Multicomponent model of deformation and detachment of a biofilm under fluid flow

Journal of the Royal Society Interface

Volumn 12, Issue 106, 2015, Pages

  Tierra, Giordano ^a,b   Pavissich, Juan P ^c,d   Nerenberg, Robert ^c   Xu, Zhiliang ^b   Alber, Mark S ^b  

^a CHARLES UNIVERSITY   (Czech Republic)

^b UNIVERSITY OF NOTRE DAME   (United States)

^c University of Notre Dame   (United States)

^d UNIVERSIDAD ADOLFO IBÁÑEZ   (Chile)

Author keywords

Biofilm; Continuum mechanics; Detachment; Energetic variation; Phase field model; Viscoelasticity

Indexed keywords

BIOFILMS; CONTINUUM MECHANICS; DEFORMATION; FLOW VELOCITY; PHASE INTERFACES; PHASE TRANSITIONS; THERMODYNAMICS; VISCOELASTICITY; VISCOSITY;

DETACHMENT; ENERGETIC VARIATION; EXTRACELLULAR POLYMERIC SUBSTANCES; MULTI-COMPONENT MODELING; PHASE FIELD MODELS; RESISTANCE TO DEFORMATION; SECOND LAWS OF THERMODYNAMICS; VARIATIONAL APPROACHES;

FLOW OF FLUIDS;

POLYMER; SOLVENT; BACTERIAL POLYSACCHARIDE;

ARTICLE; BACTERIAL CELL; BIOFILM; BIOFILM REACTOR; BIOLOGICAL MODEL; CHEMICAL INTERACTION; CHEMICAL STRUCTURE; ELASTICITY; FLOW KINETICS; FLOW RATE; FLUID FLOW; HYDRODYNAMICS; HYDROSTATIC PRESSURE; LAMINAR FLOW; MATHEMATICAL COMPUTING; MECHANICAL STRESS; PREDICTION; SHEAR STRESS; SIMULATION; THERMODYNAMICS; VISCOELASTICITY; VISCOSITY; WASTE WATER MANAGEMENT; BACTERIAL PHENOMENA AND FUNCTIONS; BACTERIUM; BACTERIUM ADHERENCE; CELL SIZE; COMPUTER SIMULATION; CYTOLOGY; GROWTH, DEVELOPMENT AND AGING; METABOLISM; MICROFLUIDICS; PHYSIOLOGY; PROCEDURES; SHEAR STRENGTH; YOUNG MODULUS;

BACTERIA; BACTERIAL ADHESION; BACTERIAL PHYSIOLOGICAL PHENOMENA; BIOFILMS; CELL SIZE; COMPUTER SIMULATION; ELASTIC MODULUS; MICROFLUIDICS; MODELS, BIOLOGICAL; POLYSACCHARIDES, BACTERIAL; SHEAR STRENGTH; STRESS, MECHANICAL;

EID: 84929493061     PISSN: 17425689     EISSN: 17425662     Source Type: Journal    
DOI: 10.1098/rsif.2015.0045     Document Type: Article

References (60)

1. Stoodley P, Sauer K, Davies DG, Costerton JW. 2002 Biofilms as complex differentiated communities. Annu. Rev. Microbiol. 56, 187-209. (doi:10.1146/annurev.micro.56.012302.160705)
2. Rosche B, Li XZ, Hauer B, Schmid A, Buehler K. 2009 Microbial biofilms: a concept for industrial catalysis?Trends Biotechnol. 3, 636-643. (doi:10.1016/j.tibtech.2009.08.001)
3. Chen AY, Deng Z, Billings AN, Seker UOS, Lu MY, Citorik RJ, Zakeri B, Lu TK. 2014 Synthesis and patterning of tunable multiscale materials with engineered cells. Nat. Mater. 13, 515-523. (doi:10.1038/NMAT3912)
4. Davies D. 2003 Understanding biofilm resistance to antibacterial agents. Nat. Rev. Drug Discov. 2, 114-122. (doi:10.1038/nrd1008)
5. Pavissich JP, Aybar M, Martin KJ, Nerenberg R. 2014 A methodology to assess the effects of biofilm roughness on substrate fluxes using image analysis, substrate profiling, and mathematical modelling. Water. Sci. Technol. 69, 1932-1941. (doi:10.2166/wst.2014.103)
6. Shaw T, Winston M, Rupp CJ, Klapper I, Stoodley P. 2004 Commonality of elastic relaxation times in biofilms. Phys. Rev. Lett. 93, 098102. (doi:10.1103/PhysRevLett.93.098102)
7. Flemming H-C, Wingender J. 2010 The biofilm matrix. Nat. Rev. Microbiol. 8, 623-633. (doi:10. 1038/nrmicro2415)
8. Liekeg O, Caldara M, Baugärtel R, Ribbeck K. 2011 Mechanical robustness of Pseudomonas aeruginosa biofilms. Soft Matter 7, 3307-3314. (doi:10.139/C0SM01467B)
9. Stewart PS. 2014 Biophysics of biofilm infection. FEMS Pathog. Dis. 70, 212-218. (doi:10.1111/2049-632X.12118)
10. Wilking JN, Angelini TE, Seminara A, Brenner MP, Weitz DA. 2011 Biofilms as complex fluids. MRS Bull. 36, 385-391. (doi:10.1557/jmr.2014.101)
11. Alpkvist E, Klapper I. 2007 Description of mechanical response including detachment using a novel particle model of biofilm/flow interaction. Water Sci. Technol. 55, 265-273. (doi:10.2166/wst.2007.267)
12. Zhang T, Cogan NG, Wang Q. 2008 Phase field models for biofilms. I. Theory and one-dimensional simulations . SIAM J. Appl. Math. 69, 641-669. (doi:10.1137/070691966)
13. Lindley B, Wang Q, Zhang T. 2012 Multicomponent hydrodynamic model for heterogeneous biofilms: two-dimensional numerical simulations of growth and interaction with flows. Phys. Rev. E. 85, 031908. (doi:10.1103/PhysRevE.85.031908)
14. Zhang T, Cogan NG, Wang Q. 2008 Phase-field models for biofilms II. 2-D numerical simulations of biofilm-flow interaction. Commun. Comput. Phys. 4, 72-101.
15. Cahn JW, Hilliard JE. 1958 Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 28, 258-267. (doi:10.1063/1.1744102)
16. van der Waals JD. 1979 The thermodynamic theory of capillarity flow under the hypothesis of a continuous variation of density. J. Stat. Phys. 20, 197-244. (doi:10.1007/BF01011514)
17. Klapper I, Dockery J. 2006 Role of cohesion in the material description of biofilms. Phys. Rev. E. 74, 031902. (doi:10.1103/PhysRevE.74.031902)
18. Alpkvist E, Picioreanu C, van Loosdrecht MCM, Heyden A. 2006 Three-dimensional biofilm model with individual cells and continuum EPS matrix. Biotechnol. Bioeng. 94, 962-979. (doi:10.1002/bit.20917)
19. Xavier J, Picioreanu C, van Loosdrecht MCM. 2005 A general description of detachment for multidimensional modelling of biofilms. Biotechnol. Bioeng. 91, 651-669. (doi:10.1002/bit.20544)
20. Cogan NG, Keener JP. 2004 The role of the biofilm matrix in structural development. Math. Med. Biol. 21, 147-166. (doi:10.1093/imammb/21.2.147)
21. Cogan NG, Guy RD. 2010 Multiphase flow models of biogels from crawling cells to bacterial biofilms. HFSP J. 4, 11-25. (doi:10.2976/1.3291142)
22. Taherzadeh D, Picioreanu C, Horn H. 2012 Mass transfer enhancement in moving biofilm structures. Biophys. J. 102, 1483-1492. (doi:10.1016/j.bpj.2012.02.033)
23. Klapper I. 2004 Effect of heterogeneous structure in mechanically unstressed biofilms on overall growth. Bull. Math. Biol. 66, 809-824. (doi:10.1016/j.bulm.2003.11.008)
24. Zhang TY, Klapper I. 2014 Critical occlusion via biofilm induced calcite precipitation in porous media. New J. Phys. 16, 055009. (doi:10.1088/1367-2630/16/5/055009)
25. Klapper I, Dockery J. 2010 Mathematical description of microbial biofilms. SIAM Rev. 52, 221-265. (doi:10.1137/080739720)
26. Wang Q, Zhang T. 2010 Review of mathematical models for biofilms. Sol. State Commun. 150, 1009-1022. (doi:10.1016/j.ssc.2010.01.021)
27. Monds RD, O'Toole GA. 2009 The developmental model of microbial biofilms: ten years of a paradigm up for review. Trends Microbiol. 17, 73-87. (doi:10.1016/j.tim.2008.11.001)
28. Wang Q, Zhang T. 2012 Kinetic theories for biofilms. Discrete Cont. Dyn. B 17, 1027-1059. (doi:10.3934/dcdsb.2012.17.1027)
29. Ehret AE, Böl M. 2013 Modelling mechanical characteristics of microbial biofilms by network theory. J. R. Soc. Interface 10, 20120676. (doi:10.1098/rsif.2012.0676)
30. Yue P, Feng JJ, Liu C, Shen J. 2004 A diffuseinterface method for simulating two-phase flows of complex fluids. J. Fluid Mech. 515, 293-317. (doi:10.1017/S0022112004000370)
31. Eisenberg B, Hyon Y, Liu C. 2010 Energy variational analysis of ions in water and channels: field theory for primitive models of complex ionic fluids. J. Chem. Phys. 133, 104104. (doi:10.1063/1.3476262)
32. Du Q, Liu C, Ryham R, Wang X. 2009 Energetic variational approaches in modeling vesicle and fluid interactions. Physica D 238, 923-930. (doi:10.1016/j.physd.2009.02.015)
33. Drescher K, Shen Y, Bassler BL, Stone HA. 2013 Biofilm streamers cause catastrophic disruption of flow with consequences for environmental and medical systems. Proc. Natl Acad. Sci. USA 110, 4345-4350. (doi:10.1073/pnas.1300321110)
34. Martin KJ, Nerenberg R. 2012 The membrane biofilm reactor (MBfR) for water and wastewater treatment: principles, applications, and recent developments. Biores. Technol. 122, 83-94. (doi:10.1016/j.biortech.2012.02.110)
35. Böl M, Ehret AE, Bolea Albero A, Hellriegel J, Krull R. 2013 Recent advances in mechanical characterisation of biofilm and their significance for material modelling. Crit. Rev. Biotechnol. 33, 145-171. (doi:10.3109/07388551.2012.679250)
36. Peterson BW, van der Mei HC, Sjollema J, Busscher HJ, Sharma PK. 2013 A distinguishable role of eDNA in the viscoelastic relaxation of biofilms. MBio 4, e00497. (doi:10.1128/mBio.00497-13)
37. Rusconi R, Lecuyer S, Autrusson N, Guglielmini L, Stone HA. 2011 Secondary flow as a mechanism for the formation of biofilm streamers. Biophys. J. 100, 1392-1399. (doi:10.1016/j.bpj. 2011.01.065)
38. Das S, Kumar A. 2013 Formation and post-formation dynamics of bacterial biofilm streamers as highly viscous liquid jets. (http://arXiv.org/abs/1312.6056)
39. Stoodley P, Cargo R, Rupp C, Wilson S, Klapper I. 2002 Biofilm material properties as related to shear-induced deformation and detachment phenomena. J. Ind. Microbiol. Biotechnol. 29, 361-367. (doi:10.1038/sj.jim.7000282)
40. Yang X, Forest MG, Li H, Liu C, Shen J, Wang Q, Chen F. 2013 Modeling and simulations of drop pinch-off from liquid crystal filaments and the leaky liquid crystal faucet immersed in viscous fluids. J. Comput. Phys. 236, 1-14. (doi:10.1016/j.jcp.2012.10.042)
41. Hyon Y, Kwak Y, Liu C. 2010 Energetic variational approach in complex fluids: maximum dissipation principle. Discrete Cont. Dyn. A 26, 1291-1304. (doi:10.3934/dcds.2010.26.1291)
42. Berdichevsky VL. 2009 Variational principles of continuum mechanics. New York, NY: Springer.
43. Brenier Y. 1989 The least action principle and the related concept of generalized flows for incompressible perfect fluids. J. Am. Math. Soc. 2 225-255. (doi:10.1090/S0894-0347-1989-0969419-8)
44. Lin FH, Liu C, Zhang P. 2005 On hydrodynamics of viscoelastic fluids. Commun. Pure Appl. Math. 58, 1437-1471. (doi:10.1002/cpa.20074)
45. Liu C, Walkington NJ. 2001 An Eulerian description of fluids containing visco-hyperelastic particles. Arch. Ration. Mech. Anal. 159, 229-252. (doi:10.1007/s002050100158)
46. Bird RB, Armstrong RC, Hassafer O. 2009 Dynamics of polymeric fluids, vol. 1. New York, NY: Wiley.
47. Lowengrub J, Truskinovsky L. 1998 Quasi-incompressible Cahn-Hilliard fluids and topological transitions. Proc. R. Soc. Lond. A 454, 2617-2654. (doi:10.1098/rspa.1998.0273)
48. Liu C, Shen J. 2003 A phase field model for the mixture of two incompressible fluids and its approximation by a Fourier-spectral method. Physica D 179, 211-228. (doi:10.1016/S0167-2789(03)00030-7)
49. Hecht F. 2012 New development in FreeFem++. J. Numer. Math. 20, 251-265. (doi:10.1515/jnum-2012-0013)
50. Guillé n-González F, Tierra G. 2013 On linear schemes for a Cahn-Hilliard diffuse interface model. J. Comput. Phys. 234 140-171. (doi:10.1016/j.jcp.2012.09.020)
51. Guillé n-González F, Tierra G. 2014 Second order schemes and time-step adaptivity for Allen-Cahn and Cahn-Hilliard models. Comput. Math. Appl. 68 821-846. (doi:10.1016/j.camwa.2014.07.014)
52. Tierra G, Guillé n-González F. 2015 Numerical methods for solving the Cahn-Hilliard equation and its applicability to related energy-based models. Arch. Comput. Methods Eng. (doi:10.1007/s11831-014-9112-1)
53. Wloka M, Rehage H, Flemming H-C, Wingender J. 2004 Rheological properties of viscoelastic biofilm extracellular polymeric substances and comparison to the behaviour of calcium alginate gels. Colloid Polym. Sci. 282, 1067-1076. (doi:10.1007/S00396-003-1033-8)
54. Vadillo-Rodriguez V, Schooling S, Dutcher JR. 2009 In situ characterization of differences in the viscoelastic response of individual Gram-negative and Gram-positive bacterial cells. J. Bacteriol. 191, 5518-5525. (doi:10.1128/JB.00528-09)
55. Rusconi R, Lecuyer S, Guglielmini L, Stone HA. 2010 Laminar flow around corners triggers the formation of biofilm streamers. J. R. Soc. Interface 7, 1293-1299. (doi:10.1098/rsif.2010.0096)
56. Stewart PS. 2012 Mini-review: convection around biofilms. Biofouling 28, 187-198. (doi:10.1080/08927014.2012.662641)
57. Galy J, Latour-Lambert P, Zrelli K, Ghigo JM, Beloin C, Henry N. 2012 Mapping of bacterial biofilm local mechanics by magnetic microparticle actuation. Biophys. J. 103, 1400-1408. (doi:10.1016/j.bpj.2012.07.001)
58. Feng JJ, Liu C, Shen J, Yue P. 2005 An energetic variational formulation with phase field methods for interfacial dynamics of complex fluids: advantages and challenges. In Modeling of soft matter, pp. 1-26. New York, NY: Springer.
59. Sweet CR, Chatterjee S, Xu ZL, Bisordi K, Rosen ED, Alber M. 2011 Modeling platelet-blood flow interaction using subcellular element langevin method. J. R. Soc. Interface 8, 1760-1771. (doi:10.1098/rsif.2011.0180)
60. Xu ZL, Kim O, Kamocka M, Rosen E, Alber M. 2012 Multi-scale models of thrombogenesis. Wiley Interdiscip. Rev. Syst. Biol Med. 4, 237-246. (doi:10.1002/wsbm.1160)