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The surprising relevance of a continuum description to granular clusters

Published online by Cambridge University Press:  21 February 2014

M. Y. Louge
M. Y. Louge*
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
*
†Email address for correspondence: MYL3@cornell.edu
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Abstract

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Nature shuns homogeneity. In turbulent clouds, industrial reactors and geophysical flows, discrete particles arrange in clusters, posing difficult challenges to theory. A persistent question is whether clusters can be modelled with continuum equations. Recent evidence presented by Mitrano et al. (J. Fluid Mech., vol. 738, 2014, R2) indicates that suitable equations can predict the formation of clusters in granular flows, despite violating the simplifying assumptions upon which they are based.

JFM classification

Rarefied Gas Flow: Kinetic theory Granular media: Granular media
Type
Focus on Fluids
Information
Journal of Fluid Mechanics , Volume 742 , 10 March 2014 , pp. 1 - 4
Copyright
© 2014 Cambridge University Press 

References

Agrawal, K., Loezos, P. N., Syamlal, M. & Sundaresan, S. 2001 The role of meso-scale structures in rapid gas–solid flows. J. Fluid Mech. 445, 151–185.Google Scholar
Agarwal, R. K., Yun, K.-Y. & Balakrishnan, R. 2001 Beyond Navier–Stokes: Burnett equations for flows in the continuum-transition regime. Phys. Fluids 13, 3061–3085.Google Scholar
Alsmeyer, H. 1976 Density profiles in argon and nitrogen shock waves measured by the absorption of an electron beam. J. Fluid Mech. 74, 497–613.Google Scholar
Bec, J., Biferale, L., Cencini, M., Lanotte, A. S. & Toschi, F. 2010 Intermittency in the velocity distribution of heavy particles in turbulence. J. Fluid Mech. 646, 527–536.Google Scholar
Brenner, H. 2005 Navier-Stokes revisited. Physica A 349, 60–132.Google Scholar
Brilliantov, N., Salueña, C., Schwager, T & Pöschel, T. 2004 Transient structures in a granular gas. Phys. Rev. Lett. 93, 134301.Google Scholar
Capecelatro, J. & Desjardins, O. 2013 An Euler–Lagrange strategy for simulating particle-laden flows. J. Comput. Phys. 238, 1–31.Google Scholar
Chun, J., Koch, D. L., Rani, S. L., Ahluwalia, A. & Collins, L. R. 2005 Clustering of aerosol particles in isotropic turbulence. J. Fluid Mech. 536, 219–251.Google Scholar
Desjardins, O., Fox, R. O. & Villedieu, P. 2008 A quadrature-based moment method for dilute fluid-particle flows. J. Comput. Phys. 227, 2514–2539.Google Scholar
Duncan, K., Mehlig, B., Östlund, S. & Wilkinson, M. 2005 Clustering by mixing flows. Phys. Rev. Lett. 95, 240602.Google Scholar
Fox, R. O. 2012 Large-eddy-simulation tools for multiphase flows. Annu. Rev. Fluid Mech. 44, 47–76.Google Scholar
Garzó, V. 2005 Instabilities in a free granular fluid described by the Enskog equation. Phys. Rev. E 72, 021106.Google Scholar
Garzó, V. & Dufty, J. W. 1999 Dense fluid transport for inelastic hard spheres. Phys. Rev. E 59, 5895–5911.Google ScholarPubMed
Goldhirsch, I. & Zanetti, G. 1993 Clustering instability in dissipative gases. Phys. Rev. Lett. 70, 1619–1622.Google Scholar
Greenshields, C. J. & Reese, J. M. 2007 The structure of shock waves as a test of Brenner’s modifications to the Navier–Stokes equations. J. Fluid Mech. 580, 407–429.Google Scholar
Helland, E., Bournot, H., Occelli, R. & Tadrist, L. 2007 Drag reduction and cluster formation in a circulating fluidised bed. Chem. Engng Sci. 62, 148–158.CrossRefGoogle Scholar
van der Hoef, M. A., van Sint Annaland, M., Deen, N. G. & Kuipers, J. A. M. 2008 Numerical simulation of dense gas–solid fluidized beds: a multiscale modelling strategy. Annu. Rev. Fluid Mech. 40, 47–70.Google Scholar
Hopkins, M. A., Jenkins, J. T. & Louge, M. Y. 1993 On the structure of three-dimensional shear flows. Mech. Mater. 16, 179–187.Google Scholar
Jenkins, J. T. & Richman, M. W. 1988 Plane simple shear of smooth inelastic circular disks: the anisotropy of the second moment in the dilute and dense limits. J. Fluid Mech. 192, 313–328.Google Scholar
Jenkins, J. T. & Zhang, C. 2002 Kinetic theory for identical, frictional, nearly elastic spheres. Phys. Fluids 14, 1228–1235.Google Scholar
Kumaran, V. 2006 The constitutive relation for the granular flow of rough particles, and its application to the flow down an inclined plane. J. Fluid Mech. 561, 1–42.Google Scholar
Longmire, E. K. & Eaton, J. K. 1992 Structure of a particle-laden round jet. J. Fluid Mech. 236, 217–257.Google Scholar
Lun, C. K. K. 1991 Kinetic theory for granular flow of dense, slightly inelastic, slightly rough spheres. J. Fluid Mech. 233, 539–559.Google Scholar
Maxey, M. R. 1987 The gravitional settling of aerosol particles in homogeneous turbulence and random flow fields. J. Fluid Mech. 174, 441–465.Google Scholar
Mitrano, P. P., Garzó, V., Hilger, A. M., Ewasko, C. J. & Hrenya, C. M. 2012 Assessing a hydrodynamic description for instabilities in highly dissipative, freely cooling granular gases. Phys. Rev. E 85, 041303.Google Scholar
Mitrano, P. P., Zenk, J., Benyahia, S., Galvin, J., Dahl, S. & Hrenya, C. 2014 Kinetic-theory predictions of clustering instabilities in granular flows: beyond the small Knudsen regime. J. Fluid Mech. 738, R2, 12 pages.Google Scholar
Pan, L. & Padoan, P. 2010 Relative velocity of inertial particles in turbulent flows. J. Fluid Mech. 661, 73–107.Google Scholar
Pepiot, P. & Desjardins, O. 2012 Numerical analysis of the dynamics of two- and three-dimensional fluidized bed reactors using an Euler–Lagrange approach. Powder Technol. 220, 104–121.CrossRefGoogle Scholar
Sela, N. & Goldhirsch, I. 1998 Hydrodynamic equations for rapid flows of smooth inelastic spheres, to Burnett order. J. Fluid Mech. 361, 41–74.Google Scholar
Simonin, O., Zaichik, L. I., Alipchenkov, V. M. & Février, P. 2006 Connection between two statistical approaches for the modelling of particle velocity and concentration distributions in turbulent flow: the mesoscopic Eulerian formalism and the two-point probability density function method. Phys. Fluids 18, 125107.Google Scholar
Wylie, J. J. & Koch, D. L. 2000 Particle clustering due to hydrodynamic interactions. Phys. Fluids 12, 964–970.Google Scholar
Wylie, J. J., Koch, D. L. & Ladd, A. J. C. 2003 Rheology of suspensions with high particle inertia and moderate fluid inertia. J. Fluid Mech. 480, 95–118.Google Scholar
Xu, H., Louge, M. & Reeves, A. 2003 Solutions of the kinetic theory for bounded collisional granular flows. Contin. Mech. Thermodyn. 15, 321–349.Google Scholar
Xu, H., Verberg, R., Koch, D. L. & Louge, M. Y. 2009 Dense, bounded shear flows of agitated solid spheres in a gas at intermediate Stokes and finite Reynolds numbers. J. Fluid Mech. 618, 181–208.Google Scholar