Acrivos A. & Chang E. 1986 A model for estimating transport quantities in two-phase materials. Phys. Fluids 29, 3–4.

Anderson T. B. & Jackson R. 1967 A fluid mechanical description of fluidized beds. Ind. Engng Chem. Fundamentals 6, 527–539.

Batchelor G. K. 1970 The stress system in a suspension of force-free particles. J. Fluid Mech. 41, 545–570.

Bizon C., Shattuck M. D., Swift J. B. & Swinney H. L. 1999 Transport coefficients for granular media from molecular dynamics simulations. Phys. Rev. E 60, 4340–4351.

Bolio E. J., Yasuna J. A. & Sinclair J. L. 1995 Dilute, turbulent gas–solid flow in risers with particle–particle interactions. AIChE J. 41, 1375–1388.

Brinkman H. C. 1949 A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles. Appl. Sci. Res. A 1, 27–34.

Carman P. C. 1937 The determination of the specific surface area of powder I. J. Soc. Chem. Ind. 57, 225–236.

Carnahan N. F. & Starling K. E. 1969 Equation of state for nonattracting rigid spheres. J. Chem. Phys. 51, 635–636.

Clift R., Grace J. R. & Weber M. E. 1978 Bubbles, Drops, and Particles. Academic.

Dasgupta S., Jackson R. & Sundaresan S. 1994 Turbulent gas–particle flow in vertical risers. AIChE J. 40, 215–228.

Ergun S. 1952 Pressure drop through granular beds. Chem. Engng Prog. 48, 84–88.

Garzó V. & Dufty J. W. 1999 Dense fluid transport for inelastic hard spheres. Phys. Rev. E 59, 5895–5911.

Goldhirsch I., Noskowicz S. H. & Bar-Lev O. 2005 Nearly smooth granular gases. Phys. Rev. Lett. 95, 068002.

Gopinath A., Chen S. B. & Koch D. L. 1997 Lubrication flows between spherical particles colliding in a compressible non-continuum gas. J. Fluid Mech. 344, 245–269.

Happel J. & Brenner H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.

Hill R. J., Koch D. L. & Ladd A. J. C. 2001 *a* The first effects of fluid inertia on flows in ordered and random arrays of spheres. J. Fluid Mech. 448, 213–241.

Hill R. J., Koch D. L. & Ladd A. J. C. 2001 *b* Moderate-Reynolds-number flows in ordered and random arrays of spheres. J. Fluid Mech. 448, 243–278.

Hopkins M. A. & Louge M. Y. 1991 Inelastic microstructure in rapid granular flows of smooth disks. Phys. Fluids A 3, 47–57.

Jenkins J. T. 2001 Boundary conditions for collisional grain flows at bumpy, frictional walls. In Granular Gases (ed. Pöschel T. & Luding S.), pp. 125–139. Springer.

Jenkins J. T. & Richman M. W. 1985 Grad's 13-moment system for a dense gas of inelastic spheres. Arch. Rat. Mech. Anal. 87, 355–377.

Jenkins J. T. & Richman M. W. 1986 Boundary conditions for plane flows of smooth, nearly elastic, circular disks. J. Fluid Mech. 171, 313–328.

Koch D. L. & Sangani A. S. 1999 Particle pressure and marginal stability limits for a homogeneous monodisperse gas fluidized bed: kinetic theory and numerical simulations. J. Fluid Mech. 400, 229–263.

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.

Liss E. D., Conway S. L. & Glasser B. J. 2002 Density waves in gravity-driven granular flow through a channel. Phys. Fluids 14, 3309–3326.

Louge M. Y., Jenkins J. T. & Hopkins M. A. 1990 Computer simulations of rapid granular shear flows between parallel bumpy boundaries. Phys. Fluids A 2, 1042–1044.

Louge M. Y., Mastorakos M. & Jenkins J. T. 1991 The role of particle collisions in pneumatic transport. J. Fluid Mech. 231, 345–359.

Louge M. Y., Jenkins J. T. & Hopkins M. A. 1993 The relaxation of the second moments in rapid shear flows of smooth disks. Mech. Mat. 16, 199–203.

Louge M. Y., Jenkins J. T., Reeves A. & Keast S. 2000 Microgravity segregation in collisional granular shearing flows. In Proc. IUTAM Symp. on Segregation in Granular Materials (ed. Rosato A. D. & Blackmore D. L.), pp. 103–112. Kluver.

Louge M. Y., Jenkins J. T., Xu H. & Arnarson B. Ö. 2001 Granular segregation in collisional shearing flows. In Mechanics for a New Millennium (ed. Aref H. & Phillips J.), pp. 239–252. Kluver.

Lun C. K. K., Savage S. B., Jeffrey D. J. & Chepurniy N. 1984 Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flow field. J. Fluid Mech. 140, 223–256.

Maxwell J. C. 1879 On stresses in rarified gases arising from inequalities of temperature. Phil. Trans. R. Soc. Lond. 170, 231–256.

Mitarai N. & Nakanishi H. 2007 Velocity correlations in dense granular shear flows: effects of energy dissipation and normal stress. Phys. Rev. E 75, 031305.

Mueth D. M., Debregeas G. F., Karczmar G. S., Eng P. J., Nagel S. R. & Jaeger H. 2000 Signatures of granular microstructure in dense shear flows. Nature 406, 385–389.

Onoda G. Y. & Liniger E. G. 1990 Random loose packing of uniform spheres and the dilatancy onset. Phys. Rev. Lett. 64, 2727–2730.

Richman M. W. 1988 Boundary conditions based upon a modified Maxwellian velocity distribution function for flows of identical, smooth, nearly elastic spheres. Acta Mech. 75, 227–240.

Richman M. W. & Chou C. S. 1988 Boundary effects on granular flows of smooth disks. Z. Angew. Mech. Phys. 39, 885–901.

Sangani A. S. & Behl S. 1989 The planar singular solutions of Stokes and Laplace equations and their application to transport processes near porous surfaces. Phys. Fluids A 1, 21–37.

Sangani A. S., Mo G., Tsao H.-K. & Koch D. L. 1996 Simple shear flows of dense gas–solid suspensions at finite Stokes numbers. J. Fluid Mech. 313, 309–341.

Sela N. & Goldhirsch I. 1998 Hydrodynamic equations for rapid flows of smooth inelastic spheres, to Burnett order. J. Fluid Mech. 361, 41–74.

Sinclair J. L. & Jackson R. 1989 Gas–particle flow in a vertical pipe with particle–particle interactions. AIChE J. 39, 1473–1486.

Smart J. R. & Leighton D. T. Jr., 1989 Measurement of the hydrodynamic surface roughness of noncolloidal spheres. Phys. Fluids A 1, 52–60.

Sundaram S. & Collins L. R. 1997 Collision statistics in an isotropic particle-laden turbulent suspension. I. Direct numerical simulations. J. Fluid Mech. 335, 75–109.

Sundararajakumar R. R. & Koch D. L. 1996 Non-continuum lubrication flows between particles colliding in a gas. J. Fluid Mech. 313, 283–308.

Torquato S. 1995 Nearest-neighbor statistics for packings of hard spheres and disks. Phys. Rev. E 51, 3170–3182.

Verberg R. & Koch D. L. 2006 Rheology of particle suspensions with low to moderate fluid inertia at finite particle inertia. Phys. Fluids 18, 083303.

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.

Xu H. 2003 Collisional granular flows with and without gas interactions in microgravity. PhD dissertation, Cornell University.

Xu H., Louge M. & Reeves A. 2003 Solution of the kinetic theory for bounded collisional granular flows. Continuum Mech. Thermodyn. 15 (4), 321–349.

Zarraga I. S., Hill D. A. & Leighton Jr D. T. 2000 The characterization of the total stress of concentrated suspensions of noncolloidal spheres in Newtonian fluids. J. Rheol. 44, 185–220.