P. Anthony, C. Geindreau, P. Sé-chet, and J. Martins, Biofilm growth in porous media: derivation of a macroscopic model from the physics at the pore scale via homogeneization, Proceedings of the International Congress Biotechniques for Air Pollution Control, pp.171-179, 2005.

G. Bertani, Studies on lysogenesis I: the mode of phage liberation by lysogenic Escherichia coli, Journal of Bacteriology, vol.62, issue.3, pp.293-300, 1951.

A. Bielefeldt, C. Mceachern, and T. Illangasekare, Hydrodynamic changes in sand due to biogrowth on naphthalene and decane, Journal of Environmental Engineering, vol.128, issue.1, pp.51-59, 2002.

M. L. Bordas, A. Cartellier, P. Sechet, and C. Boyer, Bubbly flow through fixed beds: microscale experiment in the dilute regime and modeling, AIChE Journal, vol.52, pp.3722-3743, 2006.

A. Brovelli, F. Malaguerra, and D. A. Barry, Bioclogging in porous media: model development and sensitivity to initial conditions, Environmental Modelling and Software, vol.24, pp.611-626, 2009.

W. G. Characklis, A. B. Cunningham, A. Escher, and D. Crawford, Biofilms in porous media, Proceedings of the International Symposium on Biofouled Aquifers: Prevention and Restoration. American Water Resources Association Technical Publication Series. American Water Resources Association, pp.57-78, 1987.

B. Chen-charpentier, Numerical Simulation of biofilm growth in porous media, Journal of Computational and Applied Mathematics, vol.103, pp.55-66, 1999.

T. P. Clement, B. S. Hooker, and R. S. Skeen, Macroscopic models for predicting changes in saturated porous media properties caused by microbial growth, Ground Water, vol.34, pp.934-942, 1996.

A. Cunningham, W. G. Characklis, F. Abedeen, and D. Crawford, Influence of biofilm accumulation on porous media hydrodynamics, Environmental Science & Technology, vol.25, pp.1305-1311, 1991.

D. G. Davies, M. R. Parsek, J. P. Pearson, B. H. Iglewski, J. W. Costerton et al., The involvement of cell-to-cell signals in the development of a bacterial biofilm, Science, vol.280, pp.295-298, 1998.

M. Deront, F. M. Samb, N. Adler, and P. Pé-ringer, Volumetric oxygen mass transfer coefficient in an upflow cocurrent packed-bed bioreactor, Chemical Engineering Science, vol.53, pp.1321-1330, 1998.

C. Di-iaconi, R. Ramadori, A. Lopez, and R. Passino, Influence of hydrodynamic shear forces on properties of granular biomass in a sequencing batch biofilter reactor, Biochemical Engineering Journal, vol.30, pp.152-157, 2006.

G. Lopez, L. A. Veiga, M. C. Nogueira, R. Aparicio, A. Melo et al., A technique using a membrane flow cell to determine average mass transfer coefficients and tortuosity factors in biofilms, Water Science and Technology, vol.47, issue.5, pp.61-67, 2003.

F. Golfier, B. D. Wood, L. Orgogozo, M. Quintard, and M. Bues, Biofilms in porous media: development of macroscopic transport equations via volume averaging with closure for local mass equilibrium conditions, Advances in Water Resource, vol.32, issue.3, pp.463-485, 2009.

G. A. Hill and C. W. Robinson, Substrate inhibition kinetics: phenol degradation by Pseudomonas putida, Biotechnology and Bioengineering, vol.17, pp.1599-1615, 1975.

I. Iliuta and F. Larachi, Modelling simultaneous biological clogging and physical plugging in trickle-bed bioreactors for wastewater treatment, Chemical Engineering Science, vol.60, pp.1477-1489, 2005.

K. J. Ives and V. Pienvichitr, Kinetics of the filtration of dilute suspensions, Chemical Engineering Science, vol.20, pp.965-973, 1965.

G. E. Kapellos, T. S. Alexiou, and A. C. Payatakes, A multiscale theoretical model for diffusive mass transfer in cellular biological media, Mathematical Biosciences, vol.210, pp.177-237, 2007.

M. Karrabi, Coupling between hydrodynamic and biofilm in porous media: application to a biofilter, 2009.

M. Karrabi, P. Sechet, C. Morra, I. Florensa, C. Geindreau et al., Experimental investigation of biofilm growth and hydrodynamic/ biomass interaction in a granular bioreactor, Proceedings of the Sixth, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00224482

J. Kildsgaard and P. Engesgaard, Numerical analysis of biological clogging in twodimensional sand box experiments, Journal of Contaminant Hydrology, vol.50, pp.261-285, 2001.

Y. Liu and J. H. Tay, The essential role of hydrodynamic shear force in the formation of biofilm and granular sludge, Water Research, vol.36, pp.1653-1665, 2002.

C. Menoret, Traitement d'effluents concentré s par cultures fixé es sur gravier ou pouzzolane, 2001.

A. Ortiz-arroyo, F. Larachi, and I. Iliuta, Method for inferring contact angle and for correlating static liquid hold-up in packed beds, Chemical Engineering Science, vol.58, pp.2835-2855, 2003.

B. M. Peyton, Effects of shear stress and substrate loading rate on pseudomonas aeruginosa biofilm thickness and density, Water Research, vol.30, pp.29-36, 1996.

C. Picioreanu, Multidimensional modelling of biofilm structure, 1999.

C. Picioreanu, M. C. Van-loosdrecht, and J. J. Heijnen, Effect of diffusive and convective substrate transport on biofilm structure formation: a two-dimensional modeling study, Biotechnology and Bioengineering, vol.69, pp.504-515, 2000.

P. Qi, W. Wang, and Z. Qi, Effect of Shear Stress on Biofilm Morphological Characteristics and the Secretion of Extracellular Polymeric Substances, 2008.

J. C. Shaw, B. Bramhill, N. C. Wardlaw, and J. W. Costerton, Bacterial fouling in a model core system, Applied and Environmental Microbiology, vol.49, pp.693-701, 1985.

H. Siegrist and W. Gujer, Mass transfer mechanisms in a heterotrophic biofilm, Water Research, vol.19, issue.11, pp.1369-1378, 1985.

M. Simoes, M. O. Peireira, S. Sillankorva, J. Azeredo, and M. J. Vieira, The effect of hydrodynamic conditions on the phenotype of Pseudomonas fluorescens biofilms, Biofouling, vol.23, issue.3/4, pp.249-258, 2007.

T. L. Stewart and H. S. Fogler, Biomass plug development and propagation in porous media, Biotechnology and Bioengineering, vol.72, issue.3, pp.353-363, 2001.

S. W. Taylor and P. R. Jaffé, Biofilm growth and the related changes in the physical properties of a porous medium. 1. Experimental investigations, Water Resource Research, vol.26, pp.2153-2159, 1990.

M. Thullner, L. Mauclaire, M. H. Schroth, W. Kinzelbach, and J. Zeyer, Interaction between water flow and spatial distribution of microbial growth in a twodimensional flow field in saturated porous media, Contaminant Hydrology, vol.58, pp.169-189, 2002.

M. Thullner, M. H. Schroth, J. Zeyer, and W. Kinzelbach, Modeling of a microbial growth experiment with bioclogging in a two-dimensional saturated porous media flow field, Contaminant Hydrology, vol.70, pp.37-62, 2004.

Y. Tsai, Impact of flow velocity on the dynamic behaviour of biofilm bacteria, Biofouling, vol.21, issue.5/6, pp.267-277, 2005.

M. C. Van-loosdrecht, J. J. Heijnen, H. Eberl, J. Kreft, and C. Picioreanu, Mathematical modelling of biofilm structures, Antonie van Leeuwenhoek, vol.81, pp.245-256, 2002.

P. Vandevivere and P. Baveye, Saturated hydraulic conductivity reduction caused by aerobic bacteria in sand columns, Soil Science Society of America, vol.56, pp.1-13, 1992.

P. Vandevivere, P. Baveye, D. S. De-lozada, and P. Deleo, Microbial clogging of saturated soils and aquifer materials: evaluation of mathematical models, Water Resource Research, vol.31, pp.2173-2180, 1995.

P. Vandevivere, Bacterial clogging of porous media: a new modelling approach, Biofouling, vol.8, pp.281-291, 1995.

V. P. Venugopalan, M. Kuehn, M. Hausner, D. Springael, P. A. Wilderer et al., Architecture of a nascent Sphingomonas sp. biofilm under varied hydrodynamic conditions, Applied and Environmental Microbiology, vol.71, issue.5, pp.2677-2686, 2005.

O. Wanner, H. J. Eberl, E. Morgenroth, D. R. Noguera, C. Picioreanu et al., IWA Biofilm Specialists Conference in, 2004.

B. D. Wood and R. M. Ford, Biological processes in porous media: from the pore scale to the field, Advances in Water Resource, vol.30, issue.6-7, pp.1387-1391, 2007.

A. Zysset, F. Stauffer, and T. Dracos, Modeling of reactive groundwater transport governed by biodegradation, Water Resour. Res, vol.30, pp.2423-2434, 1994.