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Critical phenomena at evaporation in a thin liquid layer at reduced pressure


This research is concerned with the problem of heat transfer in a thin liquid layer on a horizontal surface, which evaporates at reduced pressure, when structures shaped as “funnels” and “craters” appear on its surface under the action of vapor recoil force. An approximate model that takes into account the surface tension force, gravity force, vapor recoil force, and disjoining pressure is developed. For the experimentally realized shape of curved surface, in the frames of the model, the distribution of vapor recoil force, temperature, pressure, shear stresses, and local heat fluxes along the interface is found. The density of the heat flux corresponding to appearance of a crater at the place of an array of funnels is estimated. The results are in good agreement with the experimental measurements and the estimates by the Kutateladze formula for the first critical heat flux density.

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  1. 1.

    Gimbutis, G., Heat Transfer at Gravitation Flow of a Liquid Film, Vilnius: Mokslas, 1988, p. 231.

    Google Scholar 

  2. 2.

    Katto, Y., Critical Heat Flux, Int. J. Multiphase Flow, 1994, vol. 20, pp. 53–90.

    Article  MATH  Google Scholar 

  3. 3.

    Sanochkin, Yu.V., Thermocapillary Convection in a Thin Liquid Layer Heated Locally from Above, Zh. Prikl. Mekh. Tekhn. Fiz., 1983, no. 6, pp. 134–137.

    Google Scholar 

  4. 4.

    Zueva, A.Yu., Mathematical Modeling of Photoinduced Thermocapillary Convection in a Transparent Liquid Layer on an Absorbing Substrate, Cand. Sci. (Phys.-Math.) Dissertation, Tyumen, 2007.

    Google Scholar 

  5. 5.

    Avksentuyk, B.P. and Bochkarev, A.A., Interaction between a Heated Body and a Free Liquid Surface, Zh. Tekhn. Fiz., 1985, vol. 55, no. 4, pp. 797–798.

    Google Scholar 

  6. 6.

    Oron, A., Davis, S.H., and Bankoff, S.G., Long-Scale Evolution of Thin Liquid Films, Rev. Mod. Phys., 1997, vol. 69, no. 3, pp. 931–980.

    ADS  Article  Google Scholar 

  7. 7.

    Zaitsev, D.V. and Kabov, O.A., Study of the Thermocapillary Effect on a Wavy Falling Film Using a Fiber Optical Thickness Probe, Exp. Fluids, 2005, vol. 39, no. 4, pp. 712–721.

    Article  Google Scholar 

  8. 8.

    Zaitsev, D.V., Rodionov, D.A., and Kabov, O.A, Study of the Thermocapillary Film Rupture Using a Fiber Optical Thickness Probe, Micrograv. Sci. Technol., 2007, vol. 19, nos. 3/4, pp. 100–103.

    Article  Google Scholar 

  9. 9.

    Tolubinskii, V.I., Antonenko, V.A., and Ostrovskii, Yu.N., Heat Transfer in Vaporization in Thin Films, Prom. Teplotekh., 1981, vol. 3, no. 3, pp. 9–13.

    Google Scholar 

  10. 10.

    Nishikawa, K., Kusuda, H., Yamasaki, K., and Tanaka, K., Nucleate Boiling at Low Liquid Levels, Bull. JASME, 1967, vol. 10, no. 38, pp. 328–338.

    Article  Google Scholar 

  11. 11.

    Tolubinskii, V.I., Antonenko, V.A., Kriveshko, A.A., and Ostrovskii, Yu.N., Suppression of Nucleate Boiling in a Stationary Liquid Film, Teplofiz. Vys. Temper., 1977, vol. 15, no. 4, pp. 822–827.

    ADS  Google Scholar 

  12. 12.

    Tolubinskii, V.I., Antonenko, V.A., and Ostrovskii, Yu.N., Some Peculiarities of Heat Transfer in Thin Films of Boiling Liquid, in Teploobmen 1978. Sovetskie issledovaniya (Heat Transfer 1978. Soviet Investigations), Moscow: 1980, pp. 182–191.

    Google Scholar 

  13. 13.

    Grigoryev, V.A., Pavlov, Yu.M., and Ametistov, E.V., Kipenie kriogennykh zhidkostei (Cryogenic Liquid Boiling), Labuntsov, D.A., Ed., Moscow: Energiya, 1977.

  14. 14.

    Kopchikov, I.A., Voronin, G.I., Kolach, T.A., Labuntsov, D.A., and Lebedev, P.D., Liquid Boiling in a Thin Film, Int. J. Heat Mass Transfer, 1969, vol. 12, no. 7, pp. 791–796.

    Article  Google Scholar 

  15. 15.

    Jiang, S. and Dhir, V.K., Spray Cooling in a Closed System with Different Fractions of Non-Condensibles in the Environment, Int. J. Heat Mass Transfer, 2004, vol. 47, no. 25, pp. 5391–5406.

    Article  Google Scholar 

  16. 16.

    Horacek, B., Kenneth, T.K., and Jungho, K., Single Nozzle Spray Cooling Heat Transfer Mechanisms, Int. J. Heat Mass Transfer, 2005, vol. 48, pp. 1425–1438.

    Article  Google Scholar 

  17. 17.

    Yagov, V.V., Heat Transfer in Developed Nucleate Liquid Boiling, Teploenergetika, 1988, no. 2, pp. 4–9.

    Google Scholar 

  18. 18.

    Yagov, V.V. and Puzin, V.A., Approximate Model of Boiling Crisis in Forced Motion of Saturated Liquid, Teploenergetika, 1985, no. 3, pp. 2–5.

    Google Scholar 

  19. 19.

    Yagov, V.V., Physical Model and Calculated Relation for CriticalHeat Fluxes in Nucleate Liquid Pool Boiling, Teploenergetika, 1988, no. 6, pp. 53–59.

    Google Scholar 

  20. 20.

    Yagov, V.V. and Sukach, A.V., Approximate Physical Model of Boiling Crisis in the Region of Low Reduced Pressures, Teploenergetika, 2000, no. 3, pp. 14–18.

    Google Scholar 

  21. 21.

    Yagov, V.V., Mechanism of Pool Boiling Crisis, Teploenergetika, 2003, no. 3, pp. 2–10.

    Google Scholar 

  22. 22.

    Lay, J.H. and Dhir, V.K., A Nearly Theoretical Model for Fully Developed Nucleate Boiling of Saturated Liquids, Proc. Int. Heat Transfer Conf., Brighton, England, 1994, vol. 5, pp. 105–110.

    Google Scholar 

  23. 23.

    Stephan, P. and Hammer, J., A New Model for Nucleate Boiling Heat Transfer, Warme — und Stoffubertragung, 1994, vol. 30, no. 2, pp. 119–125.

    ADS  Google Scholar 

  24. 24.

    Lay, J.H. and Dhir, V.K., Shape of a Vapor Stem during Nucleate Boiling of Saturated Liquids, J. Heat Transfer, 1995, vol. 117, pp. 394–401.

    Article  Google Scholar 

  25. 25.

    Wayner, P.C., Evaporation and Stress in the Contact Line Region, Proc. Engineering Fundamentals Conf. on Pool and Flow Boiling, ASME, 1992, pp. 251–256.

    Google Scholar 

  26. 26.

    Parks, C.J. and Wayner, P.C., Jr., Surface Shear near the Contact Line of Binary Evaporating Curved Thin Film, AIChE J., 1987, vol. 33, no. 1, pp. 1–10.

    Article  Google Scholar 

  27. 27.

    Deryagin, B.V., Churaev, N.V., and Muller, V.M., Poverkhnostnye sily (Surfaces Forces), Moscow: Nauka, 1985.

    Google Scholar 

  28. 28.

    Dzyaloshinskii, I.E., Lifshitz, E.M., and Pitaevskii, L.P., The General Theory of Van der Waals Forces, Adv. Phys., 1961, vol. 10, pp. 165–209.

    MathSciNet  ADS  Article  Google Scholar 

  29. 29.

    Son, G., Dhir, V.K., and Ramanujapu, N., Dynamics and Heat Transfer Associated with a Single Bubble during Nucleate Boiling on a Horizontal Surface, Trans. ASME J. Heat Transfer, 1999, vol. 121, pp. 623–631.

    Article  Google Scholar 

  30. 30.

    Son, G. and Dhir, V.K., Numerical Simulation of Nucleate Boiling on a Horizontal Surface at High Heat Fluxes, Int. J. Heat Mass Transfer, 2008, vol. 51, pp. 2566–2582.

    Article  MATH  Google Scholar 

  31. 31.

    Gogonin, I.I., Dorokhov, A.R., and Zhukov, V.I., Investigation of Evaporation from a Thin Oil Layer under Vacuum, Izv. SO AN SSSR, Ser. Tekhn. Nauk, 1989, iss. 3, pp. 8–13.

    Google Scholar 

  32. 32.

    Zhukov, V.I., The Rate of Vapor Bubble Growth on a Heated Surface during Boiling, Pis’ma ZhTF, 1996, vol. 22,iss. 21, pp. 34–38.

    MathSciNet  Google Scholar 

  33. 33.

    Dorokhov, A.R. and Zhukov, V.I., Bubble Growth Rate and Effect of Degenerate Liquid Boiling in the Form of Film Evaporation, Inzh.-Fiz. Zh., 1999, vol. 72, no. 3, pp. 458–465.

    Google Scholar 

  34. 34.

    Pavlov, P.A., Dinamika vskipaniya sil’no peregretykh zhidkostei (The Dynamics of Boiling-up of Superheated Liquids), Sverdlovsk: UrO AN SSSR, 1988.

    Google Scholar 

  35. 35.

    Zhukov, V.I., Enhancement of Heat Transfer during Liquid Boiling in a Thin Layer under Vacuum, Teor. Osnovy Khim. Tekhnol., 2011, vol. 45, no. 5, pp. 602–606.

    Google Scholar 

  36. 36.

    Hickman, K.C.D., Studies in High Vacuum Evaporation, pt. III, Surface Behavior in the Pot Still, Ind. Eng. Chem., 1952, vol. 44, pp. 1892–1902.

    Article  Google Scholar 

  37. 37.

    Hickman, K.C.D., Torpid Phenomena and Pump Oils, J. Vac. Sci. Tech., 1972, vol. 9, no. 10, pp. 960–976.

    ADS  Article  Google Scholar 

  38. 38.

    Palmer, H.J. and Maheshri, J.C., Enhanced Interfacial Heat Transfer by DifferenceVapor Recoil Instabilities, Int. J. Heat Mass Transfer, 1981, vol. 4, no. 1, pp. 117–124.

    Article  Google Scholar 

  39. 39.

    Palmer, H.J., The Hydrodynamic Stability of Rapidly Evaporating Liquids at Reduced Pressure, J. Fluid Mech., 1976, vol. 75, pp. 487–511.

    ADS  Article  MATH  Google Scholar 

  40. 40.

    Maheshri, J.C. and Palmer, H.J., The Influence of Lateral Pressure Variations on the Stability of Rapidly Evaporating Liquids at Reduced Pressure, AJChE J., 1979, vol. 25, pp. 183–185.

    Article  Google Scholar 

  41. 41.

    Pavlenko, A.N. and Lel, V.V., Heat Transfer and Crisis Phenomena in Falling Films of Cryogenic Liquid, Russ. J. Eng. Therm., 1997, vol. 7, nos. 3/4, pp. 177–210.

    Google Scholar 

  42. 42.

    Pavlenko, A.N., Lel, V.V., Serov, A.F., Nazarov, A.D., and Matsekh, A.D., The Growth of Wave Amplitude and Heat Transfer in Falling Intensively Evaporating Liquid Films, J. Eng. Therm., 2002, vol. 11, no. 1, pp. 7–43.

    Google Scholar 

  43. 43.

    Mahmoudi, S.R., Adamaik, K., and Castle, G.S.P., Two-Phase Cooling Characteristics of a Saturated Free Falling Circular Jet of HFE7100 on Heated Disk: Effect of Jet Length, Int. J. Heat Mass Transfer, 2012, vol. 55, pp. 6181–6190.

    Article  Google Scholar 

  44. 44.

    Berdnikov, V.S. and Kirdyashkin, A.G., Cell Convection in Horizontal Liquid Layers under Different Boundary Conditions, Izv. AN SSSR, Ser. Fiz. Atmosfery Okeana, 1979, vol. 15, no. 11, pp. 1168–1174.

    ADS  Google Scholar 

  45. 45.

    Burdukov, A.P., Dorokhov, A.R., and Zhukov, V.I., Experimental Investigation of Heat Transfer for Natural Convection in Horizontal Layers of Mineral Oil at Vacuum, in Teploobmen i trenie v odnofaznykh potokakh (Heat Transfer and Friction in Single-Phase Flows), Novosibirsk: IT SO AN SSSR, 1988, pp. 45–75.

    Google Scholar 

  46. 46.

    Burdukov, A.P., Dorokhov, A.R., and Zhukov, V.I., Experimental Investigation of Heat Transfer for Free Convection in Horizontal Layers of Mineral Oil at Vacuum, Izv. SO AN SSSR, Ser. Tekhn. Nauk, 1989, iss. 2, pp. 24–33.

    Google Scholar 

  47. 47.

    Moor, F.D. and Mesler, R.B., The Measurement of Rapid Surface Temperature Fluctuations during Nucleate Boiling of Water, AIChE J., 1961, vol. 7, no. 4, pp. 620–624.

    Article  Google Scholar 

  48. 48.

    Adam, N.C., Physics and Chemistry of Surfaces, Moscow: Gostekhizdat, 1947.

    Google Scholar 

  49. 49.

    Bashforth, F. and Adams, J.C., An Attempt to Test the Theories of Capillary Action, Cambridge Univ. Press, 1883.

    Google Scholar 

  50. 50.

    Babskii, V.G., Kopachevskii, N.D., Myshkis, A.D., et al., Gidrodinamika nevesomosti (Zero-Gravity Dynamics), Myshkis, A.D., Ed., Moscow: Nauka, 1976.

  51. 51.

    Labuntsov, D.A. and Yagov, V.V., On the Conditions of Vapor Bubble Detach during Boiling at Reduced Pressures, Teplofiz. Vys. Temper., 1988, vol. 26, no. 6, pp. 54–72

    Google Scholar 

  52. 52.

    Yagov, V.V., Vapor Bubble Departure Conditions at Pool Boiling, Eurotherm Seminar no. 48, Pool Boiling 2, Paderborn, Germany Edizioni ETS, Pisa, 1996, pp. 95–104.

    Google Scholar 

  53. 53.

    Frolov, E.S., Minaichev, V.E., Aleksandrova, A.T., et al., Vakuumnaya tekhnika, Spravochnik (Vacuum Technology, Reference Book), Moscow: Mashinostroenie, 1985.

    Google Scholar 

  54. 54.

    Faw, R.E., Vavlect, R.J., and Schmidt D.L., Pre-Pressurization Effects on Initiation of Subcooled Pool Boiling during Pressure and Power Transients, Int. J. Heat Mass Transfer, 1986, vol. 29, no. 9, pp. 1427–1437.

    Article  Google Scholar 

  55. 55.

    Zuber, N., On the Stability of Boiling Heat Transfer, Trans. ASME, 1958, vol. 80, no. 3, pp. 711–720.

    Google Scholar 

  56. 56.

    Kutateladze, S.S., Hydrodynamic Model of Heat Transfer Crisis in Liquid Boiling for Free Convection, Zh. Tekh. Fiz., 1950, vol. 20, no. 11, pp. 1389–1392.

    Google Scholar 

  57. 57.

    Kutateladze, S.S., Osnovy teorii teploobmena (Fundamentals of the Heat Transfer Theory), 5th ed., Moscow: Atomizdat, 1979.

    Google Scholar 

  58. 58.

    Cooper, M.G. and Lloyd, A.J.P., The Microlayer in Nucleate Pool Boiling, Int. J. Heat Mass Transfer, 1969, vol. 12, no. 8, pp. 895–913.

    Article  Google Scholar 

  59. 59.

    Donnelly, B., O’Donovan, T.S., and Murray, D.B., Surface Heat Transfer Due to Sliding Bubble Motion, Appl. Therm. Eng., 2009, vol. 29, pp. 1319–1326.

    Article  Google Scholar 

  60. 60.

    Koffman, L.D. and Plesset, M.S., Experimental Observations of the Microlayer in Vapor Bubble Growth on a Heated Solid, J. Heat Transfer, 1983, vol. 105, no. 3, pp. 625–632.

    Article  Google Scholar 

  61. 61.

    Kandlikar, S.G., Kuan, W.K., and Mukherjee, A., Experimental Study of Heat Transfer in an Evaporating Meniscus on a Moving Heated Surface, Trans. ASME J. Heat Transfer, 2005, vol. 127, pp. 244–252.

    Article  Google Scholar 

  62. 62.

    Pavlenko, A.N., Tairov, A.A., Zhukov, V.E., Levin, A.A., and Tsoi, A.N., Investigation of Transitional Processes at Liquid Boiling under Non-Steady Heat Release, J. Eng. Therm., 2011, vol. 20, no. 4, pp. 1–27.

    Google Scholar 

  63. 63.

    Kuznetsov, V.V., Kozulin, I.A., and Vitovsky, O.V., Experimental Investigation of Adiabatic Evaporation Waves in Superheated Refrigerants, J. Eng. Therm., 2012, vol. 21, no. 2, pp. 136–143.

    Article  Google Scholar 

  64. 64.

    Pavlenko, A.N., Koverda, V.P., Reshetnikov, A.V., Surtaev, A.S., Tsoi, A.N., Mazeiko, N.A., Busov, K.A., and Skokov, V.N., Disintegration of Flows of Superheated Liquid Films and Jets, J. Eng. Therm., 2013, vol. 22, no. 3, pp. 74–193.

    Google Scholar 

  65. 65.

    Lel, V.V., Kellerman, A., Dietze, G., Kneer, R., and Pavlenko, A.N., Investigations of the Marangoni Effect on the Regular Structures in Heated Wavy Liquid Films, Exper. Fluids, 2008, vol. 44, no. 2, pp. 341–354.

    ADS  Article  Google Scholar 

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Zhukov, V.I., Pavlenko, A.N. Critical phenomena at evaporation in a thin liquid layer at reduced pressure. J. Engin. Thermophys. 22, 257–287 (2013).

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  • Heated Surface
  • Liquid Layer
  • Critical Heat Flux
  • Disjoin Pressure