Auton T. R.
1987
The lift force on a spherical body in a rotational flow. J. Fluid Mech.
183, 199–218.

Batchelor G. K.
1972
Sedimentation in a dilute dispersion of spheres. J. Fluid Mech.
52, 245–268.

Bhaga D. & Weber M. E.
1981
Bubbles in viscous liquids: shapes, wakes and velocities. J. Fluid Mech.
105, 61–85.

Brackbill J. U., Kothe D. B. & Zemach C.
1992
A continuum method for modeling surface tension. J. Comput. Phys.
100, 335–354.

Brenner H. & Cox R. G.
1963
The resistance to a particle of arbitrary shape in translational motion at small Reynolds numbers. J. Fluid Mech.
17, 561–595.

Bunner B & Tryggvason G.
2002a
Dynamics of homogeneous bubbly flows. Part 1. Rise velocity and microstructure of the bubbles. J. Fluid Mech.
466, 17–52.

Bunner B. & Tryggvason G.
2002b
Dynamics of homogeneous bubbly flows. Part 2. Velocity fluctuations. J. Fluid Mech.
466, 53–84.

Bunner B. & Tryggvason G.
2003
Effect of bubble deformation on the properties of bubbly flows. J. Fluid Mech.
495, 77–118.

Cartellier A., Andreotti M. & Sechet P.
2009
Induced agitation in homogeneous bubbly flows at moderate particle Reynolds number. Phys. Rev. E
80 (6), 065301.

Cartellier A. & Rivière N.
2001
Bubble-induced agitation and microstructure in uniform bubbly flows at small to moderate particle Reynolds numbers. Phys. Fluids
13 (8), 2165–2181.

Chorin A
1968
Numerical solution of the Navier–Stokes equations. Maths Comput.
22, 745–762.

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

Colombet D., Legendre D., Risso F., Cockx A. & Guiraud P.
2015
Dynamics and mass transfer of rising bubbles in a homogenous swarm at large gas volume fraction. J. Fluid Mech.
763, 254–285.

Davis R. H. & Acrivos A
1985
Sedimentation of noncolloidal particles at low Reynolds numbers. Annu. Rev. Fluid Mech.
17, 91–118.

Ern P., Risso F., Fabre D. & Magnaudet J.
2012
Wake-induced oscillatory paths of bodies freely rising or falling in fluids. Annu. Rev. Fluid Mech.
44, 97–121.

Esmaeeli A. & Tryggvason G.
1998
Direct numerical simulations of bubbly flows. Part 1. Low Reynolds number arrays. J. Fluid Mech.
377, 313–345.

Esmaeeli A. & Tryggvason G.
1999
Direct numerical simulations of bubbly flows. Part 2. Moderate Reynolds number arrays. J. Fluid Mech.
385, 325–358.

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.

Fabre D., Tchoufag J. & Magnaudet J.
2012
The steady oblique path of buoyancy-driven disks and spheres. J. Fluid Mech.
707, 24–36.

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.

Gillissen J. J. J., Sundaresan S. & Van Den Akker H. E. A.
2011
A lattice Boltzmann study on the drag force in bubble swarms. J. Fluid Mech.
679, 101–121.

Glendinning A. B. & Russel W. B.
1982
A pairwise additive description of sedimentation and diffusion in concentrated suspensions of hard spheres. J. Colloid Interface Sci.
89, 124–143.

Gottlieb S. & Shu C.-W.
1998
Total variation diminishing Runge–Kutta schemes. Maths Comput.
67, 73–85.

Grace J. R.
1973
Shapes and velocities of bubbles rising in infinite liquids. Trans. Inst. Chem. Engrs
51, 116–120.

Guazzelli E. & Hinch J.
2011
Fluctuations and instability in sedimentation. Annu. Rev. Fluid Mech.
43, 97–116.

Hadamard J.
1911
Mouvement permanent lent d’une sphere liquide et visqueuse dans un liquide visqueux. C. R. Acad. Sci. Paris
152, 1735–1738.

Hallez Y. & Legendre D.
2011
Interaction between two spherical bubbles rising in a viscous liquid. J. Fluid Mech.
673, 406–431.

Harper J. F.
1970
On bubbles rising in line at large Reynolds numbers. J. Fluid Mech.
41, 751–758.

Harper J. F.
1997
Bubbles rising in line: why is the first approximation so bad?
J. Fluid Mech.
351, 289–300.

Harten A., Engquist B., Osher S. & Chakravarthy S. R.
1987
Uniformly high order accurate essentially non-oscillatory schemes, III. J. Comput. Phys.
71, 231–303.

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

Hua J., Stene J. F. & Lin P.
2008
Numerical simulation of 3D bubbles rising in viscous liquids using a front tracking method. J. Comput. Phys.
227, 3358–3382.

Ishii M. & Zuber N.
1979
Drag coefficient and relative velocity in bubbly, droplet or particulate flows. AIChE J.
25, 843–855.

Jenny M., Dusek J. & Bouchet G.
2004
Instabilities and transition of a sphere falling or ascending freely in a Newtonian fluid. J. Fluid Mech.
508, 201–239.

Jiang G.-S. & Shu C.-W.
1996
Efficient implementation of weighted ENO schemes. J. Comput. Phys.
126, 202–228.

Katz J. & Meneveau C.
1996
Wake-induced relative motion of bubbles rising in line. Intl J. Multiphase Flow
22 (2), 239–258.

Keh H. J. & Tseng Y. K.
1992
Slow motion of multiple droplets in arbitrary three-dimensional configurations. AIChE J.
38, 1881–1904.

Koch D. L.
1993
Hydrodynamic diffusion in dilute sedimenting suspensions at moderate Reynolds numbers. Phys. Fluids A
5, 1141.

Kushch V. I., Sangani A. S., Spelt P. D. M. & Koch D. L.
2002
Finite Weber number motion of bubbles through a nearly inviscid liquid. J. Fluid Mech.
460, 241–280.

Legendre D. & Magnaudet J.
1998
The lift force on a spherical bubble in a viscous linear shear flow. J. Fluid Mech.
368, 81–126.

Legendre D., Magnaudet J. & Mougin G.
2003
Hydrodynamic interactions between two spherical bubbles rising side by side in a viscous liquid. J. Fluid Mech.
497, 133–166.

Loisy A.2016 Direct numerical simulation of bubbly flows: coupling with scalar transport and turbulence. PhD thesis, Université Claude Bernard Lyon 1.

Loth E.
2008
Quasi-steady shape and drag of deformable bubbles and drops. Intl J. Multiphase Flow
34, 523–546.

Martinez-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.

Mei R., Klausner J. F. & Lawrence C. J.
1994
A note on the history force on a spherical bubble at finite Reynolds number. Phys. Fluids
6, 418–420.

Meland R., Gran I. R., Olsen R. & Munkejord S. T.
2007
Reduction of parasitic currents in level-set calculations with a consistent discretization of the surface-tension force for the CSF model. In 16th Australasian Fluid Mechanics Conference (AFMC) (ed. Jacobs P.
et al. ), pp. 862–865. The University of Queensland.

Merle A., Legendre D. & Magnaudet J.
2005
Forces on a high-Reynolds-number spherical bubble in a turbulent flow. J. Fluid Mech.
532, 53–62.

Moore D. W.
1959
The rise of a gas bubble in a viscous liquid. J. Fluid Mech.
6, 113–130.

Naso A. & Prosperetti A.
2010
The interaction between a solid particle and a turbulent flow. New J. Phys.
12, 033040.

Osher S. & Sethian J. A.
1988
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations. J. Comput. Phys.
79, 12–49.

Phillips R. J., Brady J. F. & Bossis G.
1988
Hydrodynamic transport properties of hardsphere dispersions. I. Suspensions of freely mobile particles. Phys. Fluids
31, 3462–3472.

Prosperetti A. & Tryggvason G.
2007
Computational Methods for Multiphase Flow. Cambridge University Press.

Ray B. & Prosperetti A.
2014
On skirted drops in an immiscible liquid. Chem. Engng Sci.
108, 213–222.

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.

Richardson J. F. & Zaki W. N.
1954
Sedimentation and fluidisation: Part I. Trans. Inst. Chem. Engrs
32, 35–53.

Roghair I., Lau Y. M., Deen N. G., Slagter H. M., Baltussen M. W., Van Sint Annaland M. & Kuipers J. A. M.
2011
On the drag force of bubbles in bubble swarms at intermediate and high Reynolds numbers. Chem. Engng Sci.
66, 3204–3211.

Russo G. & Smereka P.
2000
A remark on computing distance functions. J. Comput. Phys.
163, 51–67.

Rybczynski W.
1911
Uber die fortschreitende Bewegung einer flussigen Kugel in einem zahen Medium. Bull. Intl Acad. Sci. Cracovie A
1, 40–46.

Ryskin G. & Leal L. G.
1984
Numerical solution of free-boundary problems in fluid mechanics. Part 2. Buoyancy-driven motion of a gas bubble through a quiescent liquid. J. Fluid Mech.
148, 19–35.

Sabelnikov V., Ovsyannikov A. Y. & Gorokhovski M.
2014
Modified level set equation and its numerical assessment. J. Comput. Phys.
278, 1–30.

Salih A. & Ghosh Moulic S.
2009
Some numerical studies of interface advection properties of level set method. Sadhana
34, 271–298.

Sangani A. S.
1987
Sedimentation in ordered emulsions of drops at low Reynolds numbers. Z. Angew. Math. Phys.
38, 542–556.

Sangani A. S. & Acrivos A.
1983
Creeping flow through cubic arrays of spherical bubbles. Intl J. Multiphase Flow
9, 181–185.

Sankaranarayanan K., Shan X., Kevrekidis I. G. & Sundaresan S.
2002
Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice Boltzmann method. J. Fluid Mech.
452, 61–96.

Sankaranarayanan K. & Sundaresan S.
2002
Lift force in bubbly suspensions. Chem. Engng Sci.
57, 3521–3542.

Spelt P. D. M.
2006
Shear flow past two-dimensional droplets pinned or moving on an adhering channel wall at moderate Reynolds numbers: a numerical study. J. Fluid Mech.
561, 439.

Spelt P. D. M. & Sangani A. S.
1998
Properties and averaged equations for flows of bubbly liquids. Appl. Sci. Res.
58, 337–386.

Sussman M., Smereka P. & Osher S.
1994
A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys.
114, 146–159.

Sussman M. & Uto S.
1998
A computational study of the spreading of oil underneath a sheet of ice. UCLA Computational and Applied Mathematics Report 98.

Taylor T. D. & Acrivos A.
1964
On the deformation and drag of a falling viscous drop at low Reynolds number. J. Fluid Mech.
18, 466–476.

Theodoropoulos C., Sankaranarayanan K., Sundaresan S. & Kevrekidis I. G.
2004
Coarse bifurcation studies of bubble flow lattice Boltzmann simulations. Chem. Engng Sci.
59, 2357–2362.

Tryggvason G., Scardovelli R. & Zaleski S.
2011
Direct Numerical Simulations of Gas–Liquid Multiphase Flows. Cambridge University Press.

Veldhuis C. H. J. & Biesheuvel A.
2007
An experimental study of the regimes of motion of spheres falling or ascending freely in a Newtonian fluid. Intl J. Multiphase Flow
33, 1074–1087.

Wacholder E.
1973
Sedimentation in a dilute emulsion. Chem. Engng Sci.
28, 1447–1453.

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.

Yuan H. & Prosperetti A.
1994
On the in-line motion of two spherical bubbles in a viscous fluid. J. Fluid Mech.
278, 325.

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.