Poiseuille flow of a dilute binary granular mixture: hydrodynamics and segregation
Source abstract
Abstract
We study the gravity-driven Poiseuille flow of a dilute binary granular mixture and report results on the hydrodynamic fields and species segregation. Direct Simulation Monte Carlo method is employed for a 50:50 binary mixture of different density, but same size particles with athermal channel walls. Effect of the mass bidispersity on velocity, granular temperature and number-density profiles is detailed, along with a quantification of energy non-equipartition in this flow. We uncover a non-monotonic species segregation along with a decreasing global segregation with increasing mass ratio.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Granular flow and fluidized beds · Heat and Mass Transfer in Porous Media · Particle Dynamics in Fluid Flows
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (49)
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1. Alam, M., Chikkadi, V.K.: Velocity distribution function and correlations in a granular Poiseuille flow. J. Fluid Mech. 653, 175–219 (2010)10.1017/S0022112010000200 ↗
2. Alam, M., Luding, S.: How good is the equipartition assumption for the transport properties of a granular mixture? Granul. Matter 4(3), 139–142 (2002)10.1007/s10035-002-0110-x ↗
3. Alam, M., Luding, S.: Rheology of bidisperse granular mixtures via event-driven simulations. J. Fluid Mech. 476, 69–103 (2003)10.1017/S002211200200263X ↗
4. Alam, M., Luding, S.: Energy nonequipartition, rheology and microstructure in sheared bidisperse granular mixtures. Phys. Fluid 17, 063303 (2005)10.1063/1.1938567 ↗
5. 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)10.1017/jfm.2015.523 ↗
6. Alam, M., Trujillo, L., Herrmann, H.J.: Hydrodynamic theory for reverse Brazil nut segregation and the non-monotonic ascension dynamics. J. Stat. Phys. 124, 587–623 (2003)10.1007/s10955-006-9078-y ↗
7. Alam, M., Willits, J.T., Arnarson, B.Ö., Luding, S.: Kinetic theory of a binary mixture of nearly elastic disks with size and mass disparity. Phys. Fluids 14(11), 4085–4087 (2002)10.1063/1.1509066 ↗
8. Alaoui, M., Santos, A.: Poiseuille flow driven by an external force. Phys. Fluids A 4(6), 1273–1282 (1992)10.1063/1.858245 ↗
9. Ansari, I.H., Rivas, N., Alam, M.: Phase-coexisting patterns, horizontal segregation, and controlled convection in vertically vibrated binary granular mixtures. Phys. Rev. E 97(1), 012911 (2018)10.1103/PhysRevE.97.012911 ↗
10. Barrat, A., Trizac, E.: Lack of energy equipartition in homogeneous heated binary granular mixtures. Granul. Matter 4(2), 57–63 (2002)10.1007/s10035-002-0108-4 ↗
11. Bird, G.A.: Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Clarendon Press, Oxford (1994)
12. Cercignani, C., Daneri, A.: Flow of a rarefied gas between two parallel plates. J. Appl. Phys. 34(12), 3509–3513 (1963)10.1063/1.1729249 ↗
13. Chikkadi, V., Alam, M.: Slip velocity and stresses in granular Poiseuille flow via event-driven simulation. Phys. Rev. E 80(2), 021303 (2009)10.1103/PhysRevE.80.021303 ↗
14. Farrell, M., Lun, C.K.K., Savage, S.B.: A simple kinetic theory for granular flow of binary mixtures of smooth, inelastic, spherical particles. Acta Mech. 63(1–4), 45–60 (1986)10.1007/BF01182539 ↗
15. Feitosa, K., Menon, N.: Breakdown of energy equipartition in a 2D binary vibrated granular gas. Phys. Rev. Lett. 88(19), 198301 (2002)10.1103/PhysRevLett.88.198301 ↗
16. Galvin, J.E., Dahl, S.R., Hrenya, C.M.: On the role of non-equipartition in the dynamics of rapidly flowing granular mixtures. J. Fluid Mech. 528, 207–232 (2005)10.1017/S002211200400326X ↗
17. Garzo, V., Dufty, J.W.: Hydrodynamics for a granular binary mixture at low density. Phys. Fluids 14, 1476 (2002)10.1063/1.1458007 ↗
18. Goldhirsch, I.: Rapid granular flows. Annu. Rev. Fluid Mech. 35(1), 267–293 (2003)10.1146/annurev.fluid.35.101101.161114 ↗
19. Gray, J.M.N.T.: Particle segregation in dense granular flows. Annu. Rev. Fluid Mech. 50, 407–433 (2018)10.1146/annurev-fluid-122316-045201 ↗
20. Gupta, R., Alam, M.: Hydrodynamics, wall-slip, and normal-stress differences in rarefied granular Poiseuille flow. Phys. Rev. E 95(2), 022903 (2017)10.1103/PhysRevE.95.022903 ↗
21. Gupta, R., Alam, M.: Disentangling the role of athermal walls on the Knudsen paradox in molecular and granular gases. Phys. Rev. E 97(1), 012912 (2018)10.1103/PhysRevE.97.012912 ↗
22. Hong, D.C., Quinn, P.V., Luding, S.: Reverse Brazil-nut problem: competition between percolation and condensation. Phys. Rev. Lett. 86, 3423–3425 (2001)10.1103/PhysRevLett.86.3423 ↗
23. Iddir, H., Arastoopour, H.: Modeling of multitype particle flow using the kinetic theory approach. AIChE J. 51(6), 1620–1632 (2005)10.1002/aic.10429 ↗
24. Jenkins, J.T., Mancini, F.: Kinetic theory for binary mixtures of smooth, nearly elastic spheres. Phys. Fluids. A 1(12), 2050–2057 (1989)10.1063/1.857479 ↗
25. Knight, J.B., Jaeger, H.M., Nagel, S.R.: Vibration-induced size separation in granular media: the convection connection. Phys. Rev. Lett. 70(24), 3728 (1993)10.1103/PhysRevLett.70.3728 ↗
26. Knudsen, M.: The laws of molecular flow and internal friction flow of gases through tubes. Ann. Phys. (N. Y.) 333(1), 75–130 (1909)10.1002/andp.19093330106 ↗
27. Kudrolli, A.: Size separation in vibrated granular matter. Rep. Prog. Phys. 67, 209–247 (2004)10.1088/0034-4885/67/3/R01 ↗
28. Liu, X., Metzger, M., Glasser, B.J.: Couette flow with a bidisperse particle mixture. Phys. Fluids 19(7), 073301 (2007)10.1063/1.2741245 ↗
29. Liu, X., Metzger, M., Glasser, B.J.: Granular and gas-particle flows in a channel with a bidisperse particle mixture. Chem. Eng. Sci. 63(23), 5696–5713 (2008)10.1016/j.ces.2008.08.011 ↗
30. Loyalka, S.K., Hamoodi, S.A.: Poiseuille flow of a rarefied gas in a cylindrical tube: solution of linearized Boltzmann equation. Phys. Fluids A 2(11), 2061–2065 (1990)10.1063/1.857681 ↗
31. Martin, P.A., Piasecki, J.: Thermalization of a particle by dissipative collisions. Europhys. Lett. 46(5), 613 (1999)10.1209/epl/i1999-00308-1 ↗
32. Montanero, J.M., Garzó, V.: Monte Carlo simulation of the homogeneous cooling state for a granular mixture. Granul. Matter 4(1), 17–24 (2002)10.1007/s10035-001-0097-8 ↗
33. Ottino, J.M., Khakhar, D.V.: Mixing and segregation of granular materials. Annu. Rev. Fluid Mech. 32(1), 55–91 (2000)10.1146/annurev.fluid.32.1.55 ↗
34. Pöschel, T., Herrmann, H.J.: Size segregation and convection. Europhys. Lett. 29, 123–128 (1993)10.1209/0295-5075/29/2/003 ↗
35. Rongali, R., Alam, M.: Asymptotic expansion and Pade approximants for acceleration-driven Poiseuille flow of a rarefied gas: Bulk hydrodynamics and rheology. Phys. Rev. E 97(1), 012115 (2018)10.1103/PhysRevE.98.012115 ↗
36. Rongali, R., Alam, M.: Asymptotic expansion and Pade approximants for gravity-driven flow of a heated granular gas: competition between inelasticity and rarefaction, up-to Burnett order. Phys. Rev. E 98(1), 052144 (2018)10.1103/PhysRevE.98.052144 ↗
37. Santos, A., Tij, M.: Gravity-driven Poiseuille flow in dilute gases: elastic and inelastic collisions. In: Modelling and Numerics of Kinetic Dissipative Systems, Nova Science Publishers, New York (2006)
38. Savage, S.B., Lun, C.K.K.: Particle size segregation in inclined chute flow of dry cohesionless granular solids. J. Fluid Mech. 189, 311–335 (1988)10.1017/S002211208800103X ↗
39. Serero, D., Goldhirsch, I., Noskowicz, S.H., Tan, M.L.: Hydrodynamics of granular gases and granular gas mixtures. J. Fluid Mech. 554, 237–258 (2006)10.1017/S0022112006009281 ↗
40. Shinbrot, T., Muzzio, F.J.: Reverse buoyancy in shaken granular beds. Phys. Rev. Lett. 81, 4365–4368 (1998)10.1103/PhysRevLett.81.4365 ↗
41. Tij, M., Sabbane, M., Santos, A.: Nonlinear Poiseuille flow in a gas. Phys. Fluids 10(4), 1021–1027 (1998)10.1063/1.869621 ↗
42. Tij, M., Santos, A.: Perturbation analysis of a stationary nonequilibrium flow generated by an external force. J. Stat. Phys. 76, 1399–1414 (1994)10.1007/BF02187068 ↗
43. Tij, M., Santos, A.: Poiseuille flow in a heated granular gas. J. Stat. Phys. 117, 901–928 (2004)10.1007/s10955-004-5710-x ↗
44. Trujillo, L., Alam, M., Herrmann, H.J.: Segregation in a fluidized binary granular mixture: competition between buoyancy and geometric forces. Europhys. Lett. 64, 190–196 (2003)10.1209/epl/i2003-00287-1 ↗
45. Vijayakumar, K.C., Alam, M.: Velocity distribution and the effect of wall roughness in granular Poiseuille flow. Phys. Rev. E 75(5), 051306 (2007)10.1103/PhysRevE.75.051306 ↗
46. Wildman, R.D., Parker, D.J.: Energy nonequipartition in a vibrated granular gas mixture. Phys. Rev. Lett. 88(19), 064301 (2002)10.1103/PhysRevLett.88.064301 ↗
47. Willits, J.T., Arnarson, B.: Kinetic theory of a binary mixture of nearly elastic disks. Phys. Fluids 11(10), 3116–3122 (1999)10.1063/1.870169 ↗
48. Windows-Yule, C.R.K., Douglas, G.J.M., Parker, D.J.: Competition between geometrically induced and density-driven segregation mechanisms in vibrofluidized granular systems. Phys. Rev. E 91(3), 032205 (2015)10.1103/PhysRevE.91.032205 ↗
49. Windows-Yule, C.R.K., Weinhart, T., Parker, D.J., Thornton, A.R.: Influence of thermal convection on density segregation in a vibrated binary granular system. Phys. Rev. E 89(2), 022202 (2014)10.1103/PhysRevE.89.022202 ↗