A Review on the Mathematical Modeling of Biofilm Processes: Advances in Fundamentals of Biofilm Modeling

Chaudhry, Muhammad Anwar; Beg, S.A.

doi:10.1002/(sici)1521-4125(199809)21:9<701::aid-ceat701>3.0.co;2-l

Cited by 46 publications

(23 citation statements)

References 55 publications

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“…Rittmann & McCarty, 1980, Kissel et al, 1984, Wanner & Gujer, 1986, and the review of Chaudhry & Beg, 1998). These first models were ordinary or one-dimensional partial differential equations assuming a biofilm which develops as a flat layer.…”

Section: Recent Mathematical Models For Heterogeneous Biofilm Structuresmentioning

confidence: 99%

A New Deterministic Spatio‐Temporal Continuum Model for Biofilm Development

Eberl

Parker

Loosdrecht

2000

Computational and Mathematical Methods in Medicine

209

205

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A new mathematical model for the development of spatially heterogeneous biofilm structures is presented. Unlike previous hybrid discrete/continuum models it is a continuum model throughout, describing the interaction of nutrient availability and biomass production. Spatial biomass spreading is described by a nonlinear density-dependent diffusion mechanism. The diffusion operator degenerates for small biomass densities and is singular at the biomass density bound. The model can be interpreted as a predator-prey model for biomass and nutrients. First numerical simulations show that the model is able to predict experimentally observed cluster-and-channel biofilm structures. The results are reliable and in qualitatively good agreement with experimental expectations.

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Section: Recent Mathematical Models For Heterogeneous Biofilm Structuresmentioning

confidence: 99%

A New Deterministic Spatio‐Temporal Continuum Model for Biofilm Development

Eberl

Parker

Loosdrecht

2000

Computational and Mathematical Methods in Medicine

209

205

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“…The majority of the PDE models follow that of Wanner and Gujer [33], focusing on the effects of diffusing agents (such as nutrients) on growth perpendicular to a solid substratum, e.g. [7,27,29]. The basis of these models is not unlike that of the current one, in which growth creates, and death removes, material volume, causing local movement that is described by a velocity field.…”

mentioning

confidence: 99%

Thin-film modelling of biofilm growth and quorum sensing

Ward

King

2011

J Eng Math

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Biofilms are slimy films of bacteria that typically grow on solid surfaces with a fluid interface. Two mathematical models for nutrient-dependent, early-stage biofilm growth and quorum sensing (QS) are proposed and studied. The aim of this study is to use thin-film methods to derive a dimensionally reduced model on a stronger theoretical basis to that of Ward et al. (J Math Biol 47:23-55, 2003). The biofilm structure is described as a viscous fluid, and the two models apply different boundary conditions between the biofilm and the solid surface: namely (1) shear-stress-free; and (2) no-slip conditions. The complexity and dimensionality of each of the models are reduced by the application of asymptotic methods in biologically relevant thin-film limits. The first model reduces to a system of first-order PDEs, whilst the second results in a high-order, degenerate Fisher-type equation. We present a hodograph solution for model (1) and analyse model (2) in the travelling-wave limit. A key difference between the models is that the long-time solutions have contrasting properties: for model (1) the large-time solutions are dependent on the initial conditions, whilst in model (2) the long-time attractor is a travelling wave, the speed of which is approximated in a certain limit that depends on conditions at the biofilm edge and substratum interface. The QS aspects of the model derived using the systematic asymptotic approach are shown to be relatively unchanged from those of Ward et al. (2003), and the results therein are thus applicable to the current models.

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“…The attached biofilm acts as buffer to reduce the concentration of toxic chemicals during process operation and thereby benefits the treatment of lowbiodegradable industrial wastewater that contains recalcitrant compounds (Bishop 1997). Compared with sludgebased systems, SBBR is generally less energy intensive and more resistant to shock loads to which wastewater treatment systems are frequently subjected (Chaudhry and Beg 1998). Besides, SBBR is particularly useful where high hydraulic loading variations occur and where slowly growing microbes with special metabolic capacities can be protected from washout (Woolard 1997).…”

Section: Introductionmentioning

confidence: 84%

Comparison of the treatment for isopropyl alcohol wastewater from silicon solar cell industry using SBR and SBBR

Yang

Xie

et al. 2014

Int. J. Environ. Sci. Technol.

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In the present study, isopropyl alcohol containing wastewater generated from silicon solar cell manufacture was sequentially treated with sequencing batch biofilm reactor and sequencing batch reactor. Sequencing batch biofilm reactor could remove 90 % of isopropyl alcohol from wastewater efficiently as the chemical oxygen demand lower than 1,200 mg L -1 . However, 1,600 mg L -1 of chemical oxygen demand damaged the biofilm. The operation mode was changed to sequencing batch reactor on day 30, and sequencing batch reactor showed a greater ability to remove isopropyl alcohol. When the influent chemical oxygen demand was 1,600 mg L -1 , the reactors achieved stable removal efficiencies of [95 % for chemical oxygen demand, and the effluent chemical oxygen demand was lower than 100 mg L -1 . Denaturing gradient gel electrophoresis analysis showed an increase in bacteria diversity as the operation mode was switched from sequencing batch biofilm reactor to sequencing batch reactor, which might increase the stability of flocs in sequencing batch reactor. Though 13 bands were sequenced from the denaturing gradient gel electrophoresis and a phylogenetic analysis was conducted based on these sequences, it is difficult to analyze the function of these predominant strains in the reactors. Two models were constructed for interpreting the structure of biofilm in sequencing batch biofilm reactor and flocs in sequencing batch reactor, respectively. Higher efficient transfer rate of dissolved oxygen in flocs was proposed as the main reason for the higher isopropyl alcohol removal ability in sequencing batch reactor.

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A Review on the Mathematical Modeling of Biofilm Processes: Advances in Fundamentals of Biofilm Modeling

Cited by 46 publications

References 55 publications

A New Deterministic Spatio‐Temporal Continuum Model for Biofilm Development

A New Deterministic Spatio‐Temporal Continuum Model for Biofilm Development

Thin-film modelling of biofilm growth and quorum sensing

Comparison of the treatment for isopropyl alcohol wastewater from silicon solar cell industry using SBR and SBBR

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