On the Reynolds equation for linearized models of the Boltzmann operator. (English) Zbl 1136.82018

Authors’ abstract: Rarefied gas flows in ultra-thin film slider bearings are studied in a wide range of Knudsen numbers. The generalized Reynolds equation, first derived by S. Fukui and R. Kaneko (1987, 1988, 1990) on the basis of the linearized Bhatnagar-Gross-Krook (BGK) Boltzmann equation, has been extended by considering a more refined kinetic model of the collisional Boltzmann operator, i.e. the linearized ellipsoidal statistical model (ES) which allows the Prandtl number to assume its proper value [C. Cercignani and G. Tironi [Phys. Fluids 9, 343–350 (1966; Zbl 0139.22701)]. Since the generalized Reynolds equations is a flow rate-based model and is obtained by calculating the fundamental flows in the lubrication film (i.e. the Poiseuille and Couette flows), the plane Poiseuille-Couette flow problem between parallel plates has been preliminary investigated by means of the linearized ES model. General boundary conditions of Maxwell’s type have been considered by allowing for bounding surfaces with different physical properties.


82B40 Kinetic theory of gases in equilibrium statistical mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics


Zbl 0139.22701
Full Text: DOI


[1] DOI: 10.1063/1.868377 · Zbl 0832.76064
[2] DOI: 10.1103/PhysRev.94.511 · Zbl 0055.23609
[3] Cercignani C., Mathematical Methods in Kinetic Theory (1969) · Zbl 0191.25103
[4] Cercignani C., The Boltzmann Equation and its Applications (1988) · Zbl 0646.76001
[5] Cercignani C., Rarefied Gas Dynamics (2000) · Zbl 0961.76002
[6] Cercignani C., Slow Rarefied Flows: Theory and Application to Micro-Electro Mechanical Systems (2006) · Zbl 1097.82001
[7] DOI: 10.1063/1.1729249
[8] DOI: 10.1081/TT-200053939 · Zbl 1076.82041
[9] DOI: 10.1063/1.1764700 · Zbl 1187.76086
[10] Cercignani, C., Lampis, M. and Lorenzani, S. Flow of a rarefied gas between parallel and almost parallel plates.Rarefied Gas Dynamics: 24th International Symposium on Rarefied Gas Dynamics, AIP Conference Proceedings 762. New York. Edited by: Capitelli, M. pp.719–724. Springer.
[11] DOI: 10.1063/1.2335847 · Zbl 1262.76087
[12] Cercignani C., Il Nuovo Cimento 43 pp 63– (1966)
[13] DOI: 10.1147/rd.345.0660
[14] Fukui S., JSME International Journal 30 pp 1660– (1987)
[15] DOI: 10.1115/1.3261594
[16] DOI: 10.1115/1.2920234
[17] DOI: 10.1115/1.555384
[18] Jiang, J. Z., Shen, C. and Fan, J. Statistical simulation of thin-film bearings.Rarefied Gas Dynamics: 24th International Symposium on Rarefied Gas Dynamics, AIP Conference Proceedings 762. New York. Edited by: Capitelli, M. pp.180–185. Springer.
[19] DOI: 10.1063/1.369810
[20] DOI: 10.1016/0043-1648(93)90197-T
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