Nonlinear stability of evaporating/condensing liquid films. J. Fluid Mech. 195, 463–494.Google Scholar
Cao, B.-Y., Xie, J.-F. & Sazhin, S. S. 2011 Molecular dynamics study on evaporation and condensation of n-dodecane at liquid–vapor phase equilibria. J. Chem. Phys. 134 (16), 164309.Google Scholar
Cheng, S., Lechman, J. B., Plimpton, S. J. & Grest, G. S. 2011 Evaporation of Lennard-Jones fluids. J. Chem. Phys. 134 (22), 224704.Google Scholar
Cleaver, P., Johnson, M. & Ho, B. 2007 A summary of some experimental data on LNG safety. J. Hazard. Mater. 140 (3), 429–438.Google Scholar
Craster, R. V. & Matar, O. K. 2009 Dynamics and stability of thin liquid films. Rev. Mod. Phys. 81 (3), 1131–1198.Google Scholar
Davis, S. H. 1987 Thermocapillary instabilities. Annu. Rev. Fluid Mech. 19 (1), 403–435.Google Scholar
Dean, J. A. 1998 Lange’s Handbook of Chemistry, 15th edn. McGraw-Hill.Google Scholar
Dhir, V. K. 1998 Boiling heat transfer. Annu. Rev. Fluid Mech. 30 (1), 365–401.Google Scholar
Epstein, L. F. & Powers, M. D. 1953 Liquid metals. Part I. The viscosity of mercury vapor and the potential function for mercury. J. Phys. Chem. 57 (3), 336–341.Google Scholar
Fletcher, D. F. 1995 Steam explosion triggering: a review of theoretical and experimental investigations. Nucl. Engng Des. 155, 27–36.Google Scholar
Gottfried, B. S. & Bell, K. J. 1966 Film boiling of spheroidal droplets: Leidenfrost phenomenon. Ind. Engng Chem. Fundam. 5 (4), 561–568.Google Scholar
Hertz, H. 1882 Ueber die Verdunstung der Flüssigkeiten, insbesondere des Quecksilbers, im luftleeren Raume. Ann. Phys. 253 (10), 177–193.Google Scholar
Huber, M. L., Laesecke, A. & Friend, D. G. 2006 Correlation for the vapor pressure of mercury. Ind. Engng Chem. Res. 45 (21), 7351–7361.Google Scholar
Ishiyama, T., Fujikawa, S., Kurz, T. & Lauterborn, W. 2013 Nonequilibrium kinetic boundary condition at the vapor–liquid interface of argon. Phys. Rev. E 88 (4), 042406.Google Scholar
Iskrenova, E. K. & Patnaik, S. S. 2017 Molecular dynamics study of octane condensation coefficient at room temperature. Intl J. Heat Mass Transfer 115, 474–481.Google Scholar
Knudsen, M. 1915 Die maximale Verdampfungsgeschwindigkeit des Quecksilbers. Ann. Phys. 352 (13), 697–708.Google Scholar
Kundu, P. K., Cohen, I. M. & Dowling, D. R. 2007 Fluid Mechanics, 5th edn. Academic.Google Scholar
Liang, Z., Biben, T. & Keblinski, P. 2017 Molecular simulation of steady-state evaporation and condensation: validity of the Schrage relationships. Intl J. Heat Mass Transfer 114, 105–114.Google Scholar
Linstrom, P. J. & Mallard, W. G.(Eds) 2017 NIST Chemistry WebBook, NIST Standard Reference Database Number 69. National Institute of Standards and Technology.Google Scholar
Luketa-Hanlin, A. 2006 A review of large-scale LNG spills: experiments and modeling. J. Hazard. Mater. 132, 119–140.Google Scholar
Mills, A. F. 1995 Heat and Mass Transfer. CRC Press.Google Scholar
Myers, T. G. 1998 Thin films with high surface tension. SIAM Rev. 40 (3), 441–462.Google Scholar
Nagai, N. & Nishio, S. 1996 Leidenfrost temperature on an extremely smooth surface. Exp. Therm. Fluid Sci. 12 (3), 373–379.Google Scholar
Oron, A., Davis, S. H. & Bankoff, S. G. 1997 Long-scale evolution of thin liquid films. Rev. Mod. Phys. 69 (3), 931–980.Google Scholar
Panzarella, C. H., Davis, S. H. & Bankoff, S. G. 2000 Nonlinear dynamics in horizontal film boiling. J. Fluid Mech. 402, 163–194.Google Scholar
Qiao, Y. M. & Chandra, S. 1997 Experiments on adding a surfactant to water drops boiling on a hot surface. Proc. R. Soc. Lond. A Math. Phys. Engng Sci. 453, 673–689.Google Scholar
Ruckenstein, E. & Jain, R. K. 1974 Spontaneous rupture of thin liquid films. J. Chem. Soc. Faraday Trans. 70, 132–147.Google Scholar
Sakurai, A., Shiotsu, M. & Hata, K. 1990 Effects of system pressure on minimum film boiling temperature for various liquids. Exp. Therm. Fluid Sci. 3 (4), 450–457.Google Scholar
Skapski, A. S. 1948 The temperature coefficient of the surface tension of liquid metals. J. Chem. Phys. 16 (4), 386–389.Google Scholar
Spiegler, P., Hopenfeld, J., Silberberg, M., Bumpus, C. F. & Norman, A. 1963 Onset of stable film boiling and the foam limit. Intl J. Heat Mass Transfer 6 (11), 987–989.Google Scholar
Theofanous, T. G., Liu, C., Additon, S., Angelini, S., Kymäläinen, O. & Salmassi, T. 1997 In-vessel coolability and retention of a core melt. Nucl. Engng Des. 169 (1–3), 1–48.Google Scholar
Tsuruta, T. & Nagayama, G. 2004 Molecular dynamics studies on the condensation coefficient of water. J. Phys. Chem. B 108 (5), 1736–1743.Google Scholar
Valencia-Chavez, J. A.1978 The effect of composition on the boiling rates of liquefied natural gas for confined spills on water. PhD thesis, Massachusetts Institute of Technology.Google Scholar
Vesovic, V. 2007 The influence of ice formation on vaporization of LNG on water surfaces. J. Hazard. Mater. 140 (3), 518–526.Google Scholar
Vinogradov, Y. K. 1981 Thermal conductivity of mercury vapor. J. Engng Phys. Thermophys. 41 (2), 868–870.Google Scholar
Xie, J.-F., Sazhin, S. S. & Cao, B.-Y. 2011 Molecular dynamics study of the processes in the vicinity of the n-dodecane vapour/liquid interface. Phys. Fluids 23 (11), 112104.Google Scholar
Yao, S.-C. & Henry, R. E. 1978 An investigation of the minimum film boiling temperature on horizontal surfaces. J. Heat Transfer 100 (2), 260–267.Google Scholar
Ytrehus, T. 1997 Molecular-flow effects in evaporation and condensation at interfaces. Multiphase Sci. Technol. 9 (3), 205–327.Google Scholar
Zuber, N.1959 Hydrodynamic aspects of boiling heat transfer. PhD thesis, University of California, Los Angeles, CA.Google Scholar