×

Evidence of higher-order effects in thermally driven rapid granular flows. (English) Zbl 1151.76611

Summary: Molecular dynamic (MD) simulations are used to probe the ability of Navier-Stokes-order theories to predict each of the constitutive quantities - heat flux, stress tensor and dissipation rate - associated with granular materials. The system under investigation is bounded by two opposite walls of set granular temperature and is characterized by zero mean flow. The comparisons between MD and theory provide evidence of higher-order effects in each of the constitutive quantities. Furthermore, the size of these effects is roughly one order of magnitude greater, on a percentage basis, for heat flux than it is for stress or dissipation rate. For the case of heat flux, these effects are attributed to super-Burnett-order contributions (third order in gradients) or greater, since Burnett-order contributions to the heat flux do not exist. Finally, for the system considered, these higher-order contributions to the heat flux outweigh the first-order contribution arising from a gradient in concentration (i.e. the Dufour effect)

MSC:

76T25 Granular flows
76M28 Particle methods and lattice-gas methods
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] MiDi, Eur. Phys. J. 14 pp 341– (2004)
[2] DOI: 10.1016/j.physa.2006.10.080 · doi:10.1016/j.physa.2006.10.080
[3] DOI: 10.1017/S0022112086002495 · Zbl 0587.76170 · doi:10.1017/S0022112086002495
[4] DOI: 10.1103/PhysRevA.35.3883 · doi:10.1103/PhysRevA.35.3883
[5] DOI: 10.1146/annurev.fl.22.010190.000421 · doi:10.1146/annurev.fl.22.010190.000421
[6] DOI: 10.1063/1.870073 · Zbl 1147.76450 · doi:10.1063/1.870073
[7] Brilliantov, Kinetic Theory of Granular Gases (2004) · Zbl 1155.76386 · doi:10.1093/acprof:oso/9780198530381.001.0001
[8] DOI: 10.1103/PhysRevLett.96.158002 · doi:10.1103/PhysRevLett.96.158002
[9] DOI: 10.1016/S0032-5910(00)00392-2 · doi:10.1016/S0032-5910(00)00392-2
[10] DOI: 10.1088/0953-8984/17/24/008 · doi:10.1088/0953-8984/17/24/008
[11] DOI: 10.1063/1.1633264 · Zbl 1186.76308 · doi:10.1063/1.1633264
[12] DOI: 10.1103/PhysRevC.63.061305 · doi:10.1103/PhysRevC.63.061305
[13] DOI: 10.1103/PhysRevLett.95.108001 · doi:10.1103/PhysRevLett.95.108001
[14] Brey, Phys. Rev. 58 pp 4638– (1998)
[15] DOI: 10.1017/S0022112097005119 · Zbl 0889.76005 · doi:10.1017/S0022112097005119
[16] DOI: 10.1103/PhysRevC.70.051301 · doi:10.1103/PhysRevC.70.051301
[17] DOI: 10.1017/S0022112088001879 · Zbl 0643.76036 · doi:10.1017/S0022112088001879
[18] DOI: 10.1017/S002211200200263X · Zbl 1163.76431 · doi:10.1017/S002211200200263X
[19] Jenkins, Physics of Dry Granular Media (1998)
[20] DOI: 10.1063/1.857863 · doi:10.1063/1.857863
[21] Herbst, Phys. Rev. 72 pp 141303– (2005) · doi:10.1103/PhysRevB.72.125120
[22] Herbst, Phys. Rev. 70 pp 051313– (2004)
[23] DOI: 10.1017/S0022112083003419 · Zbl 0537.76005 · doi:10.1017/S0022112083003419
[24] DOI: 10.1088/0953-8984/17/24/015 · doi:10.1088/0953-8984/17/24/015
[25] Wildman, Phys. Rev. 63 pp 061311– (2001)
[26] DOI: 10.1103/PhysRevLett.70.1619 · doi:10.1103/PhysRevLett.70.1619
[27] Wassgren, MRS Bull. 31 pp 900– (2006) · doi:10.1557/mrs2006.210
[28] Goldhirsch, Phys. Rev. 54 pp 4458– (1996)
[29] DOI: 10.1007/BF01182541 · doi:10.1007/BF01182541
[30] DOI: 10.1146/annurev.fluid.35.101101.161114 · Zbl 1125.76406 · doi:10.1146/annurev.fluid.35.101101.161114
[31] DOI: 10.1063/1.869183 · doi:10.1063/1.869183
[32] Garzo, Physica 313 pp 336– (2002) · Zbl 0998.82026 · doi:10.1016/S0378-4371(02)00994-9
[33] DOI: 10.1103/PhysRevC.64.041303 · doi:10.1103/PhysRevC.64.041303
[34] Garz’o, Phys. Rev. 59 pp 5895– (1999)
[35] DOI: 10.1002/aic.690460602 · doi:10.1002/aic.690460602
[36] DOI: 10.1103/PhysRevLett.83.5003 · doi:10.1103/PhysRevLett.83.5003
[37] DOI: 10.1017/S0022112007006489 · Zbl 1119.76069 · doi:10.1017/S0022112007006489
[38] DOI: 10.1017/S002211200400326X · Zbl 1165.76381 · doi:10.1017/S002211200400326X
[39] DOI: 10.1103/PhysRevLett.99.068002 · doi:10.1103/PhysRevLett.99.068002
[40] Ferziger, Mathematical Theory of Transport Processes in Gases (1972)
[41] DOI: 10.1016/S0378-4371(99)00433-1 · doi:10.1016/S0378-4371(99)00433-1
[42] DOI: 10.1063/1.1626682 · Zbl 1186.76122 · doi:10.1063/1.1626682
[43] DOI: 10.1017/S0022112098008660 · Zbl 0927.76008 · doi:10.1017/S0022112098008660
[44] DOI: 10.1002/aic.10394 · doi:10.1002/aic.10394
[45] DOI: 10.1016/S0378-4371(98)00127-7 · doi:10.1016/S0378-4371(98)00127-7
[46] Santos, Rarefied Gas Dynamics 19 (1995)
[47] Clause, Phys. Rev. 38 pp none– (1988) · doi:10.1103/PhysRevA.38.4241
[48] Risso, Phys. Rev. 65 pp 021304– (2002)
[49] DOI: 10.1007/BF01008518 · doi:10.1007/BF01008518
[50] Press, Numerical Recipes in C: The Art of Scientific Computing (1992) · Zbl 0845.65001
[51] Cercignani, The Boltzmann Equation and its Applications (1987) · Zbl 0646.76001
[52] P?schel, Computational Granular Dynamics (2005)
[53] DOI: 10.1063/1.1672048 · doi:10.1063/1.1672048
[54] DOI: 10.1209/0295-5075/79/60001 · doi:10.1209/0295-5075/79/60001
[55] DOI: 10.1017/S0022112005004866 · Zbl 1071.76061 · doi:10.1017/S0022112005004866
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.