Barnea, E. & Mizrahi, J. 1973 A generalized approach to the fluid dynamics of particulate systems: Part 1. general correlation for fluidization and sedimentation in solid multiparticle systems. Chem. Engng J. 5, 171–189.
Bhatnagar, P. L., Gross, E. P. & Krook, M. 1954 A model for collision processes in gases. Phys. Rev. 94, 511.
Blanco, A. & Magnaudet, J. 1995 The structure of the axisymmetric high-Reynolds number flow around an ellipsoidal bubble of fixed shape. Phys. Fluids 7, 1265.
Bunner, B. & Tryggvason, G. 2003 Effect of bubble deformation on the properties of bubbly flows. J. Fluid Mech. 495, 77–118.
Cercignani, C. 1988 The Boltzmann Equation and its Applications. Springer.
Chen, M., Kontomaris, K. & McLaughlin, J. B. 1998 Direct numerical simulation of droplet collisions in a turbulent channel flow. Part I: collision algorithm. Intl J. Multiphase Flow 24, 1079–1103.
Colosqui, C. E. 2010 High-order hydrodynamics via lattice Boltzmann methods. Phys. Rev. E 81, 026702.
Duineveld, P. C. 1995 The rise velocity and shape of bubbles in pure water at high Reynolds number. J. Fluid Mech. 292, 325–332.
Esmaeeli, A. & Tryggvason, G. 2005 A direct numerical simulation study of the buoyant rise of bubbles at O(100) Reynolds number. Phys. Fluids 17, 093303.
Garnier, C., Lance, M. & Marié, J. L. 2002 Measurement of local flow characteristics in buoyancy-driven bubbly flow at high void fraction. Exp. Therm. Fluid Sci. 26, 811–815.
Harteveld, W. K., Mudde, R. F. & Van Den Akker, H. E. A. 2003 Dynamics of a bubble column: Influence of gas distribution on coherent structures. Can. J. Chem. Engng 81, 389–394.
He, X. & Luo, L.-S. 1997 A priori derivation of the lattice Boltzmann equation. Phys. Rev. E 55 (6/A), 6333–6336.
Ishii, M. & Zuber, N. 1979 Drag coefficient and relative velocity in bubbly, droplet or particulate flows. AIChE J. 25, 843–855.
Kim, J., Kim, D. & Choi, H. 2001 An immersed-boundary finite-volume method for simulations of flow in complex geometries. J. Comput Phys. 171, 132–150.
Lucci, F., Ferrante, A. & Elghobashi, S. 2010 Modulation of isotropic turbulence by particles of Taylor length-scale size. J. Fluid Mech. 650, 5–55.
Martínez-Mercado, J., Palacios-Morales, C. A. & Zenit, R. 2007 Measurement of pseudoturbulence intensity in monodispersed bubbly liquids for 10 < Re < 500. Phys. Fluids 19, 103302.
Maxworthy, T., Gnann, C., Kurten, M. & Durst, F. 1996 Experiments on the rise of air bubbles in clean viscous liquids. J. Fluid Mech. 321, 421–441.
Mei, R. & Klausner, J. F. 1992 Unsteady force on a spherical bubble at finite Reynolds number with small fluctuations in the free-stream velocity. Phys. Fluids 4, 63–70.
Moore, W. D. 1965 The velocity of rise of distorted gas bubbles in a liquid of small viscosity. J. Fluid Mech. 23, 749–766.
Philippi, P. C., Hegele, L. A. Jr., dos Santos, L. O. E. & Surmas, R. 2006 From the continuous to the lattice Boltzmann equation: The discretization problem and thermal models. Phys. Rev. E 73, 056702.
Riboux, G., Risso, F. & Legendre, D. 2010 Experimental characterization of the agitation generated by bubbles rising at high Reynolds number. J. Fluid Mech. 643, 509–539.
Roma, A. M., Peskin, C. S. & Berger, M. J. 1999 An adaptive version of the immersed boundary method. J. Comput Phys. 153, 509–534.
Sangani, A. S. & Acrivos, A. 1983 Creeping flow through cubic arrays of spherical bubbles. Intl J. Multiphase Flow 9, 181–185.
Sangani, A. S. & Didwania, A. K. 1993 Dynamic simulations of flows of bubbly liquids at large Reynolds numbers. J. Fluid Mech. 250, 307–337.
Shan, X., Yuan, X.-F. & Chen, H. 2006 Kinetic theory representation of hydrodynamics: a way beyond the Navier–Stokes equation. J. Fluid Mech. 550, 413–441.
Somers, J. A. 1993 Direct simulation of fluid flow with cellular automata and the lattice-Boltzmann equation. Appl. Sci. Res. 51 (1/2), 127.
Ten Cate, A., Deksen, J. J., Portela, L. M. & Van Den Akker, H. E. A. 2004 Fully resolved simulations of colliding monodisperse spheres in forced isotropic turbulence. J. Fluid Mech. 519, 233.
Uhlmann, M. 2005 An immersed boundary method with direct forcing for the simulation of particulate flows. J. Comput. Phys. 209, 448–476.
Uhlmann, M. 2008 Interface-resolved direct numerical simulation of vertical particulate channel flow in the turbulent regime. Phys. Fluids 20, 053305.
Van Sint Annaland, M., Dijkhuizen, W., Deen, N. G. & Kuipers, J. A. M. 2006 Numerical simulation of behavior of gas bubbles using a 3-D front-tracking method. AIChE J. 52, 99–110.
Yin, X. & Koch, D. L. 2008 Lattice-Boltzmann simulation of finite Reynolds number buoyancy-driven bubbly flows in periodic and wall-bounded domains. Phys. Fluids 20, 103304.
Zenit, R., Koch, D. L. & Sangani, A. S. 2001 Measurements of the average properties of a suspension of bubbles rising in a vertical channel. J. Fluid Mech. 429, 307–342.