Couette flow of a binary mixture of rigid-sphere gases described by the linearized Boltzmann equation

European Journal of Mechanics, B/Fluids

Volumn 27, Issue 6, 2008, Pages 823-836

  Garcia, R D M ^a   Siewert, C E ^b  

^a HSH Scientific Computing   (Brazil)

^b NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Binary mixtures; Couette flow; Linearized Boltzmann equation; Rarefied gas dynamics; Rigid spheres

Indexed keywords

ARGON; BINARY MIXTURES; BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; CHANNEL FLOW; FLOW MEASURING INSTRUMENTS; HELIUM; INERT GASES; LINEAR EQUATIONS; LINEARIZATION; MAXWELL EQUATIONS; MIXTURES; MOLYBDENUM; SPHERES; TANTALUM; TRANSITION METALS;

ACCURATE NUMERICAL RESULTS; COUETTE FLOW; COUETTE FLOWS; DISCRETE ORDINATES METHODS; GAS PARTICLES; HEAT FLOWS; LINEARIZED BOLTZMANN EQUATION; MAXWELL BOUNDARY CONDITIONS; PLANE COUETTE FLOW; RAREFIED GAS DYNAMICS; RIGID SPHERES; STRESS PRO FILES;

BOLTZMANN EQUATION;

EID: 50849083801     PISSN: 09977546     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.euromechflu.2008.01.004     Document Type: Article

References (29)

1. Cercignani C. Mathematical Methods in Kinetic Theory (1969), Plenum Press, New York
2. Cercignani C. Theory and Application of the Boltzmann Equation (1975), Elsevier, New York
3. Cercignani C. Rarefied Gas Dynamics: from Basic Concepts to Actual Calculations (2000), Cambridge University Press, Cambridge
4. Williams M.M.R. Mathematical Methods in Particle Transport Theory (1971), Butterworth, London
5. Ferziger J.H., and Kaper H.G. Mathematical Theory of Transport Processes in Gases (1972), North-Holland, Amsterdam
6. Sharipov F., and Seleznev V. Data on internal rarefied gas flows. J. Phys. Chem. Ref. Data 27 (1998) 657-706
7. Williams M.M.R. A review of the rarefied gas dynamics theory associated with some classical problems in flow and heat transfer. Z. Angew. Math. Phys. 52 (2001) 500-516
8. Onishi Y. On the behavior of a slightly rarefied gas mixture over plane boundaries. Z. Angew. Math. Phys. 37 (1986) 573-596
9. Valougeorgis D. Couette flow of a binary gas mixture. Phys. Fluids 31 (1988) 521-524
10. Siewert C.E. Couette flow for a binary gas mixture. J. Quant. Spectros. Radiat. Transfer 70 (2001) 321-332
11. Sharipov F., Cumin L.M.G., and Kalempa D. Plane Couette flow of binary gaseous mixture in the whole range of Knudsen number. Eur. J. Mech. B Fluids 23 (2004) 899-906
12. Garcia R.D.M., and Siewert C.E. The McCormack model for gas mixtures: Plane Couette flow. Phys. Fluids 17 (2005) 037102
13. Garcia R.D.M., Siewert C.E., and Williams M.M.R. A formulation of the linearized Boltzmann equations for a binary mixture of rigid spheres. Eur. J. Mech. B Fluids 24 (2005) 614-620
14. Garcia R.D.M., and Siewert C.E. Some exact results basic to the linearized Boltzmann equations for a binary mixture of rigid spheres. Z. Angew. Math. Phys. 57 (2006) 999-1010
15. Garcia R.D.M., and Siewert C.E. Some solutions (linear in the spatial variables) and generalized Chapman-Enskog functions basic to the linearized Boltzmann equations for a binary mixture of rigid spheres. Z. Angew. Math. Phys. 58 (2007) 262-288
16. Garcia R.D.M., and Siewert C.E. The temperature-jump problem based on the linearized Boltzmann equation for a binary mixture of rigid spheres. Eur. J. Mech. B Fluids 26 (2007) 132-153
17. Garcia R.D.M., and Siewert C.E. The viscous-slip, diffusion-slip, and thermal-creep problems for a binary mixture of rigid spheres described by the linearized Boltzmann equation. Eur. J. Mech. B Fluids 26 (2007) 749-778
18. Garcia R.D.M., and Siewert C.E. Heat transfer between parallel plates: An approach based on the linearized Boltzmann equation for a binary mixture of rigid-sphere gases. Phys. Fluids 19 (2007) 027102
19. Garcia R.D.M., and Siewert C.E. Channel flow of a binary mixture of rigid spheres described by the linearized Boltzmann equation and driven by temperature, pressure, and concentration gradients. SIAM J. Appl. Math. 67 (2007) 1041-1063
20. McCormack F.J. Construction of linearized kinetic models for gaseous mixtures and molecular gases. Phys. Fluids 16 (1973) 2095-2105
21. Barichello L.B., and Siewert C.E. A discrete-ordinates solution for a non-grey model with complete frequency redistribution. J. Quant. Spectros. Radiat. Transfer 62 (1999) 665-675
22. Siewert C.E., and Valougeorgis D. Concise and accurate solutions to half-space binary-gas flow problems defined by the McCormack model and specular and diffuse wall conditions. Eur. J. Mech. B Fluids 23 (2004) 709-726
23. Sharipov F., and Kalempa D. Velocity slip and temperature jump coefficients for gaseous mixtures. I. Viscous slip coefficient. Phys. Fluids 15 (2003) 1800-1806
24. Lord R.G. Tangential momentum accommodation coefficients of rare gases on polycrystalline metal surfaces. In: Leith Potter J. (Ed). Rarefied Gas Dynamics, Part I. Progress in Astronautics and Aeronautics vol. 51 (1977), AIAA, New York 531-538
25. Garcia R.D.M., and Siewert C.E. The linearized Boltzmann equation: Sound-wave propagation in a rarefied gas. Z. Angew. Math. Phys. 57 (2006) 94-122
26. Siewert C.E. Poiseuille, thermal creep and Couette flow: results based on the CES model of the linearized Boltzmann equation. Eur. J. Mech. B Fluids 21 (2002) 579-597
27. Siewert C.E. The linearized Boltzmann equation: Concise and accurate solutions to basic flow problems. Z. Angew. Math. Phys. 54 (2003) 273-303
28. Chapman S., and Cowling T.G. The Mathematical Theory of Non-Uniform Gases (1952), Cambridge University Press, Cambridge
29. Pekeris C.L. Solution of the Boltzmann-Hilbert integral equation. Proc. Natl. Acad. Sci. 41 (1955) 661-669