Citation: Sarah Trinschek, Karin John, Uwe Thiele. From a thin film model for passive suspensions towards the description of osmotic biofilm spreading[J]. AIMS Materials Science, 2016, 3(3): 1138-1159. doi: 10.3934/matersci.2016.3.1138
| [1] | Donlan RM (2012) Biofilms: Microbial life on surfaces. Emerg Infect Dis 8: 881–890. |
| [2] |
Flemming H, Wingender J (2010) The biofilm matrix. Nat Rev Microbiol 8: 623–633. doi: 10.1038/nrmicro2415
|
| [3] | Picioreanu C, Loosdrecht MCM (2003) Use of mathematical modelling to study biofilm development and morphology , In Biofilms in Medicine, Industry and Environmental Biotechnology - Characteristics, Analysis and Control. IWA Publishing. 413–437. |
| [4] |
Wang Q, Zhang T (2010) Review of mathematical models for biofilms. Solid State Comm 150: 1009–1022. doi: 10.1016/j.ssc.2010.01.021
|
| [5] | Horn H, Lackner S (2014) Modeling of biofilm systems: a review In Productive Biofilms, Springer International Publishing, 150: 53–76. |
| [6] |
Picioreanu C,Van Loosdrecht MCM, Heijnen JJ, et al. (1998) Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach. Biotechnol Bioeng 58: 101–116. doi: 10.1002/(SICI)1097-0290(19980405)58:1<101::AID-BIT11>3.0.CO;2-M
|
| [7] | Eberl HJ, Parker DF, Van Loosdrecht (2001) A new deterministic spatio-temporal continuum model for biofilm development. J Theor Biol 3: 161–175. |
| [8] |
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
|
| [9] |
Hermanowicz SW (2001) A simple 2d biofilm model yields a variety of morphological features. Math Biosci 169: 1–14. doi: 10.1016/S0025-5564(00)00049-3
|
| [10] | Cogan NG, Keener JP (2004) The role of the biofilm matrix in structural development. Math Med Biol 21 147–166. |
| [11] | 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. |
| [12] | 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. |
| [13] |
Winstanley HF, Chapwanya M, McGuinness, MJ, et al. (2011) A polymer - solvent model of biofilm growth. Proc R Soc Lond 467: 1449–1467. doi: 10.1098/rspa.2010.0327
|
| [14] |
Ward JP, King JR (2012) Thin-film modelling of biofilm growth and quorum sensing. J Eng Math 73: 71–92. doi: 10.1007/s10665-011-9490-4
|
| [15] |
Dillon R, Fauci L, Fogelson A, et al. (1996) Modeling biofilm processes using the immersed boundary method. J Comput Phys 129: 57–73. doi: 10.1006/jcph.1996.0233
|
| [16] |
Picioreanu C, Van Loosdrecht MCM, Heijnen JJ (2000) Effect of diffusive and convective substrate transport on biofilm structure formation: A two-dimensional modeling study. Biotechnol Bioeng 69: 504–515. doi: 10.1002/1097-0290(20000905)69:5<504::AID-BIT5>3.0.CO;2-S
|
| [17] | Wanner O, Gujer W (2000) A multispecies biofilm model. Biotechnol Bioeng 28: 314–328. |
| [18] |
Picioreanu C, Kreft JU , van Loosdrecht MCM (2004) Particle-based multidimensional multispecies biofilm model. Appl Environ Microbiol 70: 3024–3040. doi: 10.1128/AEM.70.5.3024-3040.2004
|
| [19] |
Alpkvist E, Klapper I (2007) A multidimensional multispecies continuum model for heterogeneous biofilm development. B Math Biol 69: 765–789. doi: 10.1007/s11538-006-9168-7
|
| [20] |
Dervaux J, Maginiez JC, Libchaber A (2014) On growth and form of Bacillus subtilis biofilms. Interface Focus 4: 20130051. doi: 10.1098/rsfs.2013.0051
|
| [21] |
Seminara A, Angelini TE,Wilking JN, et al. (2012) Osmotic spreading of bacillus subtilis biofilms driven by an extracellular matrix. Proc Natl Acad Sci USA 109: 1116–1121. doi: 10.1073/pnas.1109261108
|
| [22] |
Dilanji GE, Teplitski M, Hagen SJ (2014) Entropy-driven motility of sinorhizobium meliloti on a semi-solid surface. Proc Biol Sci 281: 20132575. doi: 10.1098/rspb.2013.2575
|
| [23] | De Dier R, Fauvart M, Michiels J, et al. (2015) The role of biosurfactants in bacterial systems. In The Physical Basis of Bacterial Quorum Communication, Springer, 189–204. |
| [24] |
Fauvart M, Phillips P, Bachaspatimayum D, et al. (2012) Surface tension gradient control of bacterial swarming in colonies of pseudomonas aeruginosa. Soft Matter 8: 70–76. doi: 10.1039/C1SM06002C
|
| [25] |
Angelini TE, Roper M , Kolter R, et al. (2009) Bacillus subtilis spreads by surfing on waves of surfactant. Proc Natl Acad Sci USA 106: 18109–18113. doi: 10.1073/pnas.0905890106
|
| [26] |
Brenner MP (2014) Fluid mechanical responses to nutrient depletion in fungi and biofilms. Phys Fluids 26: 101306. doi: 10.1063/1.4896587
|
| [27] |
Leclére V, Marti R, B´echet M, Fickers P, et al. (2006) The lipopeptides mycosubtilin and surfactin enhance spreading of Bacillus subtilis strains by their surface-active properties. Arch Microbiol 186: 475–483. doi: 10.1007/s00203-006-0163-z
|
| [28] |
Lachish U (2007) Osmosis and thermodynamics. Am J Phys 75: 997–998. doi: 10.1119/1.2752822
|
| [29] |
Zhang W, Seminara A, Suaris M, et al. (2014) Nutrient depletion in bacillus subtilis biofilms triggers matrix production. New J Phys 16: 015028. doi: 10.1088/1367-2630/16/1/015028
|
| [30] | Wang X, Koehler SA, Wilking JN, et al. (2016) Probing phenotypic growth in expanding Bacillus subtilis biofilms. Appl Environ Microbiol 1–9. |
| [31] |
Thiele U, Todorova DV, Lopez H (2013) Gradient dynamics description for films of mixtures and suspensions: Dewetting triggered by coupled film height and concentration fluctuations. Phys Rev Lett 111: 117801. doi: 10.1103/PhysRevLett.111.117801
|
| [32] | Thiele U (2011) Note on thin film equations for solutions and suspensions. Europ Phys J 197: 213–220. |
| [33] |
Xu X, Thiele U, Qian T (2015) A variational approach to thin film hydrodynamics of binary mixtures. J Phys Condens Matter 27: 085005. doi: 10.1088/0953-8984/27/8/085005
|
| [34] |
Thiele U, Archer AJ, Plapp M (2012) Thermodynamically consistent description of the hydrodynamics of free surfaces covered by insoluble surfactants of high concentration. Phys Fluids 24:102107. doi: 10.1063/1.4758476
|
| [35] | de Groot SR, Mazur P (1984) Non-equilibrium Thermodynamics, Dover publications, New York. |
| [36] |
Wilking JN, Angelini TE, Seminara A, et al. (2011) Biofilms as complex fluids. MRS Bull 36: 385–391. doi: 10.1557/mrs.2011.71
|
| [37] |
Mitlin VS (1993) Dewetting of solid surface: Analogy with spinodal decomposition. J Colloid Interf Sci 156: 491–497. doi: 10.1006/jcis.1993.1142
|
| [38] |
Thiele U (2010) Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth. J Phys Condens Matter 22: 084019. doi: 10.1088/0953-8984/22/8/084019
|
| [39] |
Oron A, Davis SH, Bankoff SG (1997) Long-scale evolution of thin liquid films. Rev Mod Phys 69: 931–980. doi: 10.1103/RevModPhys.69.931
|
| [40] | Thiele U (2007) Structure formation in thin liquid films. In Kalliadasis S and Thiele U, Thin Films of Soft Matter, Wien: Springer, 25–93. |
| [41] |
Wilczek M, Tewes WBH, Gurevich SV, et al. (2015) Modelling pattern formation in dip-coating experiments. Math Model Nat Phenom 10: 44–60. doi: 10.1051/mmnp/201510402
|
| [42] |
De Gennes PG (1985) Wetting: statics and dynamics. Rev Mod Phys 57: 827. doi: 10.1103/RevModPhys.57.827
|
| [43] | Israelachvili JN (1985) Intermolecular and Surface Forces (With Applications to Colloidal and Biological Systems), Academic Press, London. |
| [44] | Israelachvili JN (2004) Capillarity and wetting phenomena: Drops, bubbles, pearls, waves, Springer, New York. |
| [45] |
Bonn D, Eggers J, Indekeu J, et al. (2009) Wetting and spreading. Rev Mod Phys 81: 739. doi: 10.1103/RevModPhys.81.739
|
| [46] |
Náraigh LÓ , Thiffeault JL (2010) Nonlinear dynamics of phase separation in thin films. Nonlinearity 23: 1559–1583. doi: 10.1088/0951-7715/23/7/003
|
| [47] |
Hall-Stoodley L, Costerton JW, Stoodley P (2004) Bacterial biofilms: from the natural environment to infectious diseases. Nat Rev Microbiol 2: 95–108. doi: 10.1038/nrmicro821
|
| [48] |
Sutherland IW (2001) Biofilm exopolysaccharides: a strong and sticky framework. Microbiology 147: 3–9. doi: 10.1099/00221287-147-1-3
|
| [49] | Lau PCY, Dutcher JR, Beveridge TJ, et al. (2009) Absolute quantitation of bacterial biofilm adhesion and viscoelasticity by microbead force spectroscopy. Biophys J 7: 2935–2948. |
| [50] |
Warner MRE, Craster RV, Matar OK (2003) Surface patterning via evaporation of ultrathin films containing nanoparticles. Colloid Interf Sci 267: 92–110. doi: 10.1016/S0021-9797(03)00640-4
|
| [51] |
Frastia L, Archer AJ, Thiele U (2012) Modelling the formation of structured deposits at receding contact lines of evaporating solutions and suspensions. Soft Matter 8: 11363–11386. doi: 10.1039/c2sm26574e
|
| [52] |
Pismen LM, Thiele U (2006) Asymptotic theory for a moving droplet driven by a wettability gradient. Phys Fluids 18: 042104. doi: 10.1063/1.2191015
|
| [53] | Todorova D, Thiele U, Pismen LM (2010) Steady evaporating droplets fed by an influx–the isothermal limit. J Eng Math 73: 17–30. |
| [54] |
Doi M (2011) Onsager's variational principle in soft matter. J Phys Condens Matter 23: 284118. doi: 10.1088/0953-8984/23/28/284118
|
| [55] |
Rednikov A, Colinet P (2013) Singularity-free description of moving contact lines for volatile liquids. Phys Rev E 87: 010401. doi: 10.1103/PhysRevE.87.010401
|
| [56] |
Dietrich L E, Okegbe C, Price-Whelan A, et al. (2013) Bacterial community morphogenesis is intimately linked to the intracellular redox state. J Bacteriol 195: 1371–1380. doi: 10.1128/JB.02273-12
|
| [57] | Blatt M, Bastian P (2006) The iterative solver template library, In: Applied Parallel Computing. State of the Art in Scientific Computing, Springer, 666–675. |
| [58] | Bastian P, Blatt M, Dedner A, et al. (2008) A generic grid interface for parallel and adaptive scientific computing. part i: abstract framework. Computing 82: 103–119. |
| [59] | Bastian P, Blatt M, Dedner A, et al. (2008) A generic grid interface for parallel and adaptive scientific computing. part ii: Implementation and tests in dune. Computing 82: 121–138. |
| [60] | Kuznetsov, YA (2013) Elements of applied bifurcation theory, Springer, New York, chapter 10. |
| [61] |
Dijkstra HA, Wubs FW, Cliffe AK, et al. (2014) Numerical Bifurcation Methods and their Application to Fluid Dynamics: Analysis beyond Simulation. Commun Comput Phys 15: 1–45. doi: 10.4208/cicp.240912.180613a
|
| [62] |
Pototsky A, Bestehorn M , Merkt D, et al. (2005) Morphology changes in the evolution of liquid two-layer films. J Chem Phys 122: 224711. doi: 10.1063/1.1927512
|
| [63] | Lin TS, Rogers S, Tseluiko D, et al. (2016) Bifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder. [submitted] |
| [64] | Doedel E, Oldeman B, Champneys A, et al. (2007) Continuation and bifurcation software for ordinary differential equations. |
| [65] |
Doedel E, Keller HB, Kernevez JP (1991) Numerical analysis and control of bifurcation problems (i): bifurcation in finite dimensions. Int J Bifurcat Chaos 1: 493–520. doi: 10.1142/S0218127491000397
|
| [66] | Thiele U, Kamps O, Gurevich SV, editors. (2014) Münsteranian Torturials on Nonlinear Science: Continuation. CeNoS, M¨unster Available from: http://www.unimuenster. de/CeNoS/Lehre/Tutorials. see in particular tutorials drop and thifi. |
| [67] | Thiele U, Velarde MG, Neuffer K, et al. (2001) Sliding drops in the di use interface model coupled to hydrodynamics. Phys Rev E 64: 061601. |
| [68] | Murray JD (1993) Mathematical Biology, Springer, New York. |