Vapor flows caused by evaporation and condensation on two parallel plane surfaces: Effect of the presence of a noncondensable gas

Physics of Fluids

Volumn 10, Issue 6, 1998, Pages 1519-1533

  Aoki, Kazuo ^a   Takata, Shigeru ^a   Kosuge, Shingo ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001742330     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869671     Document Type: Article

References (68)

1. Y. Sone and Y. Onishi, "Kinetic theory of evaporation and condensation - Hydrodynamic equation and slip boundary condition," J. Phys. Soc. Jpn. 44, 1981 (1978).
2. Y. Onishi and Y. Sone, "Kinetic theory of slightly strong evaporation and condensation - Hydrodynamic equation and slip boundary condition for finite Reynolds number," J. Phys. Soc. Jpn. 47, 1676 (1979).
3. Y. Sone, "Asymptotic theory of a steady flow of a rarefied gas past bodies for small Knudsen numbers," in Advances in Kinetic Theory and Continuum Mechanics, edited by R. Gatignol and Soubbaramayer (Springer-Verlag, Berlin, 1991), p. 29.
4. K. Aoki and Y. Sone, "Gas flows around the condensed phase with strong evaporation or condensation: Fluid dynamic equation and its boundary condition on the interface and their application," in Ref. 3, p. 43.
5. K. Aoki, K. Nishino, Y. Sone, and H. Sugimoto, "Numerical analysis of steady flows of a gas condensing on or evaporating from its plane condensed phase on the basis of kinetic theory: Effect of gas motion along the condensed phase," Phys. Fluids A 3, 2260 (1991).
6. H. Sugimoto and Y. Sone, "Numerical analysis of steady flows of a gas evaporating from its cylindrical condensed phase on the basis of kinetic theory," Phys. Fluids A 4, 419 (1992).
7. Y. Sone and H. Sugimoto, "Kinetic theory analysis of steady evaporating flows from a spherical condensed phase into a vacuum," Phys. Fluids A 5, 1491 (1993).
8. Y. Sone and H. Sugimoto, "Evaporation of a rarefied gas from a cylindrical condensed phase into a vacuum," Phys. Fluids 7, 2072 (1995).
9. S. Takata, Y. Sone, D. Lhuillier, and M. Wakabayashi, "Evaporation from and condensation onto a sphere: Numerical analysis of the Boltzmann equation for hard-sphere molecules," Comput. Math. Appl. 35, 193 (1998).
10. Y. Sone, S. Takata, and M. Wakabayashi, "Numerical analysis of a rarefied gas flow past a volatile particle using the Boltzmann equation for hard-sphere molecules," Phys. Fluids 6, 1914 (1994).
11. Y. P. Pao, "Application of kinetic theory to the problem of evaporation and condensation," Phys. Fluids 14, 306 (1971).
12. J. R. Thomas, Jr., T. S. Chang, and C. E. Siewert, "Reverse temperature gradient in the kinetic theory of evaporation," Phys. Rev. Lett. 33, 680 (1974).
13. T. Matsushita, "Kinetic analysis of the problem of evaporation and condensation," Phys. Fluids 19, 1712 (1976).
14. K. Aoki and C. Cercignani, "Evaporation and condensation on two parallel plates at finite Reynolds numbers," Phys. Fluids 26, 1163 (1983).
15. L. D. Koffman, M. S. Plesset, and L. Lees, "Theory of evaporation and condensation," Phys. Fluids 27, 876 (1984).
16. C. Cercignani, W. Fiszdon, and A. Frezzotti, "The paradox of the inverted temperature profiles between an evaporating and a condensing surface," Phys. Fluids 28, 3237 (1985).
17. T. Ytrehus and T. Aukrust, "Mott-Smith solution for weak condensation," in Rarefied Gas Dynamics, edited by V. Boffi and C. Cercignani (Teubner, Stuttgart, 1986), Vol. 2, p. 271.
18. F. Boujot and Soubbaramayer, "A non linear case of the kinetic model of evaporation-condensation," C. R. Acad. Sci. Paris Ser. II 307, 323 (1988).
19. Y. Sone, T. Ohwada, and K. Aoki, "Evaporation and condensation of a rarefied gas between its two parallel condensed phases with different temperatures and negative temperature-gradient phenomenon - Numerical analysis of the Boltzmann equation for hard-sphere molecules," in Mathematical Aspects of Fluid and Plasma Dynamics, Lecture Notes in Mathematics 1460, edited by G. Toscani, V. Boffi, and S. Rionero (Springer-Verlag, Berlin, 1991), p. 186.
20. K. Aoki and N. Masukawa, "Gas flows caused by evaporation and condensation on two parallel condensed phases and the negative temperature gradient: Numerical analysis by using a nonlinear kinetic equation," Phys. Fluids 6, 1379 (1994).
21. H. Cabannes, "Evaporation and condensation problems in discrete kinetic theory," Eur. J. Mech. B/Fluids 13, 685 (1994).
22. A. d'Almeida and R. Gatignol, "Boundary conditions in discrete kinetic theory and evaporation and condensation problems," Eur. J. Mech. B/ Fluids 16, 401 (1997).
23. Y. Pao, "Evaporation in a vapor-gas mixture," J. Chem. Phys. 59, 6688 (1973).
24. J. C. Hass and G. S. Springer, "Mass transfer through binary gas mixtures," Trans. ASME Ser. C 95, 263 (1973).
25. T. Matsushita, "Evaporation and condensation in a vapor-gas mixture," in Rarefied Gas Dynamics, edited by J. L. Potter (AIAA, New York, 1977), p. 1213.
26. T. Soga, "Kinetic analysis of evaporation and condensation in a vapor-gas mixture," Phys. Fluids 25, 1978 (1982).
27. Y. Onishi, "A two-surface problem of evaporation and condensation in a vapor-gas mixture," in Rarefied Gas Dynamics, edited by H. Oguchi (University of Tokyo Press, Tokyo, 1984), p. 875.
28. Y. Onishi, "Nonlinear analysis for evaporation and condensation of a vapor-gas mixture between the two plane condensed phases. Part I: Concentration of inert gas ∼O(1)," in Rarefied Gas Dynamics: Physical Phenomena, edited by E. P. Muntz, D. P. Weaver, and D. H. Campbell (AIAA, Washington, DC, 1989), p. 470.
29. Y. Onishi, "Nonlinear analysis for evaporation and condensation of a vapor-gas mixture between the two plane condensed phases. Part II: Concentration of inert gas ∼O(Kn)," in Ref. 28, p. 492.
30. D. Bedeaux, J. A. M. Smit, L. J. F. Hermans, and T. Ytrehus, "Slow evaporation and condensation II. A dilute mixture," Physica A 182, 388 (1992).
31. P. L. Bhatnagar, E. P. Gross, and M. Krook, "A model for collision processes in gases. I. Small amplitude processes in charged and neutral one-component systems," Phys. Rev. 94, 511 (1954).
32. P. Welander, "On the temperature jump in a rarefied gas," Ark. Fys. 7, 507 (1954).
33. M. N. Kogan, "On the equations of motion of a rarefied gas," Appl. Math. Mech. 22, 597 (1958).
34. G. A. Bird, Molecular Gas Dynamics (Oxford University Press, Oxford, 1976).
35. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford University Press, Oxford, 1994).
36. C. Cercignani, "Existence and uniqueness in the large for boundary value problems in kinetic theory," J. Math. Phys. 8, 1653 (1967).
37. L. Arkeryd, C. Cercignani, and R. Illner, "Measure solutions of the steady Boltzmann equation in a slab," Commun. Math. Phys. 142, 285 (1991).
38. S. Ukai, "Stationary solutions of the BGK model equation on a finite interval with large boundary data," Transp. Theory Stat. Phys. 21, 487 (1992).
39. L. Arkeryd and A. Nouri, "A compactness result related to the stationary Boltzmann equation in a slab, with applications to the existence theory," Indiana Univ. Math. J. 44, 815 (1995).
40. M. N. Kogan, Rarefied Gas Dynamics (Plenum, New York, 1969).
41. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases, 3rd ed. (Cambridge University Press, London, 1970).
42. F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1965), p. 301.
43. α being replaced by u [see Eq. (9c)], is also used in the literature (e.g., Refs. 40 and 41).
44. C. Cercignani, The Boltzmann Equation and Its Applications (Springer-Verlag, New York, 1988), Chap. IV.
45. H. Grad, "Principle of the kinetic theory of gases," in Handbuch der Physik, edited by S. Flügge (Springer-Verlag, Berlin, 1958), Vol. 12, p. 205.
46. Y. Sone, K. Aoki, and T. Doi, "Kinetic theory analysis of gas flows condensing on a plane condensed phase: Case of a mixture of a vapor and a noncondensable gas," Transp. Theory Stat. Phys. 21, 297 (1992).
47. K. Aoki and T. Doi, "High-speed vapor flows condensing on a plane condensed phase in the presence of a noncondensable gas," in Rarefied Gas Dynamics: Theory and simulations, edited by B. D. Shizgal and D. P. Weaver (AIAA, Washington, DC, 1994), p. 521.
48. T. Doi, K. Aoki, and Y. Sone, "Numerical analysis of unsteady evaporating flows from a plane condensed phase into a noncondensable gas on the basis of kinetic theory," J. Vac. Soc. Jpn. 37, 143 (1994) (in Japanese).
49. T. Doi, "Numerical analysis of unsteady evaporating flows from a plane condensed phase into a noncondensable gas on the basis of kinetic theory II," J. Vac. Soc. Jpn. 38, 201 (1995) (in Japanese).
50. Y. Sone, "Kinetic theory of evaporation and condensation - Linear and nonlinear problems," J. Phys. Soc. Jpn. 45, 315 (1978).
51. T. Ytrehus, "Theory and experiments on gas kinetics in evaporation," in Ref. 25, p. 1197.
52. M. D. Arthur and C. Cercignani, "Non-existence of a steady rarefied supersonic flow in a half-space," Z. Angew. Math. Phys. 31, 634 (1980).
53. Y. Sone and H. Sugimoto, "Strong evaporation from a plane condensed phase," in Adiabatic Waves in Liquid-Vapor Systems, edited by G. E. A. Meier and P. A. Thompson (Springer-Verlag, Berlin, 1990), p. 293.
54. Y. Sone and K. Aoki, Molecular Gas Dynamics (Asakura, Tokyo, 1994) (in Japanese).
55. T. Ytrehus and J. A. Alvestad, "A Mott-Smith solution for nonlinear condensation," in Rarefied Gas Dynamics, edited by S. S. Fisher (AIAA, New York, 1981), p. 330.
56. Y. Sone, K. Aoki, and I. Yamashita, "A study of unsteady strong condensation on a plane condensed phase with special interest in formation of steady profile," in Ref. 17, p. 236.
57. K. Aoki, Y. Sone, and T. Yamada, "Numerical analysis of gas flows condensing on its plane condensed phase on the basis of kinetic theory," Phys. Fluids A 2, 1867 (1990).
58. M. N. Kogan and A. A. Abramov, "Direct simulation solution of the strong evaporation and condensation problem," in Rarefied Gas Dynamics, edited by A. E. Beylich (VCH, Weinheim, 1991), p. 1251.
59. A. P. Kryukov, "Strong subsonic and supersonic condensation on a plane surface," in Ref. 58, p. 1278.
60. Y. Sone, F. Golse, T. Ohwada, and T. Doi, "Analytical study of transonic flows of a gas condensing on its plane condensed phase on the basis of kinetic theory," to appear in Eur. J. Mech. B/Fluids.
61. V. Garzó, A. Santos, and J. J. Brey, "A kinetic model for a multicomponent gas," Phys. Fluids A 1, 380 (1989).
62. The model in Ref. 61 reduces to the BGK model for a single-component gas.
63. T. Doi, Doctoral dissertation, Kyoto University, 1997 (in Japanese).
64. F. B. Pidduck, "The kinetic theory of the motion of ions in gases," Proc. Lond. Math. Soc. 15, 89 (1915).
65. C. L. Pekeris, "Solution of the Boltzmann-Hilbert integral equation," Proc. Natl. Acad. Sci. USA 41, 661 (1955).
66. H0 in the case (ii) was carried out on the basis of the model Boltzmann equation, not hardsphere molecules.
67. Y. Sone, Y. Waniguchi, and K. Aoki, "One-way flow of a rarefied gas induced in a channel with a periodic temperature distribution," Phys. Fluids 8, 2227 (1996).
68. II). This is a special case of the phenomenon of the negative temperature gradient that was pointed out in Ref. 11 and discussed in Refs. 1, 12, 14, 16, 19, and 20 (the physical mechanism was clarified in Ref. 1).