Mathematical modeling of mixed‐culture biofilms

Wanner, Oskar; Reichert, Peter

doi:10.1002/(sici)1097-0290(19960120)49:2<172::aid-bit6>3.3.co;2-6

Cited by 46 publications

(62 citation statements)

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“…One-dimensional models including all these processes exist, and they were successfully applied to describe quantitatively substrate conversion in biofilms (Wanner and Gujer, 1986;Wanner and Reichert, 1996). An appropriate description of biofilm-structure formation as the result of environmental factors must be multidimensional, as suggested by Bishop and Rittmann, 1996.…”

Section: Introductionmentioning

confidence: 99%

Two-dimensional model of biofilm detachment caused by internal stress from liquid flow

Picioreanu

Loosdrecht

Heijnen

2000

Biotechnol. Bioeng.

295

114

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A two-dimensional model for biofilm growth and detachment was used to evaluate the effect of detachment on biofilm structures. The detachment process is considered to be due to internal stress created by moving liquid past the biofilm. This model generated a variety of realistic biofilm-formation patterns. It was possible to model in a unified way two different biofilm detachment processes, erosion (small-particle loss), and sloughing (large-biomass-particle removal). The distribution of the fraction from total biomass detached as a function of detached particle mass, gives indications about which of the two mechanisms is dominant. Model simulations indicate that erosion makes the biofilm surface smoother. Sloughing, in contrast, leads to an increased biofilm-surface roughness. Faster growing biofilms have a faster detachment rate than slow-growing biofilms, under similar hydrodynamic conditions and biofilm strength. This is in perfect accordance with the experimental evidence showing that detachment is dependent on both shear-and microbial-growth rates. High growth rates trigger instability in biofilm accumulation and abrupt biomass loss (sloughing). Massive sloughing can be avoided by high liquid shear, combined with low biomass growth rates. As the modeling results show, the causes for sloughing must be sought not only in the biofilm strength, but also in its shape. Several "mushroomlike" biofilm structures like those repeatedly reported in the literature occurred, due to a combined effect of nutrient depletion and breaking at the colony base. A rough carrier surface promotes biofilm development in hydrodynamic conditions in which the biofilm on a flat surface would not form. Although biofilm patches filled completely the cavity in which they started to grow, they were unable to spill over the carrier peaks and to fully colonize the substratum.

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Section: Introductionmentioning

confidence: 99%

Two-dimensional model of biofilm detachment caused by internal stress from liquid flow

Picioreanu

Loosdrecht

Heijnen

2000

Biotechnol. Bioeng.

295

114

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“…The mathematical model describing the performance of the chemostat reactor and laboratory scale biofilm airlift reactor was implemented in the well-established AQUASIM simulation software for environmental applications [16]. At first, the model was used to demonstrate competition of L. ferrooxidans and A. ferrooxidans bacteria on the basis of substrate affinity in a chemostat reactor.…”

Section: Model Descriptionmentioning

confidence: 99%

“…In this study, the biological oxidation of ferrous iron was modeled and evaluated by AQUASIM software, a computer program for the identification and simulation of aquatic systems [16]. The competition between the two types of bacteria (mixed culture of A. ferrooxidans and L. ferrooxidans) both in the chemostat reactor and in the biofilm in the airlift reactor was studied.…”

Section: Introductionmentioning

confidence: 99%

Model-based evaluation of ferrous iron oxidation by acidophilic bacteria in chemostat and biofilm airlift reactors

Ebrahimi

Faraghi

Hosseini

2015

Journal of Industrial Microbiology and Biotechnology

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This article presents a model-based evaluation of ferrous iron oxidation in chemostat and biofilm airlift reactors inoculated with a mixed culture of Acidithiobacillus ferrooxidans and Leptospirillum ferrooxidans bacteria. The competition between the two types of bacteria in the chemostat and in the biofilm airlift reactors together with the distribution of both bacteria along the biofilm thickness at different time sections has been studied. The bacterial distribution profiles along the biofilm in the airlift reactor at different time scales show that in the beginning A. ferrooxidans bacteria are dominant, but when the reactor operates for a long time the desirable L. ferrooxidans species outcompete A. ferrooxidans as a result of the low Fe(2+) and high Fe(3+) concentrations. The results obtained from the simulation were compared with the experimental data of continuously operated internal loop airlift biofilm reactor. The model results are in good agreement with the experimental results.

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“…However, the simplest mode of mobility is that is be random; such motion can be modeled by introduction of diffusion (which has in fact been observed and measured in laboratory-grown biofilms Rogers et al 2008) into the equations for motile species. This effect was included in the AQUASIM model, an extension of BIOSIM, where it was argued that mechanical stresses lead to "temporary detachment of single cells or particles from the matrix" followed by "subsequent reattachment at another location" (Wanner and Riechert 1996). Though not directly linked to the possibility of ecological exclusion in that paper (rather, in fact, the authors motivated inclusion of material diffusion as a way to improve penetration of surface-attaching cells by allowing them to move downward; such transport appears to have been observed in practice, e.g., Klayman et al 2008), we wish to claim that material diffusion can break the basic model exclusion principle; with diffusion, ecology in the biofilm is not solely determined by ecology at the biofilm base.…”

Section: An Extended Modelmentioning

confidence: 99%

“…For illustrative purposes, the focus will be on one addition in particular, namely allowance for diffusivity of biomaterial. Diffusivity was included in the software system AQUASIM (Reichert 1994;Wanner and Riechert 1996), a replacement for BIOSIM (in fact, exclusion was predicted by the authors of BIOSIM in some circumstance Wanner and Gujer 1986), but is often not included in biofilm models. We refer to the resulting class of models as extended type and present numerical evidence that sufficiently large (but not too large) biomaterial diffusivity can break ecological exclusion.…”

mentioning

confidence: 99%

An Exclusion Principle and the Importance of Mobility for a Class of Biofilm Models

Klapper

Szomolay

2011

Bull Math Biol

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Much of the earth's microbial biomass resides in sessile, spatially structured communities such as biofilms and microbial mats, systems consisting of large numbers of single-celled organisms living within self-secreted matrices made of polymers and other molecules. As a result of their spatial structure, these communities differ in important ways from well-mixed (and well-studied) microbial systems such as those present in chemostats. Here we consider a widely used class of 1D biofilm models in the context of a description of their basic ecology. It will be shown via an exclusion principle resulting from competition for space that these models lead to restrictions on ecological structure. Mathematically, this result follows from a classification of steady-state solutions based on a 0-stability condition: 0-stable solutions are in some sense determined by competitive balance at the biofilm base, whereas solutions that are not 0-stable, while less dependent on conditions at the biofilm base, are unstable at the base. As a result of the exclusion principle, it is argued that some form of downward mobility, against the favorable substrate gradient direction, is needed at least in models and possibly in actuality.

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Mathematical modeling of mixed‐culture biofilms

Cited by 46 publications

References 0 publications

Two-dimensional model of biofilm detachment caused by internal stress from liquid flow

Two-dimensional model of biofilm detachment caused by internal stress from liquid flow

Model-based evaluation of ferrous iron oxidation by acidophilic bacteria in chemostat and biofilm airlift reactors

An Exclusion Principle and the Importance of Mobility for a Class of Biofilm Models

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