Skip to main content
SpringerLink
Log in

Approximate Kinetic Analysis of Strong Condensation

  • Chapter
  • First Online:
Non-equilibrium Evaporation and Condensation Processes

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

  • 423 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 139.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 179.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 179.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    As regards the abnormal condensation branch, it should not take place at all according to the standard approaches.

  2. 2.

    In [26], the inversion was predicted when the flow exactly reaches the sound speed condensation \(\left| {\text{M}} \right| = 1\).

  3. 3.

    Recall that in the above case of consideration the speed ratio and the Mach number are negative.

Abbreviations

BC:

Boundary condition

CPS:

Condensed-phase surface

KL:

Knudsen layer

c :

Molecular velocity vector

f :

Distribution function

J :

Molecular flux

j :

Mass flux

m :

Molecular mass

M:

Mach number

n :

Molecular gas density

p :

Pressure

\(\tilde{p}\) :

Pressure ratio

T :

Temperature

\(\widetilde{T}\) :

Temperature ratio

u ∞ :

Hydrodynamic velocity vector

u ∞ :

Hydrodynamic velocity

\(\widetilde{u}_{\infty }\) :

Speed ratio

v:

Thermal velocity

ρ :

Density

β :

Condensation coefficient

η :

Pressure factor

δ :

State at mixing surface

w :

State at condensed-phase surface

∞:

State at infinity

References

  1. Mazhukin VI, Mazhukin AV, Demin MM, 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 Eng Thermophys 22(1):69–76

    Article  Google Scholar 

  3. Zakharov VV, Crifo JF, Lukyanov GA, Rodionov AV (2002) On modeling of complex non-equilibrium 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

    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, US

    Book  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 (1971) Erratum: temperature and density jumps in the kinetic theory of gases and vapors. Phys Fluids 16:1650

    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  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  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  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  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 Phys D Appl Phys 34(8):1147–1156

    Article  Google Scholar 

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

    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. Smirnov VI (1964) A course in higher mathematics. Pergamon Press, Oxford, Addison-Wesley, Reading, Mass.

    MATH  Google Scholar 

  24. Abramov AA, Kogan MN (1984) The supersonic regime of gas condensation. Akademiia Nauk SSSR, Doklady 278(5):1078–1081 (In Russian)

    Google Scholar 

  25. Abramov AA, Butkovskii AV (2008) The effect of the flow-to-wall temperature ratio on strong condensation of gas. High Temp 46(2):229–233

    Article  Google Scholar 

  26. Bardos C, Golse F, Sone Y (2006) Half-space problems for the Boltzmann equation. Surv J Stat Phys 124(2–4):275–300

    Article  MathSciNet  Google Scholar 

  27. Kogan MN, Makashev NK (1971) On the role of Knudsen layer in the theory of heterogeneous reactions and in flows with surface reactions. Izv Akad Nauk SSSR Mekh Zhidk Gaza 6:3–11 (In Russian)

    Google Scholar 

  28. Bond M, Struchtrup H (2004) Mean evaporation and condensation coefficient based on energy dependent condensation probability. Phys Rev E 70:061605

    Article  Google Scholar 

  29. Zhakhovsky VV, Kryukov AP, Levashov VY, Shishkova IN, Anisimov SI (2018) Mass and heat transfer between evaporation and condensation surfaces: atomistic simulation and solution of Boltzmann kinetic equation. In: Proceedings of the national academy of sciences, Apr 2018. 201714503. https://doi.org/10.1073/pnas.1714503115

Download references

Author information

Authors and Affiliations

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

    Yuri B. Zudin

Authors
  1. Yuri B. Zudin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuri B. Zudin .

Rights and permissions

Reprints and permissions

Copyright information

© 2021 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Zudin, Y.B. (2021). Approximate Kinetic Analysis of Strong Condensation. In: Non-equilibrium Evaporation and Condensation Processes. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-030-67553-0_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-67553-0_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-67552-3

  • Online ISBN: 978-3-030-67553-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation