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Mathematical Modeling of Biofilms: Theory, Numerics and Applications

Alpkvist, Erik LU (2006) In Doctoral Theses in Mathematical Sciences
Abstract
A biofilm is a complex and diverse aggregation of microorganisms at surface comprised of among different things a protective adhesive matrix of extracellular polymeric substance. Biofilm research represents a broad range of sciences joining efforts within an interdisciplinary field of research. This thesis deals with the modeling of biofilms using the most fundamental laws of physics; the conservation laws of mass and momentum for fluids. Common to all parts of this work is an aim to develop robust and general mathematical models readily applicable for computational use.



Two new biofilm models for growth are derived in this thesis; one describing and combining an individual description of microbial particles with a... (More)
A biofilm is a complex and diverse aggregation of microorganisms at surface comprised of among different things a protective adhesive matrix of extracellular polymeric substance. Biofilm research represents a broad range of sciences joining efforts within an interdisciplinary field of research. This thesis deals with the modeling of biofilms using the most fundamental laws of physics; the conservation laws of mass and momentum for fluids. Common to all parts of this work is an aim to develop robust and general mathematical models readily applicable for computational use.



Two new biofilm models for growth are derived in this thesis; one describing and combining an individual description of microbial particles with a continuum representation of the biofilm matrix, and one a model based solely on a continuum framework of partial differential equations. The latter is applied in a bottom-up approach as a mass balance model for a Moving Bed biofilm process. Finally, an attempt of capturing the conservation of momentum for both water and biomass is presented. This will allow for viscoelastic and other constitutive properties to influence biomass structure (through growth or fluid shear stresses) as well as erosion and sloughing detachment; under basic laws of physics. All models are applied and demonstrated in silico; for examples such as growth, deformation and detachment under fluid shear stress. (Less)
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author
supervisor
opponent
  • Professor Dockery, Jack D., Department of Mathematical Sciences, Montana State University, Bozeman
organization
publishing date
type
Thesis
publication status
published
subject
keywords
mathematical modeling, Mathematics, conservation laws, biofilm, Matematik
in
Doctoral Theses in Mathematical Sciences
pages
185 pages
publisher
Centre for Mathematical Sciences, Lund University
defense location
Ubåtshallen, U301, Malmö Högskola
defense date
2006-12-08 10:15:00
ISSN
1404-0034
ISBN
978-91-628-6512-2
language
English
LU publication?
yes
id
70cbd970-b75b-4a89-8b93-089db9b44f7d (old id 25603)
date added to LUP
2016-04-01 17:05:47
date last changed
2019-05-21 13:42:45
@phdthesis{70cbd970-b75b-4a89-8b93-089db9b44f7d,
  abstract     = {A biofilm is a complex and diverse aggregation of microorganisms at surface comprised of among different things a protective adhesive matrix of extracellular polymeric substance. Biofilm research represents a broad range of sciences joining efforts within an interdisciplinary field of research. This thesis deals with the modeling of biofilms using the most fundamental laws of physics; the conservation laws of mass and momentum for fluids. Common to all parts of this work is an aim to develop robust and general mathematical models readily applicable for computational use.<br/><br>
<br/><br>
Two new biofilm models for growth are derived in this thesis; one describing and combining an individual description of microbial particles with a continuum representation of the biofilm matrix, and one a model based solely on a continuum framework of partial differential equations. The latter is applied in a bottom-up approach as a mass balance model for a Moving Bed biofilm process. Finally, an attempt of capturing the conservation of momentum for both water and biomass is presented. This will allow for viscoelastic and other constitutive properties to influence biomass structure (through growth or fluid shear stresses) as well as erosion and sloughing detachment; under basic laws of physics. All models are applied and demonstrated in silico; for examples such as growth, deformation and detachment under fluid shear stress.},
  author       = {Alpkvist, Erik},
  isbn         = {978-91-628-6512-2},
  issn         = {1404-0034},
  language     = {eng},
  publisher    = {Centre for Mathematical Sciences, Lund University},
  school       = {Lund University},
  series       = {Doctoral Theses in Mathematical Sciences},
  title        = {Mathematical Modeling of Biofilms: Theory, Numerics and Applications},
  year         = {2006},
}