Mathematical modeling of mixed-culture biofilms

Wanner, Oskar; Reichert, Peter

doi:10.1002/(sici)1097-0290(19960120)49:2<172::aid-bit6>3.0.co;2-n

Cited by 302 publications

(122 citation statements)

References 14 publications

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“…Also mathematical models for biofilms have been developed for many years, originally primarily in the engineering literature [29,30]. They are more complex than models of suspended growth, because they must account for the spatial aspects of biofilms, most notably the inhomogeneous distribution of bacteria and substrates across the depth of a biofilm.…”

Section: Introductionmentioning

confidence: 99%

Persistence in a Single Species CSTR Model with Suspended Flocs and Wall Attached Biofilms

Mašić

Eberl

2011

Bull Math Biol

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We consider a mathematical model for a bacterial population in a continuously stirred tank reactor (CSTR) with wall attachment. This is a modification of the Freter model, in which we model the sessile bacteria as a microbial biofilm. Our analysis indicates that the results of the algebraically simpler original Freter model largely carry over. In a computational simulation study, we find that the vast majority of bacteria in the reactor will eventually be sessile. However, we also find that suspended biomass is relatively more efficient in removing substrate from the reactor than biofilm bacteria.

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Section: Introductionmentioning

confidence: 99%

Persistence in a Single Species CSTR Model with Suspended Flocs and Wall Attached Biofilms

Mašić

Eberl

2011

Bull Math Biol

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“…For biomass fractions quantification, the granules were crushed 157 using a mortar and a pestle and then, FISH procedure was followed. The quantification 158 was performed following a modification of the procedure described in Jubany et al airlift reactor performance based on Wanner and Reichert (1996) and implemented in 168 the software package AQUASIM v.2.1d (Reichert, 1998). 169 170…”

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confidence: 99%

Stable partial nitritation for low-strength wastewater at low temperature in an aerobic granular reactor

et al. 2015

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“…While early mathematical models of biofilm implicitly assumed that it forms a uniform, smooth layer (e.g. [2][3][4][5]), improved microscopic techniques in recent decades have revealed a rich diversity of biofilm structure varying from smooth flat biofilm to forms described as towers, mushrooms, streamers, pores and channels (e.g. [6]).…”

Section: Introductionmentioning

confidence: 99%

The development of biofilm architecture

2016

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)) to deal with the problem of the growth of a patch of biofilm in more than one lateral dimension. The extension is nontrivial, as it requires consideration of the rheology of the polymer phase. We use a novel asymptotic technique to reduce the model to a free-boundary problem governed by the equations of Stokes flow with non-standard boundary conditions. We then consider the stability of laterally uniform biofilm growth, and show that the model predicts spatial instability; this is confirmed by a direct numerical solution of the governing equations. The instability results in cusp formation at the biofilm surface and provides an explanation for the common observation of patterned biofilm architectures.

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Mathematical modeling of mixed-culture biofilms

Cited by 302 publications

References 14 publications

Persistence in a Single Species CSTR Model with Suspended Flocs and Wall Attached Biofilms

Persistence in a Single Species CSTR Model with Suspended Flocs and Wall Attached Biofilms

Stable partial nitritation for low-strength wastewater at low temperature in an aerobic granular reactor

The development of biofilm architecture

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