Evaporation and condensation of a binary mixture of vapors on a plane condensed phase: Numerical analysis of the linearized Boltzman equation

Physics of Fluids

Volumn 17, Issue 4, 2005, Pages

  Yasuda, Shugo ^a   Takata, Shigeru ^a   Aoki, Kazuo ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

CHEBYSHEV APPROXIMATION; CONDENSATION; EVAPORATION; FINITE DIFFERENCE METHOD; NUMERICAL ANALYSIS; POLYNOMIAL APPROXIMATION; PROBLEM SOLVING; VAPORS;

BOLZMANN EQUATION; GAS MIXTURE; HALF-SPACE PROBLEM; HARD-SPHERE MOLECULES;

BINARY MIXTURES;

BINARY MIXTURE;

EID: 17544366526     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1882252     Document Type: Article

References (46)

1. M. N. Kogan, "Kinetic theory in aerothermodynamics," Prog. Aerosp. Sci. PAESD6 0376-0421 10.1016/0376-0421(92)90007-5 29, 271 (1992).
2. T. Ytrehus, "Molecular-flow effects in evaporation and condensation at interfaces," Multiphase Sci. Technol. ZZZZZZ 0276-1459 10.1108/ 09576069810217793 9, 205 (1997).
3. Y. Sone, "Kinetic theoretical studies of the half-space problem of evaporation and condensation," Transp. Theory Stat. Phys. TTSPB4 0041-1450 29, 227 (2000).
4. Y. Sone, Kinetic Theory and Fluid Dynamics, Modeling and Simulation in Science, Engineering and Technology (Birkhäuser, Boston, 2002).
5. V. I. Roldughin and V. M. Zhdanov, "Non-equilibrium thermodynamics and kinetic theory of gas mixtures in the presence of interfaces," Adv. Colloid Interface Sci. ACISB9 0001-8686 10.1016/ S0001-8686(01)00092-6 98, 121 (2002).
6. K. Aoki, S. Takata, and S. Taguchi, "Vapor flows with evaporation and condensation in the continuum limit: Effect of a trace of noncondensable gas," Eur. J. Mech. B/FluidsEJBFEV0997-754610.1016/ S0997-7546(02)00008-0 22, 51 (2003).
7. Y. Sone and Y. Onishi, "Kinetic theory of evaporation and condensation-Hydrodynamic equation and slip boundary condition," J. Phys. Soc. Jpn. JUPSAU 0031-9015 44, 1981 (1978).
8. 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. JUPSAU 0031-9015 47, 1676 (1979).
9. 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 Advances in Kinetic Theory and Continuum Mechanics, edited by R. Gatignol and Soubbaramayer (Springer, Berlin, 1991), p. 43.
10. S. Takata "Diffusion slip for a binary mixture of hard-sphere molecular gases: Numerical analysis based on the linearized Boltzmann equation," in Rarefied Gas Dynamics, edited by T. J. Bartel and M. A. Gallis (AIP, Melville, NY, 2001), p. 22
11. S. Takata, S. Yasuda, S. Kosuge, and K. Aoki, "Numerical analysis of thermal-slip and diffusion-slip flows of a binary mixture of hard-sphere molecular gases," Phys. Fluids PHFLE6 1070-6631 10.1063/ 1.1624075 15, 3745 (2003).
12. S. Yasuda, S. Takata, and K. Aoki, "Numerical analysis of the shear flow of a binary mixture of hard-sphere gases over a plane wall," Phys. Fluids PHFLE6 1070-6631 10.1063/1.1714665 16, 1989 (2004).
13. Y. Sone, T. Ohwada, and K. Aoki, "Temperature jump and Knudsen layer in a rarefied gas over a plane wall: Numerical analysis of the linearized Boltzmann equation for hard-sphere molecules," Phys. Fluids APFADEB 0899-8213 10.1063/1.857457 1, 363 (1989).
14. 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 Rarefied Gas Dynamics, edited by V. Boffi and C. Cercignani (Teubner, Stuttgart, 1986), Vol. II, p. 323.
15. Y. Sone, K. Aoki, H. Sugimoto, and T. Yamada, "Steady evaporation and condensation on a plane condensed phase," Theor Appl. Mech. ZZZZZZ 0285-6042 10.1016/8756-3282(96)88871-5 19 (3), 89 (1988).
16. Y. Sone and H. Sugimoto, "Strong evaporation from a plane condensed phase," in Adiabatic Waves in Liquid-Vapor Systems, IUTAM Symposium, Göttingen, 1989, edited by G. E. A. Meier and P. A. Thompson (Springer, Berlin, 1990), p. 293.
17. 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 APFADEB 0899-8213 10.1063/ 1.857907 3, 2260 (1991).
18. 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," Eur. J. Mech. B/Fluids EJBFEV 0997-7546 10.1016/S0997-7546(98)80260-4 17, 277 (1998).
19. S. Ukai, T. Yang, and S.-H. Yu, "Nonlinear boundary layers of the Boltzmann equation: I. Existence," Commun. Math. Phys. CMPHAY 0010-3616 10.1007/s00220-003-0822-8 236, 373 (2003).
20. S. Ukai, T. Yang, and S.-H. Yu, "Nonlinear stability of boundary layers of the Boltzmann equation, I. The case M∞<-1," Commun. Math. Phys. CMPHAY 0010-3616 10.1007/s00220-003-0976-4 244, 99 (2004).
21. Y. Sone, "Kinetic theory of evaporation and condensation - Linear and nonlinear problems," J. Phys. Soc. Jpn. JUPSAU 0031-9015 45, 315 (1978).
22. S. Takata, "Half-space problem of weak evaporation and condensation of a binary mixture of vapors," in Rarefied Gas Dynamics, edited by M. Capitelli (AIP, New York, in press).
23. J. W. Cipolla, Jr., H. Lang, and S. K. Loyalka, "Temperature and partial pressure jumps during evaporation and condensation of a multicomponent gas mixture," in Rarefied Gas Dynamics, edited by M. Becker and M. Fiebig (DFLR, Porz-Wahn, 1974), Vol. II, F. 4.
24. I. V. Volkov and V. S. Galkin, "Analysis of temperature jump and partial pressure coefficients of a binary evaporating gas mixture," Fluid Dyn. FLDYAH 0015-4628 26, 914 (1991).
25. Y. Onishi, "Kinetic theory analysis for temperature and density fields of a slightly rarefied binary gas mixture over a solid wall," Phys. Fluids PHFLE6 1070-6631 10.1063/1.869164 9, 226 (1997).
26. 3∞ = 0 is concluded because of the existence and uniqueness theorem to be described in Sec. III A. In contrast, for the nonlinear problem, it is not the case, and one has to consider the nonzero tangential flow in general
27. M. N. Kogan, Rarefied Gas Dynamics (Plenum, New York, 1969).
28. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases, 3rd ed. (Cambridge University Press, Cambridge, 1995).
29. J. O. Hirshfelder, C. F. Curtiss, and R. B. Bird, Molecular Theory of Gases and Liquids (Wiley, New York, 1954).
30. K. Aoki, C. Bardos, and S. Takata, "Knudsen layer for gas mixtures," J. Stat. Phys. JSTPBS 0022-4715 10.1023/A:1023876025363 112, 629 (2003).
31. H. Grad, "Singular and nonuniform limits of solutions of the Boltzmann equation," in Transport Theory, edited by R. Bellman, G. Birkhoff, and I. Abu-Shumays (AMS, Providence, RI, 1969), p. 269.
32. N. B. Maslova, "Kramers problem in the kinetic theory of gases," USSR Comput. Math. Math. Phys. CMMPA9 0965-5425 22, 208 (1982).
33. C. Bardos, R. E. Caflisch, and B. Nicolaenko, "The Milne and Kramers problems for the Boltzmann equation of a hard sphere gas," Commun. Pure Appl. Math. CPMAMV 0010-3640 39, 323 (1986).
34. C. Cercignani, "Half-space problems in the kinetic theory of gases," in Trends in Applications of Pure Mathematics to Mechanics, edited by E. Kröner and K. Kirchgässner (Springer, Berlin, 1986), p. 35.
35. F. Coron, F. Golse, and C. Sulem, "A classification of well-posed kinetic layer problems," Commun. Pure Appl. Math. CPMAMV 0010-3640 41, 409 (1988).
36. F. Golse and F. Poupaud, "Stationary solutions of the linearized Boltzmann equation in a half-space," Math. Methods Appl. Sci. MMSCDB 0170-4214 11, 483 (1989).
37. Y. Sone, T. Ohwada, and K. Aoki, "Evaporation and condensation on a plane condensed phase: Numerical analysis of the linearized Boltzmann equation for hard-sphere molecules," Phys. Fluids APFADEB 0899-8213 10.1063/1.857316 1, 1398 (1989).
38. C. Gasquet and P. Witomski, Fourier Analysis and Applications (Springer, New York, 1999).
39. A. Frezzotti, "Kinetic theory description of the evaporation of multi-component substances," in Rarefied Gas Dynamics, edited by C. Shen (Peking University Press, Beijing, 1997), p. 837.
40. Y. Sone and S. Takata, "Discontinuity of the velocity distribution function in a rarefied gas around a convex body and the S layer at the bottom of the Knudsen layer," Transp. Theory Stat. Phys. TTSPB4 0041-1450 21, 501 (1992).
41. S. Takata, "Kinetic theory analysis of the two-surface problem of a vapor-vapor mixture in the continuum limit," Phys. Fluids PHFLE6 1070-6631 10.1063/1.1723464 16, 2182 (2004).
42. Y. Sone, K. Aoki, S. Takata, H. Sugimoto, and A. V. Bobylev, "Inappropriateness of the heat-conduction equation for description of a temperature field of a stationary gas in the continuum limit: Examination by asymptotic analysis and numerical computation of the Boltzmann equation," Phys. Fluids PHFLE6 1070-6631 10.1063/1.868846 8, 628 (1996); PHFLE61070-663110.1063/1.8691338, 841(E) (1996).
43. Y. Sone, "Flows induced by temperature fields in a rarefied gas and their ghost effect on the behavior of a gas in the continuum limit," Annu. Rev. Fluid Mech. ARVFA3 0066-4189 10.1146/ annurev.fluid.32.1.779 32, 779 (2000).
44. A. V. Bobylev, "Quasistationary hydrodynamics for the Boltzmann equation," J. Stat. Phys. JSTPBS 0022-4715 80, 1063 (1995).
45. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1968).
46. S. Takata, S. Yasuda, K. Aoki, and T. Shibata, "Various transport coefficients occurring in binary gas mixtures and their database," in Rarefied Gas Dynamics, edited by A. D. Ketsdever and E. P. Muntz (AIP, New York, 2003), p. 106.