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Binary Schemes of Vapor Bubble Growth

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Non-equilibrium Evaporation and Condensation Processes

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Abstract

In applications related to the physics of boiling, one has to know the dependence of the bubble growth rate at a heated surface on the thermophysical properties of a liquid and vapor, capillary, viscous, and inertial forces, as well as on the kinetic molecular laws operating at an interface

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Abbreviations

\(\alpha\) :

Thermal diffusivity

\(c_{p}\) :

Isobaric heat capacity

\({\text{Ja}}\) :

Jakob number

\(k\) :

Thermal conductivity

\(m\) :

Growth modulus

\(p\) :

Pressure

\(q\) :

Heat flux

\(R\) :

Bubble radius

\(L\) :

Heat of phase transition

\({\text{S}}\) :

Stefan number

\(T\) :

Temperature

\(t\) :

Time

\(\beta\) :

Evaporation–Condensation coefficient

\(\mu\) :

Dynamic viscosity

\(\nu\) :

Kinematic viscosity

\(\rho\) :

Density

\({\mathbb{R}}\) :

Thermal resistance

\(b\) :

Vapor bubble

\(e\) :

State at energy spinodal

\(l\) :

Liquid

\({ \hbox{max} }\) :

Maximum

\({ \hbox{min} }\) :

Minimum

\({\text{v}}\) :

Vapor

\(s\) :

Saturation state

\(\infty\) :

State at infinity

\(*\) :

State at blocking point

References

  1. Labuntsov DA (2000) Physical foundations of power engineering. Selected works, Moscow Power Energetic Univ. (Publ.). Moscow (In Russian)

    Google Scholar 

  2. Labuntsov DA, Yagov VV (2007) Mechanics of two-phase systems. Moscow Power Energetic Univ. (Publ.), Moscow (In Russian)

    Google Scholar 

  3. Besant WH (2013) A treatise on hydrostatics and hydrodynamics. Forgotten Books, London

    Google Scholar 

  4. Prosperetti A, Plesset MS (1978) Vapor bubble growth in a superheated liquid. J Fluid Mech 85:349–368

    Article  Google Scholar 

  5. Brennen CE (1995) Cavitation and bubble dynamics. Oxford University Press, Oxford

    MATH  Google Scholar 

  6. Labuntsov DA (1974) Current views on the bubble boiling mechanism. In: Heat transfer and physical hydrodynamics. Nauka, Moscow, pp 98–115 (In Russian)

    Google Scholar 

  7. Rayleigh L (1917) On the pressure developed in a liquid during the collapse of a spherical cavity. Philos Mag 34:94–98

    Article  Google Scholar 

  8. Muratova TM, Labuntsov DA (1969) Kinetic analysis of the processes of evaporation and condensation. High Temp 7(5):959–967

    Google Scholar 

  9. Bosnjakovic F (1930) Verdampfung und Flüssigkeits Überhitzung. Technische Mechanik und Thermodynamik 1:358–362

    Google Scholar 

  10. Jakob M, Linke W (1935) Wärmeübergang beim Verdampfen von Flüssigkeiten an senkrechten und waagerechten Flächen. Phys Zeitschrift 36:267–280

    Google Scholar 

  11. Fritz W, Ende W (1936) Über den Verdampfungsvorgang nach kinematographischen Aufnahmen an Dampfblasen. Berechnung des Maximalvolumens von Dampfblase. Phys Zeitschrift 37:391–401

    Google Scholar 

  12. Plesset MS, Zwick SA (1954) The growth of vapor bubbles in superheated liquids. J Appl Phys 25:493–500

    Article  MathSciNet  Google Scholar 

  13. Birkhoff G, Margulis R, Horning W (1958) Spherical bubble growth. Phys Fluids 1:201–204

    Article  MathSciNet  Google Scholar 

  14. Scriven LE (1959) On the dynamics of phase growth. Chem Eng Sci 10(1/2):1–14

    Article  Google Scholar 

  15. Carslaw HS, Jaeger JC (1986) Conduction of heat in solids. Clarendon, London

    MATH  Google Scholar 

  16. Mccue SW, Wu B, Hill JM (2008) Classical two-phase Stefan problem for spheres. Proc R Soc Lond, Ser A Math Phys Eng Sci 464(2096):2055–2076

    Google Scholar 

  17. Labuntsov DA, Yagov VV (1978) Mechanics of simple gas-liquid structures. Moscow Power Energetic Univ. (Publ.), Moscow (In Russian)

    Google Scholar 

  18. Frank FC (1950) Radially symmetric phase growth controlled by diffusion. Proc R Soc Lond, Ser A Math Phys Eng Sci 201(1067):586–599

    Google Scholar 

  19. Papac J, Helgadottir A, Ratsch C, Gibou FA (2013) Level set approach for diffusion and Stefan-type problems with Robin boundary conditions on quadtree/octree adaptive Cartesian grids. J Comput Phys 233:241–261

    Article  MathSciNet  Google Scholar 

  20. Labuntsov DA, Kol’chugin BA, Golovin VS, Zakharova EA, Vladimirova LN (1964) High-speed cine-photography investigation of the growth of bubbles in saturated water boiling in a wide range of pressures. High Temp 2(3):446–453

    Google Scholar 

  21. Straub J (2001) Boiling heat transfer and bubble dynamics in microgravity Adv. Heat Transf 35:157–172

    Google Scholar 

  22. Winter J (1997) Kinetik des Blasenwachstums. Dissertation. Technische Universität München, München

    Google Scholar 

  23. Avdeev AA (2014) Laws of vapor bubble growth in the superheated liquid volume (thermal growth scheme). High Temp 40(2):588–602

    Article  Google Scholar 

  24. Mikic BB, Rosenow WM, Griffith P (1970) On bubble growth rates. Int J Heat Mass Transf 13:657–666

    Article  Google Scholar 

  25. Yagov VV (1988) On the limiting law of growth of vapor bubbles in the region of very low pressures (high Jakob numbers). High Temp 26(2):251–257

    Google Scholar 

  26. Korabelnikov AV, Nakoryakov VE, Shraiber IR (1981) Taking account of non-equilibrium evaporation in the problems of the vapor bubble dynamics. High Temp 19(4):586–590

    Google Scholar 

  27. Aktershev SP (2004) Growth of a vapor bubble in an extremely superheated liquid. Thermophysics and Aeromechanics 12 (3): 445–457 Skripov VP (1974) Metastable Liquid. Wiley, New York

    Google Scholar 

  28. Debenedetti PG (1996) metastable liquids: concepts and principles. Princeton University Press, Princeton

    Google Scholar 

  29. Kryukov AP, Levashov VY (2011) About evaporation-condensation coefficients on the vapor-liquid interface of high thermal conductivity matters. Int J Heat Mass Transf 54(13–14):3042–3048

    Article  Google Scholar 

  30. Kryukov AP, Levashov VY, Pavlyukevich NV (2014) Condensation coefficient: Definitions, estimations, modern experimental and calculation data. J Eng Phys Thermophys 87(1):237–245

    Article  Google Scholar 

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Zudin, Y.B. (2021). Binary Schemes of Vapor Bubble Growth. In: Non-equilibrium Evaporation and Condensation Processes. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-67553-0_7

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  • DOI: https://doi.org/10.1007/978-3-030-67553-0_7

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