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Non-equilibrium Evaporation and Condensation Processes pp 79–96Cite as

Approximate Kinetic Analysis of Strong Condensation

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Part of the book series: Mathematical Engineering ((MATHENGIN))

Abstract

In recent years, there has been a growing interest in new fundamental and application problems focused on the study of strong phase transitions like evaporation and condensation. Problems of this kind arise in the study of many processes.

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Notes

  1. 1.

    Strictly speaking, the concept of hydrodynamic velocity cannot be applied to the Knudsen layer, so parameter \( \tilde{u} \) can be described as a second (along with \( \varepsilon \)) ellipsoidal parameter.

Abbreviations

\( {\mathbf{c}} \) :

Molecular velocity vector

\( c_{x} ,c_{y} \) :

Projections of molecular velocity vector to the axis x, y parallel to the surface

\( c_{z} \) :

Component of molecular velocity normal to the surface

\( f \) :

Distribution function

\( I,K \) :

Dimensionless molecular fluxes

J :

Molecular flux

j :

Mass flux

\( k_{B} \) :

Boltzmann constant

m :

Molecular mass

M:

Mach number

n :

Molecular gas density

p :

Pressure

\( \tilde{p} \) :

Pressure ratio

T :

Temperature

\( \tilde{T} \) :

Temperature ratio

\( u \) :

Hydrodynamic velocity

v:

Hydrodynamic velocity vector

\( \tilde{u} \) :

Velocity factor

v:

Thermal velocity of molecules

\( \alpha_{\rho } ,\,\alpha_{\text{v}} ,\,\alpha_{\text{u}} \) :

Coefficients

\( \rho \) :

Density

\( \varepsilon \) :

Ellipsoidal parameter

\( w \) :

Condensed phase surface

\( \delta \) :

Mixing surface

\( \infty \) :

Infinity

1:

Mass flux

2:

Momentum flux

3:

Energy flux

References

  1. Mazhukin VI, Mazhukin AV, Demin MM, and Shapranov AV (2013) The dynamics of the surface treatment of metals by ultra-short high-power laser pulses. In: Sudarshan TS, Jeandin M, Firdirici V (eds) Surface Modification Technologies XXVI (SMT 26), vol. 26, pp 557–566

    Google Scholar 

  2. Lezhnin SI, Kachulin DI (2013) The various factors influence on the shape of the pressure pulse at the liquid-vapor contact. J. Engng Termophysics 22(1):69–76

    Article  Google Scholar 

  3. Zakharov VV, Crifo JF, Lukyanov GA, Rodionov AV (2002) On modeling of complex nonequilibrium gas flows in broad range of Knudsen numbers on example of inner cometary atmosphere. Math Models Comput Simul 14(8):91–95

    MATH  Google Scholar 

  4. Kogan MN (1995) Rarefied gas dynamics. Springer, Berlin

    Google Scholar 

  5. Labuntsov DA (1967) An analysis of the processes of evaporation and condensation. High Temp 5(4):579–647

    Google Scholar 

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

    Google Scholar 

  7. Cercignani C (1990) Mathematical methods in kinetic theory. Springer, New York

    Book  MATH  Google Scholar 

  8. Pao YP (1971) Temperature and density jumps in the kinetic theory of gases and vapors. Phys Fluids 14:1340–1346

    Article  MathSciNet  Google Scholar 

  9. Pao YP (1973) Erratum: temperature and density jumps in the kinetic theory of gases and vapors. Phys Fluids 16:1650

    Article  Google Scholar 

  10. Aristov VV, Panyashkin MV (2011) Study of spatial relaxation by means of solving a kinetic equation. Comput Math Math Phys 51(1):122–132

    Article  MathSciNet  MATH  Google Scholar 

  11. Tcheremissine FG (2012) Method for solving the Boltzmann kinetic equation for polyatomic gases. Comput Math Math Phys 52(2):252–268

    Article  MathSciNet  Google Scholar 

  12. Zhakhovskii VV, Anisimov SI (1997) Molecular-dynamics simulation of evaporation of a liquid. J Exp Theor Phys 84(4):734–745

    Article  Google Scholar 

  13. Anisimov SI (1968) Vaporization of metal absorbing laser radiation. Sov Phys JETP 27(1):182–183

    Google Scholar 

  14. Labuntsov DA, Kryukov AP (1979) Analysis of intensive evaporation and condensation. Int J Heat Mass Transf 2(7):989–1002

    Article  MATH  Google Scholar 

  15. Ytrehus T (1977) Theory and experiments on gas kinetics in evaporation. In: Potter JL (ed) Rarefied gas dynamics: technical papers selected from the 10th international symposium on rarefied gas dynamics. Snowmass-at-Aspen, CO, July 1976. In: Progress in astronautics and aeronautics, vol 51. American Institute of Aeronautics and Astronautics, pp 1197–1212

    Google Scholar 

  16. Aoki K, Sone Y, Yamada T (1990) Numerical analysis of gas flows condensing on its plane condensed phase on the basis of kinetic theory. Phys Fluids 2:1867–1878

    Article  MATH  Google Scholar 

  17. Gusarov AV, Smurov I (2002) Gas-dynamic boundary conditions of evaporation and condensation: numerical analysis of the Knudsen layer. Phys Fluids 14(12):4242–4255

    Article  MathSciNet  MATH  Google Scholar 

  18. Frezzotti A, Ytrehus T (2006) Kinetic theory study of steady condensation of a polyatomic gas. Phys Fluids 18 (2): 027101-027101-12

    Google Scholar 

  19. Gusarov AV, Smurov I (2001) Target-vapour interaction and atomic collisions in pulsed laser ablation. J Physics D: Appl Phys 34(8):1147–1156

    Article  Google Scholar 

  20. Kuznetsova IA, Yushkanov AA, Yalamov YI (1997) Supersonic condensation of monatomic gas. High Temp 35(2):342–346

    MATH  Google Scholar 

  21. Kuznetsova IA, Yushkanov AA, Yalamov YI (1997) Intense condensation of molecular gas. Fluid Dyn 6:168–174

    MATH  Google Scholar 

  22. Vinerean MC, Windfäll A, Bobylev AV (2010) Construction of normal discrete velocity models of the Boltzmann equation. Nuovo Cimento C 33(1):257–264

    MATH  Google Scholar 

  23. Kuznetsova IA, Yushkanov AA, Yalamov YI (2000) Supersonic condensation of molecular gas. High Temp 38(4):614–620

    Article  MATH  Google Scholar 

  24. Zudin YB (2015) Approximate kinetic analysis of intense evaporation. J Engng Phys Thermophys 88(4):1015–1022

    Article  Google Scholar 

  25. Zudin YB (2015) The approximate kinetic analysis of strong condensation. Thermophys Aeromech 22(1):73–84

    Article  Google Scholar 

  26. Zudin YB (2016) Linear kinetic analysis of evaporation and condensations. Thermophys Aeromech 23(3):437–449

    Article  Google Scholar 

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Authors and Affiliations

  1. National Research Center, Kurchatov Institute, Moscow, Russia

    Yuri B. Zudin

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  1. Yuri B. Zudin
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Zudin, Y.B. (2018). Approximate Kinetic Analysis of Strong Condensation. In: Non-equilibrium Evaporation and Condensation Processes. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-67306-6_5

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  • DOI: https://doi.org/10.1007/978-3-319-67306-6_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67151-2

  • Online ISBN: 978-3-319-67306-6

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