Nonlinear transport for a dilute gas in steady Couette flow

Physics of Fluids

Volumn 9, Issue 3, 1997, Pages 776-787

  Garzo V ^a   Lopez De Haro M ^b  

^a UNIVERSITY OF EXTREMADURA   (Spain)

^b INSTITUTO DE CIENCIAS FÍSICAS   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

COUETTE FLOW; HYDRODYNAMICS; TEMPERATURE; VELOCITY GRADIENT;

EID: 0030846474     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.869232     Document Type: Article

References (22)

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2. M. Tijs and A. Santos, "Combined heat and momentum transport in a dilute gas," Phys. Fluids 7, 2858 (1995).
3. 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).
4. J. J. Brey, A. Santos, and J. W. Dufty, "Heat and momentum trandport far from equilibrium," Phys. Rev. A 36, 2842 (1987).
5. V. Garzó and M. López de Haro, "Kinetic model for heat and momentum transport," Phys. Fluids 6, 3787 (1994).
6. G. Liu, "A method for constructing a model for the Boltzmann equation," Phys. Fluids A 2, 277 (1990).
7. L. H. Holway, "New statistical models for kinetic theory: Methods of construction," Phys. Fluids 9, 1658 (1966).
8. C. Truesdell and R. Muncaster, Fundamentals of Maxwell's Kinetic Theory of a Simple Monoatomic Gas (Academic, New York, 1980), Chap. XIV: R. Zwanzig, "Nonlinear shear viscosity of a gas," J. Chem. Phys. 71, 4416 (1979); A. Santos and J. J. Brey, "Far from equilibrium velocity distribution of a dilute gas," Physica A 174, 355 (1991).
9. C. Truesdell and R. Muncaster, Fundamentals of Maxwell's Kinetic Theory of a Simple Monoatomic Gas (Academic, New York, 1980), Chap. XIV: R. Zwanzig, "Nonlinear shear viscosity of a gas," J. Chem. Phys. 71, 4416 (1979); A. Santos and J. J. Brey, "Far from equilibrium velocity distribution of a dilute gas," Physica A 174, 355 (1991).
10. C. Truesdell and R. Muncaster, Fundamentals of Maxwell's Kinetic Theory of a Simple Monoatomic Gas (Academic, New York, 1980), Chap. XIV: R. Zwanzig, "Nonlinear shear viscosity of a gas," J. Chem. Phys. 71, 4416 (1979); A. Santos and J. J. Brey, "Far from equilibrium velocity distribution of a dilute gas," Physica A 174, 355 (1991).
11. E. S. Asmolov, N. K. Makashev, and V. I. Nosik, "Heat transfer between parallel plates in a gas of Maxwellian molecules," Sov. Phys. Dokl. 24, 892 (1979); A. Santos, J. J. Brey, and V. Garzó, "Kinetic model for steady heat flow," Phys. Rev. A 34, 5047 (1986).
12. E. S. Asmolov, N. K. Makashev, and V. I. Nosik, "Heat transfer between parallel plates in a gas of Maxwellian molecules," Sov. Phys. Dokl. 24, 892 (1979); A. Santos, J. J. Brey, and V. Garzó, "Kinetic model for steady heat flow," Phys. Rev. A 34, 5047 (1986).
13. S. Chapman and T. G. Cowling, The Mathematical Theory of Nonuniform Gases (Cambridge University Press, Cambridge, 1970).
14. V. Garzó, "Transport equation from the Liu model," Phys. Fluids A 3, 1980 (1991).
15. In the case of the uniform shear flow, see J. Gómez Ordoñez, J. J. Brey, and A. Santos, "Velocity distribution function of a dilute gas under uniform shear flow: Comparison between a Monte Carlo simulation method and the Bhatnagar-Gross-Krook equation," Phys. Rev. A 41, 810 (1990); J. M. Montanero, A. Santos, and V. Garzó, "Monte Carlo simulation of the Boltzmann equation for uniform shear flow," Phys. Fluids 8, 1981 (1996). In the case of the steady Fourier flow, see J. M. Montanero, M. Alaoui, A. Santos, and V. Garzó, "Monte Carlo simulation of the Boltzmann equation for steady Fourier flow," Phys. Rev. E 49, 367 (1994).
16. In the case of the uniform shear flow, see J. Gómez Ordoñez, J. J. Brey, and A. Santos, "Velocity distribution function of a dilute gas under uniform shear flow: Comparison between a Monte Carlo simulation method and the Bhatnagar-Gross-Krook equation," Phys. Rev. A 41, 810 (1990); J. M. Montanero, A. Santos, and V. Garzó, "Monte Carlo simulation of the Boltzmann equation for uniform shear flow," Phys. Fluids 8, 1981 (1996). In the case of the steady Fourier flow, see J. M. Montanero, M. Alaoui, A. Santos, and V. Garzó, "Monte Carlo simulation of the Boltzmann equation for steady Fourier flow," Phys. Rev. E 49, 367 (1994).
17. In the case of the uniform shear flow, see J. Gómez Ordoñez, J. J. Brey, and A. Santos, "Velocity distribution function of a dilute gas under uniform shear flow: Comparison between a Monte Carlo simulation method and the Bhatnagar-Gross-Krook equation," Phys. Rev. A 41, 810 (1990); J. M. Montanero, A. Santos, and V. Garzó, "Monte Carlo simulation of the Boltzmann equation for uniform shear flow," Phys. Fluids 8, 1981 (1996). In the case of the steady Fourier flow, see J. M. Montanero, M. Alaoui, A. Santos, and V. Garzó, "Monte Carlo simulation of the Boltzmann equation for steady Fourier flow," Phys. Rev. E 49, 367 (1994).
18. C. S. Kim, J. W. Dufty, A. Santos, and J. J. Brey, "Analysis of nonlinear transport in Couette flow," Phys. Rev. A 40, 7165 (1989).
19. In the uniform shear flow state, the system is sheared by applying Lees-Edwards periodic boundary conditions so that the density and tempetature are homogeneous. As a consequence, the rheological properties derived in this problem are different to those obtained in the planar Coutte state [see for instance, A. Santos, V. Garzó, and J. J. Brey, "Comparison berween the homogeneous-shear and the sliding-boundary methods to produce shear flow," Phys. Rev. A 46, 8018 (1992)]. Anyway, recently one of the authors has proved that the ES and BGK models lead to the same transport coefficients in the uniform shear flow problem with a suitable scaling of the collision frequency (V. Garzó, unpublished).
20. In the uniform shear flow state, the system is sheared by applying Lees-Edwards periodic boundary conditions so that the density and tempetature are homogeneous. As a consequence, the rheological properties derived in this problem are different to those obtained in the planar Coutte state [see for instance, A. Santos, V. Garzó, and J. J. Brey, "Comparison berween the homogeneous-shear and the sliding-boundary methods to produce shear flow," Phys. Rev. A 46, 8018 (1992)]. Anyway, recently one of the authors has proved that the ES and BGK models lead to the same transport coefficients in the uniform shear flow problem with a suitable scaling of the collision frequency (V. Garzó, unpublished).
21. ij, and consequently the ES model reduce to the BGK model.
22. It is worth pointing out that when one not consider atomic particales but mesoscopic ones, such as colloids or micelles, the shear rates required to observe non-Newtonian effects can be attainable in laboretory conditons.