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Non-equilibrium dynamics of dense gas under tight confinement. (English) Zbl 1462.76203


MSC:

76T25 Granular flows
76N15 Gas dynamics (general theory)
82D05 Statistical mechanics of gases
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[1] Alam, M.; Mahajan, A.; Shivanna, D., On Knudsen-minimum effect and temperature bimodality in a dilute granular Poiseuille flow, J. Fluid Mech., 782, 99-126, (2015) · Zbl 1381.76380
[2] Aoki, K.; Takata, S.; Nakanishi, T., Poiseuille-type flow of a rarefied gas between two parallel plates driven by a uniform external force, Phys. Rev. E, 65, (2002)
[3] Aranson, I. S.; Tsimring, L. S., Patterns and collective behavior in granular media: theoretical concepts, Rev. Mod. Phys., 78, 641-692, (2006)
[4] Barbante, P.; Frezzotti, A.; Gibelli, L., A kinetic theory description of liquid menisci at the microscale, Kinet. Relat. Models, 8, 235-254, (2015) · Zbl 1362.82044
[5] Baus, M.; Colot, J. L., Thermodynamics and structure of a fluid of hard rods, disks, spheres, or hyperspheres from rescaled virial expansions, Phys. Rev. A, 36, 3912-3925, (1987)
[6] Bobylev, A. V.; Carrillo, J. A.; Gamba, I. M., On some properties of kinetic and hydrodynamic equations for inelastic interactions, J. Stat. Phys., 98, 743-773, (2000) · Zbl 1056.76071
[7] Brey, J. J.; Dufty, J. W.; Santos, A., Dissipative dynamics for hard spheres, J. Stat. Phys., 87, 1051-1066, (1997) · Zbl 0945.82562
[8] Brilliantov, N.; Pöschel, T., Kinetic Theory of Granular Gases, (2004), Oxford University Press · Zbl 1155.76386
[9] Cercignani, C.1963Plane Poiseuille flow and Knudsen minimum effect. In Rarefied Gas Dynamics (ed. Laurmann, J. A.), vol. II, pp. 92-101.
[10] Cercignani, C.; Lampis, M.; Lorenzani, S., On the Reynolds equation for linearized models of the Boltzmann operator, Transp. Theory Stat. Phys., 36, 257-280, (2007) · Zbl 1136.82018
[11] Chapman, S.; Cowling, T. G., The Mathematical Theory of Non-Uniform Gases, (1970), Cambridge University Press · JFM 65.1541.01
[12] Darabi, H.; Ettehad, A.; Javadpour, F.; Sepehrnoori, K., Gas flow in ultra-tight shale strata, J. Fluid Mech., 710, 641-658, (2012) · Zbl 1275.76196
[13] Esteban, M. J.; Perthame, B., On the modified Enskog equation for elastic and inelastic collisions. Models with spin, Ann. Inst. Henri Poincaré, 8, 289-308, (1991) · Zbl 0850.70141
[14] Frezzotti, A., A particle scheme for the numerical solution of the Enskog equation, Phys. Fluids, 9, 1329-1335, (1997) · Zbl 1185.76835
[15] Frezzotti, A., Molecular dynamics and Enskog theory calculation of shock profiles in a dense hard sphere gas, Comput. Math. Applics., 35, 103-112, (1998) · Zbl 0907.35101
[16] Frezzotti, A.; Gibelli, L.; Lorenzani, S., Mean field kinetic theory description of evaporation of a fluid into vacuum, Phys. Fluids, 17, (2005) · Zbl 1187.76165
[17] Fukui, S.; Kaneko, R., Analysis of ultra-thin gas film lubrication based on the linearized Boltzmann equation (influence of accommodation coefficient), JSME Intl J., 30, 1660-1666, (1987)
[18] Fukui, S.; Kaneko, R., A database for interpolation of Poiseuille flow rates for high Knudsen number lubrication problems, J. Tribol., 112, 78-83, (1990)
[19] Galvin, J. E.; Hrenya, C. M.; Wildman, R. D., On the role of the Knudsen layer in rapid granular flows, J. Fluid Mech., 585, 73-92, (2007) · Zbl 1119.76069
[20] Garcia-Rojo, R.; Luding, S.; Brey, J. J., Transport coefficients for dense hard-disk systems, Phys. Rev. E, 74, (2006)
[21] Garzó, V.; Dufty, J. W., Dense fluid transport for inelastic hard spheres, Phys. Rev. E, 59, 5895-5911, (1999)
[22] Goldstein, A.; Shapiro, M., Mechanics of collisional motion of granular materials. Part 1. General hydrodynamic equations, J. Fluid Mech., 282, 75-114, (1995) · Zbl 0881.76010
[23] Grmela, M., Kinetic equation approach to phase transitions, J. Stat. Phys., 3, 347-364, (1971)
[24] Gu, X. J.; Emerson, D. R., A high-order moment approach for capturing non-equilibrium phenomena in the transition regime, J. Fluid Mech., 636, 177-216, (2009) · Zbl 1183.76850
[25] Hadjiconstantinou, N. G., Comment on Cercignani’s second-order slip coefficient, Phys. Fluids, 15, 2352-2354, (2003)
[26] Henderson, D., Simple equation of state for hard disks, Mol. Phys., 30, 971-972, (1975)
[27] Holt, J. K.; Park, H. G.; Wang, Y.; Stadermann, M.; Artyukhin, A. B.; Grigoropoulos, C. P.; Noy, A.; Bakajin, O., Fast mass transport through sub-2-nanometer carbon nanotubes, Science, 312, 1034-1037, (2006)
[28] Karkheck, J.; Stell, G., Mean field kinetic theories, J. Chem. Phys., 75, 1475-1487, (1981)
[29] Karniadakis, G.; Beskok, A.; Aluru, N. R., Microflows and Manoflows: Fundamentals and Simulations, (2005), Springer
[30] Knudsen, M., Die Gesetze der Molekularströmung und der inneren Reibungsströmung der Gase durch Röhren, Ann. Phys., 333, 75-130, (1909) · JFM 40.0825.02
[31] Kon, M.; Kobayashi, K.; Watanabe, M., Method of determining kinetic boundary conditions in net evaporation/condensation, Phys. Fluids, 26, (2014)
[32] Lunati, I.; Lee, S. H., A dual-tube model for gas dynamics in fractured nanoporous shale formations, J. Fluid Mech., 757, 943-971, (2014)
[33] Lutsko, J. F., Transport properties of dense dissipative hard-sphere fluids for arbitrary energy loss models, Phys. Rev. E, 72, (2005)
[34] Ma, J.; Sanchez, J. P.; Wu, K.; Couples, G. D.; Jiang, Z., A pore network model for simulating non-ideal gas flow in micro- and nano-porous materials, Fuel, 116, 498-508, (2014)
[35] Mehmani, A.; Prodanović, M.; Javadpour, F., Multiscale, multiphysics network modeling of shale matrix gas flows, Transp. Porous Med., 88, 377-390, (2013)
[36] Meng, J. P.; Wu, L.; Reese, J. M.; Zhang, Y., Assessment of the ellipsoidal-statistical Bhatnagar-Gross-Krook model for force-driven Poiseuille flows, J. Comput. Phys., 251, 383-395, (2013) · Zbl 1349.82058
[37] Ohwada, T.; Sone, Y.; Aoki, K., Numerical analysis of the Poiseuille and thermal transpiration flows between two parallel plates on the basis of the Boltzmann equation for hard sphere molecules, Phys. Fluids, 1, 2042-2049, (1989) · Zbl 0696.76092
[38] Ohwada, T.; Sone, Y.; Aoki, K., Numerical analysis of the shear and thermal creep flows of a rarefied gas over a plane wall on the basis of the linearzied Boltzmann equation for hard-sphere molecules, Phys. Fluids A, 1, 1588-1599, (1989) · Zbl 0695.76032
[39] Sanchez, I. C., Virial coefficients and close-packing of hard spheres and discs, J. Chem. Phys., 101, 7003-7006, (1994)
[40] Takata, S.; Funagane, H., Poiseuille and thermal transpiration flows of a highly rarefied gas: over-concentration in the velocity distribution function, J. Fluid Mech., 669, 242-259, (2011) · Zbl 1225.76258
[41] Tij, M.; Santos, A., Poiseuille flow in a heated granular gas, J. Stat. Phys., 117, 901-928, (2004) · Zbl 1094.82014
[42] Wang, Q.; Chen, X.; Jha, A.; Rogers, H., Natural gas from shale formation – the evolution, evidences and challenges of shale gas revolution in United States, Renew. Sust. Energ. Rev., 30, 1-28, (2014)
[43] Wu, L.; Zhang, Y.; Reese, J. M., Fast spectral solution of the generalized Enskog equation for dense gases, J. Comput. Phys., 303, 66-79, (2015) · Zbl 1349.76778
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