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Biofouling
The Journal of Bioadhesion and Biofilm Research
Volume 33, 2017 - Issue 4
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Articles

One-domain approach for studying multiphase transport phenomena in biofilm growing systems

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Pages 336-351 | Received 21 Dec 2016, Accepted 16 Mar 2017, Published online: 13 Apr 2017

References

  • Aguilar-Madera CG, Valdés-Parada FJ, Goyeau B, Alberto Ochoa-Tapia JA. 2011. Convective heat transfer in a channel partially filled with a porous medium. Int J Heat Mass Transfer. 54:2089–2099. doi:10.1016/j.ijheatmasstransfer.2010.12.020
  • Alonso C, Suidan MT, Kim BR, Kim BI. 1998. Dynamic mathematic model for the biodegradation of VOCs in a biofilter: biomass accumulation study. Environ Sci Technol. 32:3118–3123. doi:10.1021/es9711021
  • Araújo PA, Malheiro J, Machado I, Mergulhão F, Melo L, Simões M. 2016. Influence of flow velocity on the characteristics of Pseudomonas fluorescens biofilms. J Environ Eng. 142:04016031. doi:10.1061/(ASCE)EE.1943-7870.0001068
  • Baber K, Mosthaf K, Flemisch B, Helmig R, Muthing S, Wohlmuth B. 2012. Numerical scheme for coupling two-phase compositional porous-media flow and one-phase compositional free flow. IMA J Appl Math. 77:887–909. doi:10.1093/imamat/hxs048
  • Bagchi A, Kulacki FA. 2011. Natural convection in fluid–superposed porous layers heated locally from below. Int J Heat Mass Transfer. 54:3672–3682.
  • Bakke R, Kommedal R, Kalvenes S. 2001. Quantification of biofilm accumulation by an optical approach. J Microbiol Methods. 44:13–26. doi:10.1016/S0167-7012(00)00236-0
  • Bathia SN, Ingber DE. 2014. Microfluidic organs-on-chips. Nat Biotechnol. 32:760–772.
  • Beckermann C, Ramadhyani S, Viskanta R. 1987. Natural convection flow and heat transfer between a fluid layer and a porous layer inside a rectangular enclosure. J Heat Transfer. 109:363–371. doi:10.1115/1.3248089
  • Bhadauria BS, Kiran P, Shams A. 2014. Effect of rotational speed modulation on heat transport in a fluid layer with temperature dependent viscosity and internal heat source. Eng J. 5:1287–1297.
  • Bissett A, de Beer D, Schoon R, Shiraishi F, Reimer A, Arp G. 2008. Microbial mediation of stromatolite formation in karst-water creeks. Limnol Oceanogr. 53:1159–1168. doi:10.4319/lo.2008.53.3.1159
  • Böl M, Möhle RB, Haesner M, Neu TR, Horn H, Krull R. 2009. 3D finite element model of biofilm detachment using real biofilm structures from CLSM data. Biotechnol Bioeng. 103:177–186. doi:10.1002/bit.v103:1
  • Boraey MA, Guaily A, Epstein M. 2015. A hybrid model for biofilm growth on a deformable substratum. Can J Chem Eng. 93:789–797. doi:10.1002/cjce.v93.5
  • Brouwers HJH. 1995. Stagnant film model for effect of diffusional layer thickness on heat transfer and exerted friction. AIChE J. 41:1821–1825. doi:10.1002/(ISSN)1547-5905
  • Chamkha AJ, Muneer AI. 2013. Conjugate heat transfer in a porous cavity filled with nanofluids and heated by a triangular thick wall. Numer Heat Transfer Part A. 67:135–151.
  • Characklis WG, McFeters GA, Marshall KC. 1990. Physiological ecology in biofilm systems. In: Characklis WG, Marshall KC, editors. Biofilms. New York: John Wiley & Sons, p. 341–394.
  • Chen H, Wang XP. 2014. A one-domain approach for modeling and simulation of free fluid over a porous medium. J Comput Phys. 259:650–671. doi:10.1016/j.jcp.2013.12.008
  • Chrysikopoulos CV, Hsuana PY, Fyrillas MM, Lee KY. 2003. Mass transfer coefficient and concentration boundary layer thickness for a dissolving NAPL pool in porous media. J Hazard Mater. 97(1-3):245–255. doi:10.1016/S0304-3894(02)00264-9
  • Cogan N, Keener JP. 2004. The role of biofilm matrix in structural development. Math Med Biol. 21:147–166. doi:10.1093/imammb/21.2.147
  • Comini G, Manzan M, Cortella G. 1997. Open boundary conditions for the streamfunction-vorticity formulation of unsteady laminar convection. Numer Heat Transfer Part B. 31:217–234. doi:10.1080/10407799708915106
  • Cumsille P, Asenjo J, Conca C. 2014. A hybrid immersed interface-level set method for simulating the evolution of a biofilm. Comput Math Appl. 67:34–51.
  • de Dreuzy JR, Carrera J. 2016. On the validity of effective formulations for transport through heterogeneous porous media. Hydrol. Earth Syst. Sci. 20:1319–1330. doi:10.5194/hess-20-1319-2016
  • Deng C, Martinez DM. 2005. Viscous flow in a channel partially filled with a porous medium and with wall suction. Chem Engng Sci. 60:329–336. doi:10.1016/j.ces.2004.08.010
  • Duddu R, Chopp DL, Moran B. 2009. A two-dimensional continuum model of biofilm growth incorporating fluid flow and shear stress based detachment. Biotechnol Bioeng. 103:92–104. doi:10.1002/bit.v103:1
  • Eberl HJ, Parker DF, Van Loosdrecht MCM. 2001. A new deterministic spatio-temporal continuum model for biofilm development. J Theor Med. 3:161–175. doi:10.1080/10273660108833072
  • Friedman A, Hu B, Xue C. 2014. On a multiphase multicomponent model of biofilm growth. Arch Ration Mech Anal. 211:257–300. doi:10.1007/s00205-013-0665-1
  • Fux CA, Costerton JW, Stewart P, Stoodley P. 2005. Survival strategies of infectious biofilms. Trends Microbiol. 13:34–40. doi:10.1016/j.tim.2004.11.010
  • Gapes DJ, Keller J. 2009. Impact of oxygen mass transfer on nitrification reactions in suspended carrier reactor biofilms. Process Biochem. 44:43–53. doi:10.1016/j.procbio.2008.09.004
  • Golfier F, Wood BD, Orgogozo L, Quintard M, Buès M. 2009. Biofilms in porous media: development of macroscopic transport equations via volume averaging with closure for local mass equilibrium conditions. Adv Water Resour. 32:463–485. doi:10.1016/j.advwatres.2008.11.012
  • Goyeau B, Lhuillier D., Gobin D, Velarde MG. 2003. Momentum transport at a fluid-porous interface. Int J Heat Mass Transfer. 46:4071–4081. doi:10.1016/S0017-9310(03)00241-2
  • Halan B, Buehler K, Schmid A. 2012. Biofilms as living catalysts in continuous chemical syntheses. Trends Biotechnol. 30:453–465. doi:10.1016/j.tibtech.2012.05.003
  • Han Y, Zhang W, Xu J. 2011. A simplified mathematical model of multi-species biofilm for simultaneous removal of sulfur dioxide (SO2) and nitric oxide (NO) using a biotrickling-filter. Afr J Microbiol Res. 5:541–550.
  • Hanspal NS, Waghode AN, Nassehi V, Wakeman RJ. 2009. Development of a predictive mathematical model for coupled stokes/Darcy flows in cross-flow membrane filtration. Chem Eng J. 149:132–142. doi:10.1016/j.cej.2008.10.012
  • Hee-Wook R, Kyung-Suk C, Chung DJ. 2010. Relationships between biomass, pressure drop, and performance in a polyurethane biofilter. Bioresour Technol. 101:1745–1751.
  • Hill AA, Carr M. 2010. Nonlinear stability of the one-domain approach to modelling convection in superposed fluid and porous layers. Proc R Soc A. 466:2695–2705. doi:10.1098/rspa.2010.0014
  • Horn H, Lackner S. 2014. Modeling of biofilm systems: a review. Adv Biochem Eng Biotechnol. 146:53–76.
  • Jiménez-Islas H, Calderón-Ramírez M, Navarrete-Bolaños JL, Botello-Álvarez JE, López-Isunza F, Martínez-González GM. 2009. Numerical study of natural convection in a 2-D square cavity with fluid-porous medium interface and heat generation. Rev Mex Ing Quím. 8:169–185.
  • Klapper I, Dockery J. 2010. Mathematical description of microbial biofilms. Soc Ind Appl Math. 52:221–265.
  • Kommedal R, Bakke R. 2003. Modeling Pseudomonas aeruginosa biofilm detachment. HiT Working Paper no. 3. Telemark University College.
  • Li C, Zhang Yilei, Yehuda Cohen. 2015. Individual based modeling of Pseudomonas aeruginosa biofilm with three detachment mechanisms. RSC Adv. 5:79001–79010. doi:10.1039/C5RA11041F
  • Manga M, Weeraratne D. 2001. Boundary-layer thickness and instabilities in Benard convection of a fluid with variable viscosity. Phys Fluids. 13:802–805. doi:10.1063/1.1345719
  • Marques MPC, Fernandes P. 2011. Microfluidic devices: useful tools for bioprocess intensification. Molecules. 16:8368–8401. doi:10.3390/molecules16108368
  • Miller JK, Brantner JS, Clemons C, Kreider KL, Milsted A, Wilber P. 2014. Mathematical modelling of Pseudomonas aeruginosa biofilm growth and treatment in the cystic fibrosis lung. Math Med Biol. 31:1–26.
  • Nishihara GN, Ackerman JD. 2007. The effect of hydrodynamics on the mass transfer of dissolved inorganic carbon to the freshwater macrophyte Vallisneria americana. Limnol Oceanogr Methods. 5:73–96.
  • Nourollahi M, Farhadi M, Sedighi K. 2010. Numerical study of mixed convection and entropy generation in the Poiseulle-Benard channel in different angles. Therm Sci. 14(2):329–340. doi:10.2298/TSCI1002329N
  • Orgogozo L, Golfier F, Buès MA. 2009. Upscaling of transport processes in porous media with biofilms in equilibrium and non-equilibrium conditions. Appl Anal. 88:1579–1588. doi:10.1080/00036810902913862
  • Orgogozo L, Golfier F, Buès MA, Quintard M, Koné T. 2013. A dual-porosity theory for solute transport in biofilm-coated porous media. Adv Water Resour. 62(PartB):266–279. doi:10.1016/j.advwatres.2013.09.011
  • Peszynska M, Trykozko A, Iltis G, Schlueter S, Wildenschilde D. 2015. Biofilm growth in porous media: experiments, computational modeling at the porescale, and upscaling. Adv Water Resour. 95:288–301.
  • Picioreanu C, van Loosdrecht MCM, Heijnen JJ. 1998. Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach. Biotechnol Bioeng. 58:101–116. doi:10.1002/(ISSN)1097-0290
  • Picioreanu C, van Loosdrecht MCM, Heijnen JJ. 2000a. A theoretical study on the effect of surface roughness on mass transport and transformation in biofilms. Biotechnol Bioeng. 68:355–369. doi:10.1002/(ISSN)1097-0290
  • Picioreanu C, van Loosdrecht MCM, Heijnen JJ. 2000b. Effect of diffusive and convective substrate transport on biofilm structure formation: a twodimensional modeling study. Biotechnol Bioeng. 69:504–515. doi:10.1002/(ISSN)1097-0290
  • Picioreanu C, Vrouwenvelder JS, van Loosdrecht MCM. 2009. Three-dimensional modeling of biofouling and fluid dynamics in feed spacer channels of membrane devices. J Membr Sci. 345:340–354. doi:10.1016/j.memsci.2009.09.024
  • Radu AI, Bergwerff L, van Loosdrecht MCM, Picioreanu C. 2014. Combined biofouling and scaling in membrane feed channels: a new modeling approach. Chem Eng J. 241:77–91. doi:10.1016/j.cej.2013.12.021
  • Rittmann BE, McCarty PL. 2001. Environmental biotechnology: principles and applications. New York (NY): McGraw-Hill.
  • Roache PJ. 2003. Fundamentals of computational fluid dynamics. Albuquerque (NM): Hermosa.
  • Roberts RD, Revsbech NP, Damgaard LR. 2007. Effect of water velocity and benthic diatom morphology on the water chemistry experienced by postlarval abalone. J Shellfish Res. 26:745–750. doi:10.2983/0730-8000(2007)26[745:EOWVAB]2.0.CO;2
  • Sherwood TK, Brian P, Fisher R, Dresner L. 1965. Salt Concentration at phase boundaries in desalination by reverse osmosis. Ind Eng Chem Fundam. 4:113–118. doi:10.1021/i160014a001
  • Stewart PS. 2002. Mechanisms of antibiotic resistance in bacterial biofilms. Int J Med Microbiol. 292:107–113. doi:10.1078/1438-4221-00196
  • Stewart PS. 2012. Mini-review: convection around biofilms. Biofouling. 28:187–198. doi:10.1080/08927014.2012.662641
  • Stoodley P, Sauer K, Davies DG, Costerton W. 2002. Biofilms as complex differentiated communities. Annu Rev Microbiol. 56:187–209. doi:10.1146/annurev.micro.56.012302.160705
  • Taherzadeh D. 2011. Mechanics and substrate transport of moving biofilm structures [ dissertation]. Technische Universität München.
  • Thullner M, Schroth M, Zeyer J, Kinzelbach W. 2004. Modeling of a microbial growth experiment with bioclogging in a two-dimensional saturated porous media flow field. J Contm Hydrol. 70:37–62. doi:10.1016/j.jconhyd.2003.08.008
  • Valdés-Parada FJ, Alberto Ochoa-Tapia JA, Alvarez-Ramirez J. 2007. Diffusive mass transport in the fluid–porous medium inter-region: closure problem solution for the one-domain approach. Chem Eng Sci. 62:6054–6068. doi:10.1016/j.ces.2007.06.012
  • Vemuri V, Karplus WJ. 1981. Digital computer treatment of partial differential equations. Ann Arbor, MI: Prentice-Hall.
  • Wang Q, Zhang T. 2010. Review of mathematical models for biofilms. Commun Solid State Phys. 150:1009–1022. doi:10.1016/j.ssc.2010.01.021
  • Wang Q, Zhang T. 2012. Kinetic theories for biofilms. Discrete Continuous Dyn Syst Ser B. 17:1027–1059. doi:10.1021/es9711021
  • Webb JS, Givskov M, Kjelleberg S. 2003. Bacterial biofilms: prokaryotic adventures in multicellularity. Curr Opin Microbiol. 6:578–585. doi:10.1016/j.mib.2003.10.014
  • Wimpenny JWT, Colasanti R. 1997. A unifying hypothesis for the structure of microbial biofilms based on cellular automaton models. FEMS Microbiol Ecol. 22: 1–16. doi:10.1111/j.1574-6941.1997.tb00351.x
  • Wright WF, Schroeder ED, Chang DPY. 2005. Transient response of flow-direction-switching vapor-phase biofilters. J Env Eng. 131:999–1009. doi:10.1061/(ASCE)0733-9372(2005)131:7(999)
  • Xavier J, Picioreanu C, van Loosdrecht MCM. 2005a. A general description of detachment for multidimensional modelling of biofilms. Biotechnol Bioeng. 91:651–669. doi:10.1002/bit.20544
  • Xavier J, Picioreanu C, van Loosdrecht MCM. 2005b. A framework for multidimensional modelling of activity and structure of multispecies biofilms. Environ Microbiol. 7:1085–1103. doi:10.1111/emi.2005.7.issue-8
  • Xu R. 2004. Spatial growth patterns of Pseudomonas aeruginosa biofilms. [ dissertation]. Montana State University.
  • Yamamoto T, Ueda S. 2013. Numerical simulation of biofilm growth in flow channels using a cellular automaton approach coupled with a macro flow computation. Biorheology. 50:203–216.
  • Zhang T, Cogan N, Wang Q. 2008. Phase-field models for biofilms II. 2-D numerical simulations of biofilm-flow interaction. Commun Comput Phys. 4:72–101.
  • Zhao P, Chen CF. 2001. Stability analysis of double-diffusive convection in superposed fluid and porous layers using a one-equation model. Int J Heat Mass Transfer. 44:4625–4633. doi:10.1016/S0017-9310(01)00102-8
  • Zhao J, Wang Q. 2016. A 3D multi-phase hydrodynamic model for cytokinesis of eukaryotic cells. Comm Comp Phys. 19:663–681. doi:10.4208/cicp.181014.140715a
  • Zhao J, Shen Y, Haapasalo M, Wang Zhejun. 2016. A 3D numerical study of antimicrobial persistence in heterogeneous multi-species biofilms. J Theor Bio. 392:83–98. doi:10.1016/j.jtbi.2015.11.010
  • Zhu S, Chen S. 2001. Impacts of Reynolds number on nitrification biofilm kinetics. Aquacult Eng. 24:213–229. doi:10.1016/S0144-8609(00)00071-6
  • Znad HT, Katoh K, Kawase Y. 2007. High loading toluene treatment in a compost based biofilter using up-flow and down-flow swing operation. J Hazard Mater. 141:745–752. doi:10.1016/j.jhazmat.2006.07.039

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