Front Cover -- Advanced Methods and Mathematical Modeling of Biofilms -- Advanced Methods and Mathematical Modeling of Biofilms -- Contents -- Author bios -- Preface -- 1 -- Introduction -- 1.1 Background -- 1.2 History of biofilms studies -- 1.2.1 Biofilm and bioaggregates -- 1.2.2 Biofilm modeling -- 1.3 Problems and objectives of biofilm research -- 1.3.1 Objectives of biofilm modeling -- References -- Further reading -- 2 -- Concept and fundamentals of biofilms -- 2.1 Overview -- 2.1.1 Biofilm formation and development -- 2.1.2 Biofilm characteristics -- 2.2 Spatiotemporal heterogeneity
2.2.1 Time scale of biofilm processes -- 2.2.2 Spatial scale of biofilm processes -- 2.3 Nutrient availability and environmental conditions -- 2.3.1 Hydrodynamics and nutrient availability -- 2.3.2 Biofilm heterogeneity -- 2.3.3 Environmental conditions -- 2.4 Competition and cooperation -- 2.5 Modeling approaches and selection -- 2.5.1 Mathematical models -- 2.5.1.1 Governing equations of transport -- 2.5.1.1.1 Flow equations -- 2.5.1.1.2 Energy transports -- 2.5.2 Solute transports -- 2.5.2.1 Biomass transformation rates and biofilm growth -- 2.5.2.2 Biofilm spreading and structural dynamics
2.5.2.2.1 Continuum models -- 2.5.2.2.1.1 One-dimensional mixed-culture biofilm model -- 2.5.2.2.1.2 Multidimensional approach -- 2.5.2.2.2 Discrete models -- 2.5.2.2.2.1 Cellular Automaton models -- 2.5.2.2.2.2 Individual-based models -- 2.6 Numerical solutions -- 2.7 Classification and selection of mathematical models -- 2.7.1 Modeling classifications -- 2.7.2 Model selection -- References -- Further reading -- 3 -- Kinetic models -- 3.1 Monod model -- 3.2 Extended Monod's models -- 3.2.1 Two substrate and multiple substrate Monod's models -- 3.2.2 Monod kinetics for inhibitor
3.2.2.1 Luong model -- 3.2.2.2 Moser model -- 3.2.2.3 Aiba-Edward model -- 3.2.2.4 Yano and Koga model -- 3.2.2.5 Han and Levenspiel -- 3.2.2.6 Haldane model -- 3.2.3 Inactive and maintenance description -- 3.3 Substrate consideration -- 3.3.1 Substrate diffusion -- 3.3.2 Classifications of analytical solutions for different biofilm thickness -- 3.3.3 Inhibition effects -- 3.4 Other unstructured models -- 3.4.1 Blackman model -- 3.4.2 Tessier model -- 3.4.3 Contois model -- 3.4.4 Logarithmic model -- 3.4.5 Logistic model -- 3.4.6 Webb model -- 3.5 Summary -- References -- Further reading
4 -- Continuum models -- 4.1 Continuum models overview -- 4.2 One-dimensional continuum models -- 4.2.1 Biomass spreading model -- 4.2.2 Multiple species model -- 4.3 Multidimensional continuum models -- 4.3.1 Classifications of multidimensional continuum models -- 4.3.2 Convective transport approach -- 4.3.3 Submerged boundary method -- 4.3.4 Two-species cross-diffusion model -- 4.3.5 Modeling of EPS -- 4.4 Quorum sensing, antimicrobial persistence, and EPS modeling -- 4.4.1 Reactive transport model of the quorum sensing system -- 4.4.2 Mass and momentum conservation equations
