A. B. Basset, Treatise on Hydrodynamics, 1888.

G. S. Beavers and D. D. Joseph, Boundary conditions at a naturally permeable wall, Journal of Fluid Mechanics, vol.none, issue.01, pp.197-207, 1967.
DOI : 10.1017/S0022112067001375

A. S. Berman, Laminar Flow in Channels with Porous Walls, Journal of Applied Physics, vol.24, issue.9, p.1232, 1953.
DOI : 10.1063/1.1721476

E. J. Bisset, Mathematical model of the thermal regeneration of a wall-flow monolith diesel particulate filter, Chemical Engineering Science, vol.39, issue.7-8, pp.1233-1244, 1983.
DOI : 10.1016/0009-2509(84)85084-8

J. Boussinesq, Sur la résistance qu'oppose un fluide indéfini en repos, sans pesanteur, au mouvement varié d'une sphère solide qu'il mouille sur toute sa surface, quand les vitesses restent bien continues et assez faibles pour que leurs carrés et produits soient négligeables, C.R.A.S, vol.100, 1885.

J. F. Brady, Flow development in a porous channel and tube, Physics of Fluids, vol.27, issue.5, pp.1061-1067, 1984.
DOI : 10.1063/1.864735

H. H. Bruun, Hot-Wire Anemometry: Principles and Signal Analysis, Measurement Science and Technology, vol.7, issue.10, 1995.
DOI : 10.1088/0957-0233/7/10/024

S. G. Chatterjee and G. Belfort, Fluid flow in an idealized spiral wound membrane module, Journal of Membrane Science, vol.28, issue.2, pp.191-208, 1986.
DOI : 10.1016/S0376-7388(00)82210-3

M. R. Doshi, W. N. Gill, and V. N. Kabadi, Optimal design of hollow fiber modules, AIChE Journal, vol.23, issue.5, pp.765-768, 1977.
DOI : 10.1002/aic.690230520

J. Dufreche, M. Prat, P. Schmitz, and J. D. Sherwood, On the overall permeability of a porous layer limited by a perforated plate, Chemical Engineering science, issue.57, pp.2933-2944, 2002.

F. A. Dullien, Porous media -Fluid transport and Pore structure, 1979.

L. Durlofski and J. F. Brady, The spatial stability of a class of similarity solutions, Physics of Fluids, vol.27, issue.5, pp.1068-1076, 1984.
DOI : 10.1063/1.864736

A. Einstein, Uber die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendiertenTeilchen, Ann. Phys. Leipzig, vol.17, pp.549-560, 1905.

S. K. Friedlander, Smoke, Dust, and Haze : Fundamentals of Aerosol Dynamics, 2000.

C. Gouverneur, Etude expérimentale du champ hydrodynamique dans un tube poreux avec transfert de masse pariétal, 1991.

A. G. Konstandopoulos, E. Skaperdas, and M. Masoudi, Inertial Contributions to the Pressure Drop of Diesel Particulate Filters, SAE Technical Paper Series, 2001.
DOI : 10.4271/2001-01-0909

T. Lücke and H. Fissan, The prediction of filtration performance of high efficiency gas filter elements, Chemical Engineering Science, vol.51, issue.8, pp.1199-1208, 1995.
DOI : 10.1016/0009-2509(95)00366-5

J. Magnaudet, M. Rivero, and J. Fabre, Accelerated flows past a rigid sphere or a spherical bubble. Part 1. Steady straining flow, Journal of Fluid Mechanics, vol.16, issue.-1, pp.97-135, 1995.
DOI : 10.1016/0301-9322(79)90024-7

F. Marcuccilli, Etude expérimentale et théorique de la structure et de la réactivité de suies issues de moteurs Diesel, 1993.

F. Noel, P. Schmitz, and M. Prat, Effective Hydraulic Resistance of the first cake Layer at the filter surface : A Three Dimensional Solution, 9th World Filtration Congress, 2004.

R. Noirot, Etude expérimentale et paramétrique de la combustion de suies sur filtres à particules (Application à l'epuration des échappements des moteurs Diesel), 1990.

L. Oxarango, K. Benmachou, and P. Schmitz, Modelling of particulate loading of multi-channel filtration systems, 5th International Filtration Conference, 2002.

L. Oxarango, S. Bardon, P. Schmitz, and M. Quintard, 3D Macroscopic Model for Fluid Flow and Soot Deposit in Wall Flow Honeycomb DPF, SAE Technical Paper Series, 2003.
DOI : 10.4271/2003-01-0834

L. Oxarango, P. Schmitz, and M. Quintard, Laminar flow in channels with wall suction or injection: a new model to study multi-channel filtration systems, Chemical Engineering Science, vol.59, issue.5, pp.1039-1051, 2004.
DOI : 10.1016/j.ces.2003.10.027

J. P. Quaile and E. K. Levy, Laminar Flow in a Porous Tube With Suction, Journal of Heat Transfer, vol.97, issue.1, pp.66-71, 1975.
DOI : 10.1115/1.3450290

E. J. Bisset, Mathematical model of the thermal regeneration of a wall-flow monolith diesel particulate filter, Chemical Engineering Science, vol.39, issue.7-8, pp.1233-1244, 1983.
DOI : 10.1016/0009-2509(84)85084-8

E. J. Bisset and F. Shadman, Thermal regeneration of diesel-particulate monolithic filters, AIChE Journal, vol.31, issue.5, pp.753-758, 1985.
DOI : 10.1002/aic.690310508

F. Bonnefoy, P. Gilot, B. Stanmore, and G. Prado, A comparative study of carbon black and diesel soot reactivity in the temperature range 500???600??C???effect of additives, Carbon, vol.32, issue.7, pp.1333-1340, 1994.
DOI : 10.1016/0008-6223(94)90120-1

Y. Caillabet, P. Fabrie, D. Lasseux, and M. Quintard, Computation of largescale parameters for dispersion in fissured porous medium using finite-volume method, Computational Geosciences, issue.5, pp.121-150, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00295137

D. Soete and G. , Catalysis of soot combustion by metal oxides". Western States section meeting, 1988.

Z. Du, A. F. Sarofim, and J. P. Longwell, Activation energy in temperatureprogrammed desorption : Modeling end application to the soot-oxygen system, Energy Fuels, issue.4, pp.296-302, 1990.

F. Duval, F. Fichot, and M. Quintard, Thermal non-equilibrium model for twophase flow with phase-change in porous media, International Journal of Heat and Mass Transfer, issue.47, pp.613-639, 2004.

M. W. Farthing and C. T. Miller, A comparison of high-resolution, finitevolume , adaptative stencil schemes for simulating advective-dispersive transport, Advances in Water Resources, issue.24, pp.29-48, 2001.

O. Haralampous and G. C. Koltsakis, Intra-layer temperature gradients during regeneration of diesel particulate filters, Chemical Engineering Science, vol.57, issue.13, pp.2345-2355, 2002.
DOI : 10.1016/S0009-2509(02)00135-5

W. M. Kays, M. E. , and C. , Convective Heat and Mass Transfer, Journal of Applied Mechanics, vol.34, issue.1, 1987.
DOI : 10.1115/1.3607663

A. G. Konstandopoulos and M. Kostoglou, Reciprocating flow regeneration of soot filters, Combustion and Flame, vol.121, issue.3, pp.488-500, 2000.
DOI : 10.1016/S0010-2180(99)00156-X

A. G. Konstandopoulos, M. Kostoglou, and P. Housiada, Spatial nonuniformities in diesel particulate trap regeneration, SAE Technical paper series, 2001.

A. G. Konstandopoulos and M. Kostoglou, Microstructural Aspects of Soot Oxidation in Diesel Particulate Filters, SAE Technical Paper Series, 2004.
DOI : 10.4271/2004-01-0693

K. M. Leung, R. P. Lindsedt, and W. P. Jones, A simplified reaction mechanism for soot formation in nonpremixed flames, Combustion and Flame, vol.87, issue.3-4, pp.289-305, 1991.
DOI : 10.1016/0010-2180(91)90114-Q

F. Marcuccilli, Etude expérimentale et théorique de la structure et de la réactivité de suies issues de moteurs Diesel, 1993.

F. Marcuccilli, P. Gillot, B. Stanmore, and G. Prado, Experimental study of Diesel soot reactivity, 25th Symposium (International) on Combustion, 1994.

J. Nagle and R. F. Strickland-constable, Fifth conference on carbon, 1962.

A. Nakayama, F. Kuwahara, A. Naoki, and G. Xu, A volume averaging theory and its sub-control-volume model for analysing heat and fluid flow within heat transfer equipment, 12th International Heat Transfer Conference, 2002.

J. P. Neeft, T. Xander-nijhuis, E. Smakman, M. Makkee, and J. A. Moulijn, Kinetics of the oxidation of diesel soot, Fuel, vol.76, issue.12, pp.1129-1136, 1997.
DOI : 10.1016/S0016-2361(97)00119-1

C. N. Opris and J. H. Johnson, A 2-D Computational Model Describing the Heat Transfer, Reaction Kinetics and Regeneration Characteristics of a Ceramic Diesel Particulate Trap, SAE Technical Paper Series, 1998.
DOI : 10.4271/980546

G. N. Pontikakis, Modeling, reaction schemes and kinetic parameter estimation in automotive catalytic converters and Diesel particulate filters, 2003.

N. Puiroux, Transferts thermiques et d'Humidité dans les Matériaux composites Ablatables : Effets des Hétérogénéités, INPT, 2004.

M. Quintard and S. Whitaker, One- and Two-Equation Models for Transient Diffusion Processes in Two-Phase Systems, Advances in Heat Transfer, vol.23, pp.369-464, 1993.
DOI : 10.1016/S0065-2717(08)70009-1

M. Quintard, M. Kaviany, and S. Whitaker, Two-medium treatment of heat transfer in porous media: numerical results for effective properties, Advances in Water Resources, vol.20, issue.2-3, pp.77-94, 1997.
DOI : 10.1016/S0309-1708(96)00024-3

B. Stanmore, J. F. Brilhac, and P. Gilot, The Ignition and Combustion of Cerium Doped Diesel Soot, SAE Technical Paper Series, 1999.
DOI : 10.4271/1999-01-0115

B. R. Stanmore, J. F. Brilhac, and P. Gilot, The oxidation of soot: a review of experiments, mechanisms and models, Carbon, vol.39, issue.15, pp.2247-2268, 2001.
DOI : 10.1016/S0008-6223(01)00109-9

G. A. Stratakis and A. Stamatelos, Thermogravimetric analysis of soot emitted by a modern diesel engine run on catalyst-doped fuel, Combustion and Flame, vol.132, issue.1-2, pp.157-169, 2003.
DOI : 10.1016/S0010-2180(02)00432-7

M. Tancrez, Modélisation du rayonnement et des transferts couplés des milieux poreux réactifs. Application aux brûleurs radiants à gaz, 2002.

B. Van-leer, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov's method, Journal of Computational Physics, vol.32, issue.1, pp.101-136, 1979.
DOI : 10.1016/0021-9991(79)90145-1

R. Vonarb, Contribution à l'étude des phénomènes d'inflammation et de propagation de la combustion d'un lit de suies Diesel additivées, 1999.

S. Whitaker, /. Dordrecht, and . Boston, The method of volume averaging, 1999.
DOI : 10.1007/978-94-017-3389-2

A. Yezerets, N. W. Currier, H. A. Eadler, A. Suresh, P. F. Madden et al., Investigation of the oxidation behavior of diesel particulate matter, Catalysis Today, vol.88, issue.1-2, pp.17-25, 2003.
DOI : 10.1016/j.cattod.2003.08.003

E. J. Bisset, Mathematical model of the thermal regeneration of a wall-flow monolith diesel particulate filter, Chemical Engineering Science, vol.39, issue.7-8, pp.1233-1244, 1983.
DOI : 10.1016/0009-2509(84)85084-8

R. Vonarb, Contribution à l'étude des phénomènes d'inflammation et de propagation de la combustion d'un lit de suies Diesel additivees, 1999.

M. Masoudi, A. Heibel, and P. M. Then, Predicting pressure drop of wall-flow diesel particulate filter, SAE Technical paper series, 2000.

K. Ohno, K. Shimati, N. Taoka, H. Santae, T. Ninomiya et al., Characterisation of SiC DPF for passenger car, SAE Technical paper series, 2000.

S. C. Sorenson, J. W. Hoj, and P. Stobbe, Flow Characteristics of SiC Diesel Particulate Filter Materials, SAE Technical Paper Series, 1994.
DOI : 10.4271/940236

J. F. Brady, Flow development in a porous channel and tube, Physics of Fluids, vol.27, issue.5, pp.1061-1067, 1984.
DOI : 10.1063/1.864735

K. Damak, A. Ayadi, B. Zeghmati, and P. Schmitz, A new Navier-Stokes and Darcy's law combined model for fluid flow in crossflow filtration tubular membranes, Desalination, vol.161, issue.1, pp.67-77, 2004.
DOI : 10.1016/S0011-9164(04)90041-0

V. Nassehi, Modelling of combined Navier???Stokes and Darcy flows in crossflow membrane filtration, Chemical Engineering Science, vol.53, issue.6, pp.1253-1265, 1997.
DOI : 10.1016/S0009-2509(97)00443-0

P. Schmitz, Mécanismes d'interaction : hydrodynamique et agrégation, dans la formation du dépôt en microfiltration tangentielle, 1990.