Cylindrical Couette flow of a vapor-gas mixture: Ghost effect and bifurcation in the continuum limit

Physics of Fluids

Volumn 18, Issue 8, 2006, Pages

  Yoshida, Hiroaki ^a   Aoki, Kazuo ^a  

^a KYOTO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); BINARY MIXTURES; CONDENSATION; EVAPORATION; KINETIC THEORY; VAPORS;

COUETTE FLOW; CYLINDRICAL FLOW; FLOW BIFURCATION; GHOST EFFECT; VAPOR-GAS MIXTURE;

FLOW OF FLUIDS;

BIFURCATION (MATHEMATICS); BINARY MIXTURES; CONDENSATION; EVAPORATION; FLOW OF FLUIDS; KINETIC THEORY; VAPORS;

EID: 33748265276     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2336455     Document Type: Article

References (50)

1. C. Cercignani and F. Sernagiotto, "Cylindrical Couette flow of a rarefied gas," Phys. Fluids PFLDAS0031-917110.1063/1.1762263 10, 1200 (1967).
2. K. Nanbu, "Analysis of cylindrical Couette flows by use of the direction simulation method," Phys. Fluids PFLDAS0031-917110.1063/ 1.864565 27, 2632 (1984).
3. R. E. Khayat and B. C. Eu, "Nonlinear transport processes and fluid dynamics: Cylindrical Couette flow of Lennard-Jones fluids," Phys. Rev. A PLRAAN1050-294710.1103/PhysRevA.38.2492 38, 2492 (1988); R. E. Khayat and B. C. Eu,erratum, Phys. Rev. APLRAAN1050-294710.1103/ PhysRevA.40.1150.2 40, 1150 (1989).
4. R. E. Khayat and B. C. Eu, "Generalized hydrodynamics, normal-stress effects, and velocity slips in the cylindrical Couette flow of Lennard-Jones fluids," Phys. Rev. A PLRAAN1050-294710.1103/ PhysRevA.39.728 39, 728 (1989); R. E. Khayat and B. C. Eu,erratum, Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.40.1150.2 40, 1150 (1989).
5. F. Sharipov and G. Kremer, "Linear Couette flow between two rotating cylinders," Eur. J. Mech. B/Fluids EJBFEV0997-7546 15, 493 (1996).
6. F. Sharipov and G. Kremer, "Nonlinear Couette flow between two rotating cylinders," Transp. Theory Stat. Phys. TTSPB40041-1450 25, 217 (1996).
7. K. W. Tibbs, F. Baras, and A. L. Garcia, "Anomalous flow profile due to the curvature effect on slip length," Phys. Rev. E PLEEE81063-651X10.1103/PhysRevE.56.2282 56, 2282 (1997).
8. L. M. de Socio, N. Ianiro, and L. Marino, "Effects of the centrifugal forces on a gas between rotating cylinders," J. Thermophys. Heat Transfer JTHTEO0887-8722 14, 269 (2000).
9. L. M. de Socio and L. Marino, "Simulation and modelling of flows between rotating cylinders. Influence of Knudsen number," Math. Models Meth. Appl. Sci. MMMSEU0218-202510.1016/S0218-2025(00)00006-9 10, 73 (2000).
10. K. Aoki, H. Yoshida, T. Nakanishi, and A. L. Garcia, "Inverted velocity profile in the cylindrical Couette flow of a rarefied gas," Phys. Rev. E PLEEE81063-651X10.1103/PhysRevE.68.016302 68, 016302 (2003).
11. S. Yuhong, R. W. Barber, and D. R. Emerson, "Inverted velocity profiles in rarefied cylindrical Couette gas flow and the impact of the accommodation coefficient," Phys. Fluids PHFLE61070-663110.1063/ 1.1868034 17, 047102 (2005).
12. Y. Sone, H. Sugimoto, and K. Aoki, "Cylindrical Couette flows of a rarefied gas with evaporation and condensation: Reversal and bifurcation of flows," Phys. Fluids PHFLE61070-663110.1063/1.869863 11, 476 (1999).
13. Y. Sone, T. Ohwada, and Y. Makihara, "Bifurcation in cylindrical Couette flow with evaporation and condensation: Effect of initial condition," in Rarefied Gas Dynamics, edited by R. Brun, R. Campargue, R. Gatignol, and J.-C. Lengrand (Cépaduès-Éditions, Toulouse, 1999), Vol. 1, p. 511.
14. Y. Sone and T. Doi, "Analytical study of bifurcation of a flow of a gas between coaxial circular cylinders with evaporation and condensation," Phys. Fluids PHFLE61070-663110.1063/1.1289398 12, 2639 (2000).
15. Y. Sone, M. Handa, and H. Sugimoto, "Bifurcation studies of flows of a gas between rotating coaxial circular cylinders with evaporation and condensation by the Boltzmann system," Transp. Theory Stat. Phys. TTSPB40041-145010.1081/TT-120015504 31, 299 (2002).
16. L. Arkeryd and A. Nouri, "The stationary nonlinear Boltzmann equation in a Couette setting with multiple, isolated Lq-solutions and hydrodynamic limits," J. Stat. Phys.JSTPBS0022-471510.1007/ s10955-004-2708-3 118, 849 (2005).
17. 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.
18. Y. Sone, S. Takata, and H. Sugimoto, "The behavior of a gas in the continuum limit in the light of kinetic theory: The case of cylindrical Couette flows with evaporation and condensation," Phys. FluidsPHFLE61070-663110.1063/1.869125 8, 3403 (1996); Y. Sone, S. Takata, and H. Sugimoto,erratum, Phys. FluidsPHFLE61070-663110.1063/ 1.869648 10, 1239 (1998).
19. 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 PHFLE61070-663110.1063/1.868846 8, 628 (1996); Y. Sone, K. Aoki, S. Takata, H. Sugimoto, and A. V. Bobylev,erratum, Phys. FluidsPHFLE61070-663110.1063/1.869133 8, 841 (1996).
20. Y. Sone, "Continuum gas dynamics in the light of kinetic theory and new features of rarefied gas flows," in Rarefied Gas Dynamics, edited by C. Shen (Peking University Press, Beijing, 1997), p. 3.
21. 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. ARVFA30066-418910.1146/ annurev.fluid.32.1.779 32, 779 (2000).
22. Y. Sone, Kinetic Theory and Fluid Dynamics (Birkhäuser, Boston, 2002).
23. Y. Sone, M. Handa, and T. Doi, "Ghost effect and bifurcation in a gas between coaxial circular cylinders with different temperatures," Phys. Fluids PHFLE61070-663110.1063/1.1601614 15, 2903 (2003).
24. Y. Sone and T. Doi, "Ghost effect of infinitesimal curvature in the plane Couette flow of a gas in the continuum limit," Phys. FluidsPHFLE61070-663110.1063/1.1649738 16, 952 (2004).
25. Y. Sone, Molecular Gas Dynamics: Theory, Techniques, and Applications (Birkhäuser, Boston, 2006).
26. S. Takata and K. Aoki, "Two-surface problems of a multicomponent mixture of vapors and noncondensable gases in the continuum limit in the light of kinetic theory," Phys. Fluids PHFLE61070-663110.1063/ 1.870133 11, 2743 (1999).
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. C. Cercignani, Rarefied Gas Dynamics: From Basic Concepts to Actual Calculations (Cambridge University Press, 2000).
30. F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1965).
31. C. Cercignani and M. Lampis, "Kinetic models for gas-surface interactions," Transp. Theory Stat. Phys. TTSPB40041-1450 1, 101 (1971).
32. G. Nagayama and T. Tsuruta, "A general expression for the condensation coefficient based on transition state theory and molecular dynamics simulation," J. Chem. Phys. JCPSA60021-960610.1063/ 1.1528192 118, 1392 (2003).
33. R. Meland, A. Frezzotti, T. Ytrehus, and B. Hafskjold, "Nonequilibrium molecular-dynamics simulation of net evaporation and net condensation, and evaluation of the gas-kinetic boundary condition at the interphase," Phys. FluidsPHFLE61070-663110.1063/ 1.1630797 16, 223 (2004).
34. T. Ishiyama, T. Yano, and S. Fujikawa, "Molecular dynamics study of kinetic boundary condition at an interface between argon vapor and its condensed phase," Phys. Fluids PHFLE61070-663110.1063/1.1763936 16, 2899 (2004).
35. A. Frezzotti, L. Gibelli, and S. Lorenzani, "Mean field kinetic theory description of evaporation of a fluid into vacuum," Phys. Fluids PHFLE61070-663110.1063/1.1824111 17, 012102 (2005).
36. T. Ishiyama, T. Yano, and S. Fujikawa, "Kinetic boundary condition at a vapor-liquid interface," Phys. Rev. Lett. PRLTAO0031-900710.1103/PhysRevLett.95.084504 95, 084504 (2005).
37. Y. Sone, "Asymptotic theory of flow of rarefied gas over a smooth boundary I," in Rarefied Gas Dynamics, edited by L. Trilling and H. Y. Wachman (Academic, New York, 1969), p. 243.
38. Y. Sone, "Asymptotic theory of flow of rarefied gas over a smooth boundary II," in Rarefied Gas Dynamics, edited by D. Dini (Editrice Tecnico Scientifica, Pisa, Italy, 1971), Vol. II, p. 737.
39. 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, Berlin, 1991), p. 19.
40. 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/Fluids EJBFEV0997-754610.1016/ S0997-7546(02)00008-0 22, 51 (2003).
41. K. Aoki, S. Takata, and S. Kosuge, "Vapor flows caused by evaporation and condensation on two parallel plane surfaces: Effect of the presence of a noncondensable gas," Phys. Fluids PHFLE61070-663110.1063/1.869671 10, 1519 (1998).
42. S. Taguchi, K. Aoki, and S. Takata, "Vapor flows in the continuum limit in the presence of a small amount of noncondensable gas," Phys. Fluids PHFLE61070-663110.1063/1.1795271 16, 4105 (2004).
43. A. V. Bobylev, "Quasistationary hydrodynamics for the Boltzmann equation," J. Stat. Phys. JSTPBS0022-471510.1007/BF02179864 80, 1063 (1995).
44. Takata, K. Aoki, and T. Muraki, "Behavior of a vapor-gas mixture between two parallel plane condensed phases in the continuum limit," in Rarefied Gas Dynamics, edited by R. Brun, R. Campargue, R. Gatignol, and J.-C. Lengrand (Cépaduès-Éditions, Toulouse, 1999), Vol. 1, p. 479.
45. S. Takata and K. Aoki, "The ghost effect in the continuum limit for a vapor-gas mixture around condensed phases: Asymptotic analysis of the Boltzmann equation," Transp. Theory Stat. Phys.TTSPB40041-145010.1081/TT-100105368 30, 205 (2001); S. Takata and K. Aoki,erratum, Transp. Theory Stat. Phys.TTSPB40041-1450 31, 289 (2002).
46. S. Takata, "Kinetic theory analysis of the two-surface problem of a vapor-vapor mixture in the continuum limit," Phys. Fluids PHFLE61070-663110.1063/1.1723464 16, 2182 (2004).
47. 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, Melville, NY, 2003), p. 106.
48. G. A. Bird, Molecular Gas Dynamics (Oxford University Press, Oxford, 1976).
49. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Oxford University Press, Oxford, 1994).
50. C. F. Delale, "The Hilbert theory of transport phenomena in multiple gas mixtures," J. Chem. Phys. JCPSA60021-9606 83, 3069 (1985).