B. Alazmi and K. Vafai, Analysis of fluid flow and heat transfer interfacial conditions between a porous medium and a fluid layer, International Journal of Heat and Mass Transfer, vol.44, issue.9, pp.1735-1749, 2001.
DOI : 10.1016/S0017-9310(00)00217-9

B. J. Alder and T. E. Wainwright, Phase Transition for a Hard Sphere System, The Journal of Chemical Physics, vol.27, issue.5, 1957.
DOI : 10.1063/1.1743957

B. J. Alder and T. E. Wainwright, Studies in Molecular Dynamics. I. General Method, The Journal of Chemical Physics, vol.31, issue.2, pp.459-466, 1959.
DOI : 10.1063/1.1730376

A. Amirtharajah and S. Jeffcoat, « Modeling and analysis of deep bed filtration»

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

R. Beetstra, « Drag force in random arrays of mono-and bidisperse spheres, Thèse de doctorat, 2005.

R. Beetstra, M. A. Van-der-hoef, and J. A. Kuipers, Drag force of intermediate Reynolds number flow past mono- and bidisperse arrays of spheres, AIChE Journal, vol.62, issue.2, pp.489-501, 2007.
DOI : 10.1002/aic.11065

T. Belytschko, Y. Y. Lu, and L. Gu, Element-free Galerkin methods, Element free Galerkin methods, pp.229-256, 1994.
DOI : 10.1002/nme.1620370205

S. Benyahia, M. Syamlal, and T. J. O-'brien, Extension of Hill???Koch???Ladd drag correlation over all ranges of Reynolds number and solids volume fraction, Powder Technology, vol.162, issue.2, pp.166-174, 2006.
DOI : 10.1016/j.powtec.2005.12.014

M. J. Biggs, S. J. Humby, A. Buts, and U. Tuzun, Explicit numerical simulation of suspension flow with deposition in porous media: influence of local flow field variation on deposition processes predicted by trajectory methods, Chemical Engineering Science, vol.58, issue.7, pp.1271-1288, 2003.
DOI : 10.1016/S0009-2509(02)00555-9

F. Bouchelaghem and A. Almosni, « Experimental Determination of the Longitudinal Dispersivity During the Injection of a Micro-Cement Grout in a One-Dimensional Soil Column, Trans. porous med, pp.67-93, 2003.

D. B. Brackbil, J. U. Kothe, H. M. Ruppel, and . Flip, Flip: A low-dissipation, particle-in-cell method for fluid flow, Computer Physics Communications, vol.48, issue.1, pp.25-38, 1988.
DOI : 10.1016/0010-4655(88)90020-3

J. Bridgwater, N. W. Sharpe, and D. C. Stocker, « Particle mixing by percolation, Trans. Inst. Chem. Engrs, vol.47, pp.114-119

P. P. Brown and D. F. Lawler, Sphere Drag and Settling Velocity Revisited, Journal of Environmental Engineering, vol.129, issue.3, pp.222-231, 2003.
DOI : 10.1061/(ASCE)0733-9372(2003)129:3(222)

V. N. Burganos, E. D. Skouras, C. A. Paraskeva, and A. C. Payatakes, Simulation of the dynamics of depth filtration of non-Brownian particles, AIChE Journal, vol.4, issue.4, pp.880-894, 2001.
DOI : 10.1002/aic.690470411

J. S. Chong, E. B. Christiansen, and A. D. Baer, Rheology of concentrated suspensions, Journal of Applied Polymer Science, vol.15, issue.8, 1971.
DOI : 10.1002/app.1971.070150818

P. A. Cundall and O. D. Strack, A discrete numerical model for granular assemblies, G??otechnique, vol.29, issue.1, pp.47-65, 1979.
DOI : 10.1680/geot.1979.29.1.47

J. M. Dallavalle, The technology of fine particle », 1948.

H. Darcy, Les fontaines publiques de la ville de, p.1856

R. H. Davis and H. Gecol, Hindered settling function with no empirical parameters for polydisperse suspensions, AIChE Journal, vol.40, issue.3, p.1994
DOI : 10.1002/aic.690400317

D. Felice and R. «. , The voidage function for fluid-particle interaction systems, International Journal of Multiphase Flow, vol.20, issue.1, pp.153-159, 1994.
DOI : 10.1016/0301-9322(94)90011-6

D. Felice and R. «. , Hydrodynamics of liquid fluidisation, Chemical Engineering Science, vol.50, issue.8, pp.1213-1245, 1995.
DOI : 10.1016/0009-2509(95)98838-6

D. Felice and R. «. , The particle-in-a-tube analogy for a multiparticle suspension, International Journal of Multiphase Flow, vol.22, issue.3, pp.515-525, 1996.
DOI : 10.1016/0301-9322(96)00005-5

D. Felice and R. , A relationship for the wall effect on the settling velocity of a sphere at any flow regime, International Journal of Multiphase Flow, vol.22, issue.3, pp.527-533, 1996.
DOI : 10.1016/0301-9322(96)00004-3

D. Felice and R. , The sedimentation velocity of dilute suspensions of nearly monosized spheres, International Journal of Multiphase Flow, vol.25, issue.4, pp.559-574, 1999.
DOI : 10.1016/S0301-9322(98)00084-6

F. A. Dullien, « Porous Media: Fluid Transport and Pore Structure, 1992.

H. Edelsbruner and E. P. Mücke, Three-dimensional alpha shapes, ACM Transactions on Graphics, vol.13, issue.1, pp.43-72, 1994.
DOI : 10.1145/174462.156635

I. «. Fatt, The Network Model of Porous Media. III, Dynamic Properties of Networks with Tube Radius Distribution, J. Petr. Tech., Pet. Trans., AIME, vol.207, pp.164-181, 1956.

V. Fidleris and R. L. Whitmore, Experimental determination of the wall effect for spheres falling axially in cylindrical vessels, British Journal of Applied Physics, vol.12, issue.9, pp.490-494, 1961.
DOI : 10.1088/0508-3443/12/9/311

J. M. Frey, P. Schmitz, and J. Dufreche, Gohr Pinheiro I. « Particle Deposition in Porous Media: Analysis of Hydrodynamic and Weak Inertial Effects, Transport in Porous Media, vol.37, issue.1, pp.25-54, 1999.
DOI : 10.1023/A:1006546717409

N. A. Fuchs and I. B. Stechkina, « A note on the theory of fibrous filters, Ann. Occup. Hyg, vol.6, issue.27, p.1963

C. Ghidaglia, « Filtration en profondeur de particules, Thèse de Doctorat, 1994.

C. Ghidaglia, L. De-arcangelis, J. Hinch, and E. Guazzelli, Transition in particle capture in deep bed filtration, Physical Review E, vol.53, issue.4, pp.3028-3031, 1996.
DOI : 10.1103/PhysRevE.53.R3028

R. A. Gingold and J. J. Monaghan, Smoothed particle hydrodynamics: theory and application to non-spherical stars, Monthly Notices of the Royal Astronomical Society, vol.181, issue.3, pp.375-389, 1977.
DOI : 10.1093/mnras/181.3.375

R. A. Gingold and J. J. Monaghan, Kernel estimates as a basis for general particle methods in hydrodynamics, Journal of Computational Physics, vol.46, issue.3, pp.429-453, 1982.
DOI : 10.1016/0021-9991(82)90025-0

A. Hamrani and I. Belaidi, « Résolution des problèmes de distorsion en grande déformation dans les procédés de mise en forme des matériaux basée sur la Méthode EFG », 2010.

J. Happel, Viscous flow in multiparticle systems: Slow motion of fluids relative to beds of spherical particles, AIChE Journal, vol.4, issue.2, pp.197-201, 1958.
DOI : 10.1002/aic.690040214

J. Happel and N. Epstein, « Viscous flow in multiparticle systems: cubical assemblages of uniform spheres

H. Hasimoto, On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres, Journal of Fluid Mechanics, vol.13, issue.02, pp.317-328, 1959.
DOI : 10.1143/JPSJ.13.633

J. Hardy, Y. Pomeau, and O. De-pazzis, Time evolution of a two???dimensional model system. I. Invariant states and time correlation functions, Journal of Mathematical Physics, vol.14, issue.12, pp.1746-1759, 1973.
DOI : 10.1063/1.1666248

J. P. Herzig, D. M. Leclerc, L. Goff, and P. , Flow of Suspensions through Porous Media???Application to Deep Filtration, Industrial & Engineering Chemistry, vol.62, issue.5, pp.8-35, 1970.
DOI : 10.1021/ie50725a003

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, pp.213-241, 2001.
DOI : 10.1017/S0022112001005948

R. J. Hill, D. L. Koch, and A. J. Ladd, Moderate-Reynolds-number flows in ordered and random arrays of spheres, Journal of Fluid Mechanics, vol.448, pp.243-278, 2001.
DOI : 10.1017/S0022112001005936

D. W. Holmes, J. R. Williams, and P. Tilke, Smooth particle hydrodynamics simulations of low Reynolds number flows through porous media, International Journal for Numerical and Analytical Methods in Geomechanics, vol.72, issue.9, pp.419-437, 2011.
DOI : 10.1002/nag.898

X. Y. Hu and N. A. Adams, A multi-phase SPH method for macroscopic and mesoscopic flows, Journal of Computational Physics, vol.213, issue.2, pp.844-861, 2006.
DOI : 10.1016/j.jcp.2005.09.001

S. R. Idelsohn and E. Oñate, A Lagrangian meshless finite element method applied to fluid???structure interaction problems, Computers & Structures, vol.81, issue.8-11, pp.655-671, 2003.
DOI : 10.1016/S0045-7949(02)00477-7

I. Ippolito, L. Samson, and J. P. Hulin, Diffusion of a single particle in a 3D random packing of spheres, The European Physical Journal E, vol.3, issue.3, pp.227-236, 2000.
DOI : 10.1007/PL00013679

T. «. Iwasaki, Some notes on sand filtration, J. Am. Water Works Ass, vol.29, pp.1591-1602, 1937.

M. «. Jean, Frictional contact in collections of rigid or deformable bodies: numerical simulation of geomaterial motions, Mech. Geom. Inter, vol.42, pp.463-486, 1995.
DOI : 10.1016/S0922-5382(06)80022-X

S. W. Jeong and M. Y. Corapcioglu, Force analysis and visualization of NAPL removal during surfactant-related floods in a porous medium, Journal of Hazardous Materials, vol.126, issue.1-3, pp.8-13, 2005.
DOI : 10.1016/j.jhazmat.2005.06.015

P. X. Jiang, M. Li, Y. C. Ma, and Z. P. Ren, Boundary conditions and wall effect for forced convection heat transfer in sintered porous plate channels, International Journal of Heat and Mass Transfer, vol.47, issue.10-11, pp.2073-2083, 2004.
DOI : 10.1016/j.ijheatmasstransfer.2003.12.003

A. Kmiec, Equilibrium of forces in fluidized bed ??? experimental verification, The Chemical Engineering Journal, vol.23, issue.2, pp.133-136, 1982.
DOI : 10.1016/0300-9467(82)80003-8

D. L. Koch and A. S. Sangani, Particle pressure and marginal stability limits for a homogeneous monodisperse gas-fluidized bed: kinetic theory and numerical simulations, Journal of Fluid Mechanics, vol.400, issue.229, 1999.
DOI : 10.1017/S0022112099006485

S. Koo and A. S. Sangani, Effective-medium theories for predicting hydrodynamic transport properties of bidisperse suspensions, Physics of Fluids, vol.14, issue.10, 2002.
DOI : 10.1063/1.1503352

J. «. Koplik, J. Koplik, and T. J. Lasseter, Creeping flow in two-dimensional networks, Journal of Fluid Mechanics, vol.207, issue.-1, pp.219-247, 1982.
DOI : 10.1146/annurev.fl.11.010179.002103

A. J. Ladd, Hydrodynamic transport coefficients of random dispersions of hard spheres, The Journal of Chemical Physics, vol.93, issue.5, 1990.
DOI : 10.1063/1.458830

R. E. Larson and J. J. Hingdon, A periodic grain consolidation model of porous media, Physics of Fluids A: Fluid Dynamics, vol.1, issue.1, pp.38-46, 1989.
DOI : 10.1063/1.857545

J. Lanru and S. Ove, « Fundamentals of Discrete Element Methods for Rock Engineering: Theory and applications, 2007.

D. «. Leclerc, Vingt-cinq ans de contribution à l'étude de la filtration, Thèse de doctorat, 1988.

J. Lee and J. Koplik, Network model for deep bed filtration, Physics of Fluids, vol.13, issue.5, pp.1076-1086, 2001.
DOI : 10.1063/1.1359747

S. «. Liao, An analytic approximation of the drag coefficient for the viscous flow past a sphere, International Journal of Non-Linear Mechanics, vol.37, issue.1, pp.1-18, 2002.
DOI : 10.1016/S0020-7462(00)00092-5

C. T. Lin, B. Amadei, J. Jung, and J. Dwyer, Extensions of discontinuous deformation analysis for jointed rock masses, International Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts, vol.33, issue.7, pp.671-694, 1996.
DOI : 10.1016/0148-9062(96)00016-2

F. «. Lominé, Ecoulements de particules dans un milieu poreux, Thèse de Doctorat, 2007.

F. Lominé and L. Oger, Transport of small particles through a 3D packing of spheres: experimental and numerical approaches, Journal of Statistical Mechanics: Theory and Experiment, vol.2006, issue.07, 2006.
DOI : 10.1088/1742-5468/2006/07/P07019

F. Lominé and L. Oger, Transit time during the interparticle percolation process, Physical Review E, vol.82, issue.4, p.41301, 2010.
DOI : 10.1103/PhysRevE.82.041301

R. S. Maier, D. M. Kroll, Y. E. Kutsovsky, H. T. Davis, and R. S. Bernard, Simulation of flow through bead packs using the lattice Boltzmann method, Physics of Fluids, vol.10, issue.1, pp.60-74, 1998.
DOI : 10.1063/1.869550

I. F. Macdonald, M. S. El-sayed, K. Mow, and F. A. Dullien, Flow through Porous Media-the Ergun Equation Revisited, Industrial & Engineering Chemistry Fundamentals, vol.18, issue.3, pp.199-208, 1979.
DOI : 10.1021/i160071a001

S. Marusic, A note on permeability for a network of thin channels, Glasnik Matematicki, vol.39, issue.2, pp.341-348, 2004.
DOI : 10.3336/gm.39.2.16

L. Mazzei and P. Lettieri, A drag force closure for uniformly dispersed fluidized suspensions, Chemical Engineering Science, vol.62, issue.22
DOI : 10.1016/j.ces.2007.06.028

R. D. Mindlin and H. Deresiewicz, Elastic Spheres in Contact Under Varying Oblique Forces, J. App. Mech, vol.20, pp.327-344, 1953.
DOI : 10.1007/978-1-4613-8865-4_35

D. C. Moran, M. C. Moran, R. S. Cushing, and D. F. Lawler, « Particle behavior in Deep-Bed Filtration: Parti- Ripening and Breakthrough, Part 2-Particle Detachment, J. AWWA, pp.69-93, 1993.

J. J. Moreau, Unilateral Contact and Dry Friction in Finite Freedom Dynamics, pp.1-82, 1988.
DOI : 10.1007/978-3-7091-2624-0_1

G. Mo and A. S. Sangani, A method for computing Stokes flow interactions among spherical objects and its application to suspensions of drops and porous particles, Physics of Fluids, vol.6, issue.5, p.1637, 1994.
DOI : 10.1063/1.868227

L. N. Moresi and V. S. Solomatov, Numerical investigation of 2D convection with extremely large viscosity variations, Physics of Fluids, vol.7, issue.9, pp.2154-2162, 1995.
DOI : 10.1063/1.868465

D. «. Nadji, Colmatage d'un milieu modèle par une suspension d'argile : application au colmatage des chaussées poreuses, Thèse de Doctorat, 1998.

D. Nemec and J. Levec, Flow through packed bed reactors: 1. Single-phase flow, Chemical Engineering Science, vol.60, issue.24, pp.6947-6957, 2005.
DOI : 10.1016/j.ces.2005.05.068

K. M. Ng and A. C. Payatakes, Critical evaluation of the flow rate-pressure drop relation assumed in permeability models, AIChE Journal, vol.31, issue.9, pp.1569-1571, 1985.
DOI : 10.1002/aic.690310922

A. V. Nguyen, H. Stechemesser, G. Zobel, and H. J. Schulze, An improved formula for terminal velocity of rigid spheres, International Journal of Mineral Processing, vol.50, issue.1-2, pp.53-61, 1997.
DOI : 10.1016/S0301-7516(97)00007-0

J. Oliver, J. Cante, R. Weyler, C. González, and J. Hernández, Particle Finite Element Methods in Solid Mechanics Problems, Computational Methods in Applied Sciences, vol.1, pp.87-103, 2007.
DOI : 10.1007/978-1-4020-6577-4_6

J. Oliver, J. C. Cante, and C. Gonzalez, Particle Finite Element Methods in Solid Mechanics Problems
DOI : 10.1007/978-1-4020-6577-4_6

E. Oñate and S. R. Idelsohn, A mesh-free finite point method for advective-diffusive transport and fluid flow problems, Comp. Mech, vol.21, pp.283-292, 1998.

E. Oñate, S. R. Idelsohn, F. Del-pin, and R. Aubry, « The particle finite element method. An overview

E. Oñate, S. R. Idelsohn, M. A. Celigueta, and R. «. Rossi, Advances in the particle finite element method for fluid-structure interaction problems, First South-East Euro. Conf. Comp. Mech, 2006.

A. C. Payatakes, C. Tien, and R. M. Turian, A new model for granular porous media: Part I. Model formulation, AIChE Journal, vol.19, issue.1, pp.58-67, 1973.
DOI : 10.1002/aic.690190110

M. S. Peker and S. Helvac?, « Solid?Liquid Two Phase Flow, 2008.

D. O. Potyondy and P. Cundall, A bonded-particle model for rock, International Journal of Rock Mechanics and Mining Sciences, vol.41, issue.8, pp.1329-1364, 2004.
DOI : 10.1016/j.ijrmms.2004.09.011

F. Radjai, M. Jean, J. J. Moreau, and S. Roux, Force Distributions in Dense Two-Dimensional Granular Systems, Physical Review Letters, vol.77, issue.2, pp.274-277, 1996.
DOI : 10.1103/PhysRevLett.77.274

URL : https://hal.archives-ouvertes.fr/hal-00759668

S. D. Rege and H. S. Fogler, A network model for deep bed filtration of solid particles and emulsion drops, AIChE Journal, vol.34, issue.11, pp.1761-1772, 1988.
DOI : 10.1002/aic.690341102

S. «. Remond, DEM simulation of small particles clogging in the packing of large beads ». Physica A: Statistical Mechanics and its Applications, pp.4485-4496, 2010.

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

A. Rushton, A. S. Ward, and R. G. Holdich, « Solid-Liquid Filtration and Separation Technology, p.69451, 1996.
DOI : 10.1002/9783527614974

M. «. Sahimi, Flow and transport in porous media and fractured rock: From classical methods to modern approaches Second, Revised and enlarged edition, 2011.
DOI : 10.1002/9783527636693

A. S. Sangani and A. Acrivos, Slow flow through a periodic array of spheres, International Journal of Multiphase Flow, vol.8, issue.4, p.343, 1982.
DOI : 10.1016/0301-9322(82)90047-7

S. Sarkar, M. A. Van-der-hoef, and J. A. Kuipers, Fluid???particle interaction from lattice Boltzmann simulations for flow through polydisperse random arrays of spheres, Chemical Engineering Science, vol.64, issue.11, pp.2683-2691, 2009.
DOI : 10.1016/j.ces.2009.02.045

L. Schiller and A. Nauman, « A drag coefficient correlation», V.D.I. Zeitung, vol.77, p.318, 1935.

G. «. Shi, Discontinuous Deformation Analysis -A New Numerical Model for the Statics and Dynamics of Block Systems, Thèse de Doctorat, 1988.

A. Shojaei and R. «. Arefinia, Analysis of the sedimentation process in reactive polymeric suspensions, Chemical Engineering Science, vol.61, issue.23
DOI : 10.1016/j.ces.2006.08.050

C. Tien and B. V. Ramarao, « Granular Filtration of Aerosols and Hydrosols », 2007.

S. Tran-cong, . M. Gay, and E. E. Michaelides, « Drag coefficients of irregularly shaped particles ». Powder Tech, pp.21-32, 2004.

R. Turton and O. Levenspiel, A short note on the drag correlation for spheres, Powder Technology, vol.47, issue.1, pp.83-86, 1986.
DOI : 10.1016/0032-5910(86)80012-2

M. A. Van-der-hoef, R. Beetstra, and J. A. Kuipers, Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force, Journal of Fluid Mechanics, vol.528, pp.233-254, 2005.
DOI : 10.1017/S0022112004003295

B. H. Xu and A. B. Yu, Numerical simulation of the gas-solid flow in a fluidized bed by combining discrete particle method with computational fluid dynamics, Chemical Engineering Science, vol.52, issue.16, pp.2785-2809, 1997.
DOI : 10.1016/S0009-2509(97)00081-X

A. Yiotis, J. Psicogios, M. Kainourgiakis, A. Papaioannou, and A. Stubos, A lattice Boltzmann study of viscous coupling effects in immiscible two-phase flow in porous media, Col. Surf. A: Physicochem
DOI : 10.1016/j.colsurfa.2006.12.045

H. Yoshida, Tien C « Dynamic Behavior of Aerosol Filtration in a Two-Dimensional Model Filter

H. P. Zhu, M. Rahman, A. B. Yu, J. Bridgwater, and P. Zulli, Effect of particle properties on particle percolation behaviour in a packed bed, Minerals Engineering, vol.22, issue.11, pp.961-969, 2009.
DOI : 10.1016/j.mineng.2009.03.002

A. A. Zick and G. M. Homsy, Stokes flow through periodic arrays of spheres, Journal of Fluid Mechanics, vol.12, issue.-1, pp.13-26, 1982.
DOI : 10.1016/0009-2509(74)80200-9

C. Y. Wen and Y. H. Yu, Mechanics of fluidization », AIChE J, vol.62, issue.100, 1966.