A simple model of biofilm growth in a porous medium that accounts for detachment and attachment of suspended biomass and their contribution to substrate degradation

Gaebler, Harry J.; Eberl, Hermann J.

doi:10.1017/s0956792518000189

Cited by 20 publications

(9 citation statements)

References 29 publications

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“…The third group lies between the lengthscales of the first two groups. These include the combining of chemostat approaches with that of Wanner & Gujer to analyse invasion of cells into biofilms in an an idealisation of moving bed biofilm reactors (D'Acunto et al, 2018), an upscaling approach to modelling biofilms, suspended bacteria and substrate removal in porous media reactors (Gaebler & Eberl, 2018) and a statistical physics approach to investigate how the assumptions on the microscale effect mesoscale mechanical properties of biofilm aggregates (Stotsky et al, 2018). These papers are a small demonstration of the diversity of problems and mathematics arising from biofilms, and with their continuing concern in industry and in the age of AMR, they will continue to provide new challenges and opportunities to mathematicians for many years to come.…”

Section: Editorialmentioning

confidence: 99%

Editorial

Eberl¹,

Ward²

2018

Eur. J. Appl. Math

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Biofilms are colonies of microorganisms, usually growing on solid-liquid interfaces, consisting of cells and a matrix of extracellular polymeric substances (EPS). Such colonies are often elaborately structured and highly dynamic, expanding through cell division and recruitment of cells from outside, and contracting via individual cells or flocs (groups of cells and biofilm matrix) detachment from the biofilm surface. Even amongst simplest single species bacterial biofilms, the behaviour (phenotype) of individual cells is highly heterogenous across the biofilm due to microenvironment variation (e.g. nutrient concentration, pH) and cell-cell signalling (quorum sensing); consequently, many researchers consider biofilms as more akin to multi-cellular organisms rather than a colony of autonomous individual cells.

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Section: Editorialmentioning

confidence: 99%

Editorial

Eberl¹,

Ward²

2018

Eur. J. Appl. Math

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“…Mass transfer between the fracture and the matrix is by molecular diffusion and can lead to mineraldissolution-precipitation depending on the distance or connection to the fracture. Another important example is mass exchange between pore water and biofilms (e.g., Chen-Charpentier, 1999;Tiwari & Bowers, 2001;Gaebler & Eberl, 2018;Brangarí et al, 2018). Biological reactions mainly take place in biofilms composed of cellular material and extracellular polymeric substances (EPS).…”

Section: Introductionmentioning

confidence: 99%

A general and efficient numerical solution of reactive transport with multirate mass transfer

Wang

Carrera

Saaltink

et al. 2022

Computers & Geosciences

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This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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“…This strongly affects the biofilm development and maturation as highlighted by a recent work [13] where the attachment has been incorporated as a discrete stochastic process in a density-dependent diffusion-reaction model for cellulolytic biofilms. Furthermore, the Wanner-Gujer-type models [7,[14][15][16] can lead, in some cases, to ecological restrictions on the number of species constituting the biofilm [17]. Indeed, they are characterized by a restriction on the number of species that can inhabit the biofilm under the detachment regime: that is, if a species is not initially present within the biofilm on the support, it will be washed out from the system.…”

Section: Introductionmentioning

confidence: 99%

Free boundary problem for the role of planktonic cells in biofilm formation and development

D’Acunto

Frunzo

Luongo

et al. 2021

Z. Angew. Math. Phys.

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The dynamics of biofilm lifecycle are deeply influenced by the surrounding environment and the interactions between sessile and planktonic phenotypes. Bacterial biofilms typically develop in three distinct stages: attachment of cells to a surface, growth of cells into colonies, and detachment of cells from the colony into the surrounding medium. The attachment of planktonic cells from the surrounding environment plays a prominent role in the initial phase of biofilm lifecycle as it initiates the colony formation. During the maturation stage, biofilms harbor numerous microenvironments which lead to metabolic heterogeneity. Such microniches provide conditions suitable for the growth of new species, which are present in the bulk liquid as planktonic cells and can penetrate the porous biofilm matrix. We present a 1D continuum model on the interaction of sessile and planktonic phenotypes in biofilm lifestyle. Such a model is able to reproduce the key role of planktonic cells in the formation and development of biofilms by considering the initial attachment and colonization phenomena. The model is formulated as a hyperbolic–elliptic free boundary value problem with vanishing initial value which considers the concentrations of planktonic and sessile cells as state variables. Hyperbolic equations reproduce the transport and growth of sessile species, while elliptic equations model the diffusion and conversion of planktonic cells and dissolved substrates. The attachment is modeled as a continuous, deterministic process which depends on the concentrations of the attaching species. The growth of new species is modeled through a reaction term in the hyperbolic equations which depends on the concentration of planktonic species within the biofilm. Existence and uniqueness of solutions are discussed and proved for the attachment regime. Finally, some numerical examples show that the proposed model correctly reproduces the growth of new species within the biofilm and overcomes the ecological restrictions characterizing the Wanner–Gujer-type models.

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A simple model of biofilm growth in a porous medium that accounts for detachment and attachment of suspended biomass and their contribution to substrate degradation

Cited by 20 publications

References 29 publications

Editorial

Editorial

A general and efficient numerical solution of reactive transport with multirate mass transfer

Free boundary problem for the role of planktonic cells in biofilm formation and development

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