T. R. Auton, The lift force on a spherical body in a rotational flow, Journal of Fluid Mechanics, vol.169, issue.-1, pp.199-218, 1987.
DOI : 10.1017/S0022112070000307

G. K. Batchelor, Sedimentation in a dilute dispersion of spheres, Journal of Fluid Mechanics, vol.5, issue.02, pp.245-268, 1972.
DOI : 10.1063/1.1726036

D. Bhaga and M. E. Weber, Bubbles in viscous liquids: shapes, wakes and velocities, Journal of Fluid Mechanics, vol.25, issue.-1, pp.61-85, 1981.
DOI : 10.1016/0009-2509(68)80027-2

J. U. Brackbill, D. B. Kothe, and C. Zemach, A continuum method for modeling surface tension, Journal of Computational Physics, vol.100, issue.2, pp.335-354, 1992.
DOI : 10.1016/0021-9991(92)90240-Y

H. Brenner and R. G. Cox, The resistance to a particle of arbitrary shape in translational motion at small Reynolds numbers, Journal of Fluid Mechanics, vol.10, issue.04, pp.561-595, 1963.
DOI : 10.1016/0009-2509(63)80001-9

B. Bunner and G. Tryggvason, Dynamics of homogeneous bubbly flows Part 1. Rise velocity and microstructure of the bubbles, Journal of Fluid Mechanics, vol.466, issue.33, pp.17-52, 2002.
DOI : 10.1017/S0022112002001179

B. Bunner and G. Tryggvason, Effect of bubble deformation on the properties of bubbly flows, Journal of Fluid Mechanics, vol.495, issue.4, pp.77-118, 2003.
DOI : 10.1017/S0022112003006293

A. Cartellier and N. Rivière, Bubble-induced agitation and microstructure in uniform bubbly flows at small to moderate particle Reynolds numbers, Physics of Fluids, vol.13, issue.8, p.2165, 2001.
DOI : 10.1063/1.1381562

URL : https://hal.archives-ouvertes.fr/hal-00202159

A. Chorin, Numerical solution of the Navier-Stokes equations, Math. Comput. 22, pp.745-762, 1968.
DOI : 10.1090/S0025-5718-1968-0242392-2

R. Clift, J. R. Grace, and M. E. Weber, Bubbles, drops, and particles, 1978.

D. Colombet, D. Legendre, F. Risso, A. Cockx, and P. Guiraud, Dynamics and mass transfer of rising bubbles in a homogenous swarm at large gas volume fraction, Journal of Fluid Mechanics, vol.31, pp.254-285, 2015.
DOI : 10.1063/1.2430645

URL : https://hal.archives-ouvertes.fr/hal-01269183

R. H. Davis and A. Acrivos, Sedimentation of Noncolloidal Particles at Low Reynolds Numbers, Annual Review of Fluid Mechanics, vol.17, issue.1, pp.91-118, 1985.
DOI : 10.1146/annurev.fl.17.010185.000515

P. Ern, F. Risso, D. Fabre, and J. Magnaudet, Wake-Induced Oscillatory Paths of Bodies Freely Rising or Falling in Fluids, Annual Review of Fluid Mechanics, vol.44, issue.1, pp.97-121, 2012.
DOI : 10.1146/annurev-fluid-120710-101250

A. Esmaeeli and G. Tryggvason, Direct numerical simulations of bubbly flows. Part 1. Low Reynolds number arrays, Journal of Fluid Mechanics, vol.377, pp.313-345, 1998.
DOI : 10.1017/S0022112098003176

A. Esmaeeli and G. Tryggvason, Direct numerical simulations of bubbly flows Part 2. Moderate Reynolds number arrays, Journal of Fluid Mechanics, vol.385, issue.8 9, pp.325-358, 1999.
DOI : 10.1017/S0022112099004310

A. Esmaeeli and G. Tryggvason, A direct numerical simulation study of the buoyant rise of bubbles at O(100) Reynolds number, Physics of Fluids, vol.17, issue.9, p.93303, 2005.
DOI : 10.1063/1.2056617

D. Fabre, J. Tchoufag, and J. Magnaudet, The steady oblique path of buoyancy-driven disks and spheres, Journal of Fluid Mechanics, vol.707, pp.24-36, 2012.
DOI : 10.1017/S0022112093002150

URL : https://hal.archives-ouvertes.fr/hal-00877022

C. Garnier, M. Lance, and J. Marié, Measurement of local flow characteristics in buoyancy-driven bubbly flow at high void fraction, Experimental Thermal and Fluid Science, vol.26, issue.6-7, pp.811-815, 2002.
DOI : 10.1016/S0894-1777(02)00198-X

J. J. Gillissen, S. Sundaresan, H. E. Van-den, and . Akker, A lattice Boltzmann study on the drag force in bubble swarms, Journal of Fluid Mechanics, vol.679, pp.101-121, 2011.
DOI : 10.1017/jfm.2011.125

A. B. Glendinning and W. B. , A pairwise additive description of sedimentation and diffusion in concentrated suspensions of hard spheres, Journal of Colloid and Interface Science, vol.89, issue.1, pp.124-143, 1982.
DOI : 10.1016/0021-9797(82)90127-8

S. Gottlieb and C. Shu, Total variation diminishing Runge-Kutta schemes, Mathematics of Computation of the American Mathematical Society, vol.67, issue.221, pp.73-85, 1998.
DOI : 10.1090/S0025-5718-98-00913-2

J. R. Grace, Shapes and velocities of bubbles rising in infinite liquids, In: Trans. Inst. Chem. Engng, vol.51, pp.116-120, 1973.

E. Guazzelli and J. Hinch, Fluctuations and Instability in Sedimentation, Annual Review of Fluid Mechanics, vol.43, issue.1, pp.97-116, 2011.
DOI : 10.1146/annurev-fluid-122109-160736

URL : https://hal.archives-ouvertes.fr/hal-01432510

J. Hadamard, Mouvement permanent lent d'une sphere liquide et visqueuse dans un liquide visqueux, C.R. Acad. Sci, vol.152, issue.39, pp.1735-1738, 1911.

Y. Hallez and D. Legendre, Interaction between two spherical bubbles rising in a viscous liquid, Journal of Fluid Mechanics, vol.12, issue.15, pp.406-431, 2011.
DOI : 10.1017/S0022112093001478

A. Harten, B. Engquist, S. Osher, and S. R. Chakravarthy, Uniformly high order accurate essentially non-oscillatory schemes, III, Journal of Computational Physics, vol.71, issue.2, pp.231-303, 1987.
DOI : 10.1016/0021-9991(87)90031-3

R. J. Hill, D. L. Koch, and A. J. Ladd, The first effects of fluid inertia on flows in ordered and random arrays of spheres, Journal of Fluid Mechanics, vol.448, issue.39, pp.213-241, 2001.
DOI : 10.1017/S0022112001005948

J. Hua, J. F. Stene, and P. Lin, Numerical simulation of 3D bubbles rising in viscous liquids using a front tracking method, Journal of Computational Physics, vol.227, issue.6, pp.3358-3382, 2008.
DOI : 10.1016/j.jcp.2007.12.002

M. Ishii and N. Zuber, Drag coefficient and relative velocity in bubbly, droplet or particulate flows, AIChE Journal, vol.25, issue.5, pp.843-855, 1979.
DOI : 10.1002/aic.690250513

M. Jenny, J. Dusek, and G. Bouchet, Instabilities and transition of a sphere falling or ascending freely in a Newtonian fluid, Journal of Fluid Mechanics, vol.508, pp.201-239, 2004.
DOI : 10.1017/S0022112004009164

URL : https://hal.archives-ouvertes.fr/hal-01447013

G. Jiang and C. Shu, Efficient Implementation of Weighted ENO Schemes, Journal of Computational Physics, vol.126, issue.1, pp.202-228, 1996.
DOI : 10.1006/jcph.1996.0130

H. J. Keh and Y. K. Tseng, Slow motion of multiple droplets in arbitrary three-dimensional configurations, AIChE Journal, vol.38, issue.12, pp.1881-1904, 1992.
DOI : 10.1002/aic.690381205

D. L. Koch, Hydrodynamic diffusion in dilute sedimenting suspensions at moderate Reynolds numbers, Physics of Fluids A: Fluid Dynamics, vol.5, issue.5, p.1141, 1993.
DOI : 10.1063/1.858600

V. I. Kushch, A. S. Sangani, P. D. Spelt, and D. L. Koch, Finite-Weber-number motion of bubbles through a nearly inviscid liquid, Journal of Fluid Mechanics, vol.460, pp.241-280, 2002.
DOI : 10.1017/S0022112002008145

D. Legendre and J. Magnaudet, The lift force on a spherical bubble in a viscous linear shear flow, Journal of Fluid Mechanics, vol.368, pp.81-126, 1998.
DOI : 10.1017/S0022112098001621

D. Legendre, J. Magnaudet, and G. Mougin, Hydrodynamic interactions between two spherical bubbles rising side by side in a viscous liquid, Journal of Fluid Mechanics, vol.497, pp.133-166, 2003.
DOI : 10.1017/S0022112003006463

E. Loth, Quasi-steady shape and drag of deformable bubbles and drops, International Journal of Multiphase Flow, vol.34, issue.6, pp.523-546, 2008.
DOI : 10.1016/j.ijmultiphaseflow.2007.08.010

J. Martinez-mercado, C. A. Palacios-morales, and R. Zenit, Measurement of pseudoturbulence intensity in monodispersed bubbly liquids for 10<Re<500, Physics of Fluids, vol.19, issue.10, pp.103302-103334, 2007.
DOI : 10.1063/1.2772256

R. Mei, J. F. Klausner, and C. J. Lawrence, A note on the history force on a spherical bubble at finite Reynolds number, Physics of Fluids, vol.6, issue.1, pp.418-420, 1994.
DOI : 10.1063/1.868039

R. Meland, I. R. Gran, R. Olsen, and S. T. Munkejord, 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), pp.862-865, 2007.

A. Merle, D. Legendre, and J. Magnaudet, Forces on a high-Reynolds-number spherical bubble in a turbulent flow, Journal of Fluid Mechanics, vol.532, pp.53-62, 2005.
DOI : 10.1017/S0022112005004180

D. W. Moore, The rise of a gas bubble in a viscous liquid, Journal of Fluid Mechanics, vol.1, issue.01, pp.113-130, 1959.
DOI : 10.1017/S0022112059000520

A. Naso and A. Prosperetti, The interaction between a solid particle and a turbulent flow, New Journal of Physics, vol.12, issue.3, p.33040, 2010.
DOI : 10.1088/1367-2630/12/3/033040

S. Osher and J. A. Sethian, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, Journal of Computational Physics, vol.79, issue.1, pp.12-49, 1988.
DOI : 10.1016/0021-9991(88)90002-2

R. J. Phillips, J. F. Brady, and G. Bossis, Hydrodynamic transport properties of hard-sphere dispersions. I. Suspensions of freely mobile particles, Physics of Fluids, vol.31, issue.12, pp.3462-3472, 1988.
DOI : 10.1063/1.866914

A. Prosperetti and G. Tryggvason, Computational Methods for Multiphase Flow, 2007.
DOI : 10.1017/CBO9780511607486

B. Ray and A. Prosperetti, On skirted drops in an immiscible liquid, Chemical Engineering Science, vol.108, pp.213-222, 2014.
DOI : 10.1016/j.ces.2014.01.007

J. F. Richardson and W. N. Zaki, Sedimentation and fluidisation: Part I, Chemical Engineering Research and Design, vol.75, issue.2, pp.35-53, 1954.
DOI : 10.1016/S0263-8762(97)80006-8

I. Roghair, Y. M. Lau, N. G. Deen, H. M. Slagter, M. W. Baltussen et al., On the drag force of bubbles in bubble swarms at intermediate and high Reynolds numbers, Chemical Engineering Science, vol.66, issue.14, pp.3204-3211, 2011.
DOI : 10.1016/j.ces.2011.02.030

G. Russo and P. Smereka, A Remark on Computing Distance Functions, Journal of Computational Physics, vol.163, issue.1, pp.51-67, 2000.
DOI : 10.1006/jcph.2000.6553

W. Rybczynski, Uber die fortschreitende Bewegung einer flussigen Kugel in einem zahen Medium, In: Bull. Int. Acad. Sci. Cracovie A, vol.1, issue.39, pp.40-46, 1911.

G. Ryskin and L. G. Leal, Numerical solution of free-boundary problems in fluid mechanics. Part 2. Buoyancy-driven motion of a gas bubble through a quiescent liquid, Journal of Fluid Mechanics, vol.10, issue.-1, pp.19-35, 1984.
DOI : 10.1017/S0022112064000349

V. Sabelnikov, A. Y. Ovsyannikov, and M. Gorokhovski, Modified level set equation and its numerical assessment, Journal of Computational Physics, vol.278, pp.1-30, 2014.
DOI : 10.1016/j.jcp.2014.08.018

URL : https://hal.archives-ouvertes.fr/hal-01296872

A. Salih and S. G. Moulic, Some numerical studies of interface advection properties of level set method, Sadhana, vol.102, issue.2, pp.271-298, 2009.
DOI : 10.1007/s12046-009-0013-1

A. S. Sangani, Sedimentation in ordered emulsions of drops at low Reynolds numbers, ZAMP Zeitschrift f???r angewandte Mathematik und Physik, vol.26, issue.4, pp.542-556, 1987.
DOI : 10.1007/BF00946336

A. S. Sangani and A. Acrivos, Creeping flow through cubic arrays of spherical bubbles, International Journal of Multiphase Flow, vol.9, issue.2, pp.181-185, 1983.
DOI : 10.1016/0301-9322(83)90052-6

K. Sankaranarayanan and S. Sundaresan, Lift force in bubbly suspensions, Chemical Engineering Science, vol.57, issue.17, pp.3521-3542, 2002.
DOI : 10.1016/S0009-2509(02)00269-5

K. Sankaranarayanan, X. Shan, I. G. Kevrekidis, and S. Sundaresan, Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice Boltzmann method, Journal of Fluid Mechanics, vol.452, issue.21, pp.61-96, 2002.
DOI : 10.1017/S0022112001006619

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

P. D. Spelt and A. S. Sangani, Properties and Averaged Equations for Flows of Bubbly Liquids, In: Appl. Sci. Res, vol.58, pp.337-386, 1998.
DOI : 10.1007/978-94-011-4986-0_19

M. Sussman, P. Smereka, and S. Osher, A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow, Journal of Computational Physics, vol.114, issue.1, pp.146-159, 1994.
DOI : 10.1006/jcph.1994.1155

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

T. D. Taylor and A. Acrivos, On the deformation and drag of a falling viscous drop at low Reynolds number, Journal of Fluid Mechanics, vol.152, issue.03, pp.466-476, 1964.
DOI : 10.1016/0009-2509(60)87003-0

C. Theodoropoulos, K. Sankaranarayanan, S. Sundaresan, and I. G. Kevrekidis, Coarse bifurcation studies of bubble flow lattice Boltzmann simulations, Chemical Engineering Science, vol.59, issue.12, pp.2357-2362, 2004.
DOI : 10.1016/j.ces.2003.10.029

G. Tryggvason, R. Scardovelli, and S. Zaleski, Direct Numerical Simulations of Gas- Liquid Multiphase Flows, 2011.

C. H. Veldhuis and A. Biesheuvel, An experimental study of the regimes of motion of spheres falling or ascending freely in a Newtonian fluid, International Journal of Multiphase Flow, vol.33, issue.10, pp.1074-1087, 2007.
DOI : 10.1016/j.ijmultiphaseflow.2007.05.002

E. Wacholder, Sedimentation in a dilute emulsion, Chemical Engineering Science, vol.28, issue.7, pp.1447-1453, 1973.
DOI : 10.1016/0009-2509(73)85149-8

X. Yin and D. L. Koch, Lattice-Boltzmann simulation of finite Reynolds number buoyancy-driven bubbly flows in periodic and wall-bounded domains, Physics of Fluids, vol.20, issue.10, pp.103304-103331, 2008.
DOI : 10.1063/1.3001728

R. Zenit, D. L. Koch, and A. S. Sangani, Measurements of the average properties of a suspension of bubbles rising in a vertical channel, Journal of Fluid Mechanics, vol.429, issue.2 3, pp.307-342, 2001.
DOI : 10.1017/S0022112000002743