Advanced Mathematical Modelling of Biofilms and its Applications covers the concepts and fundamentals of biofilms, including sections on numerical discrete and numerical continuum models and different biofilms methods, e.g., the lattice Boltzmann method (LBM) and cellular automata (CA) and integrated LBM and individual-based model (iBM). Other sections focus on design, problem-solving and state-of-the-art modelling methods. Addressing the needs to upgrade and update information and knowledge for students, researchers and engineers on biofilms in health care, medicine, food, aquaculture and industry, this book also covers areas of uncertainty and future needs for advancing the use of biofilm models.

Over the past 25-30 years, there have been rapid advances in various areas of computer technologies, applications and methods (e.g. complex programming and algorithms, lattice Boltzmann method, high resolution visualization and high-performance computation). These new and emerging technologies are providing unprecedented opportunities to develop modeling frameworks of biofilms and their applications. .

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 4.4.3 Quorum sensing volume fraction equations 4.4.4 EPS transport equations 4.4.5 AHL transport equations 4.4.6 Nutrient transport equations 4.4.7 Transport equation for antibiotic (or antimicrobial) agents 4.5 Summary References Further reading 5. Discrete models 5.1 Discrete models overview 5.2 Biological cellular automata 5.2.1 Deterministic cellular automata 5.2.2 Lattice gases 5.2.3 Solidification models 5.3 Individual-based models 5.3.1 Single-substrate and single-cell species 5.3.1.1 Uptake rate 5.3.1.2 Substrate diffusion 5.3.1.3 Biomass growth 5.3.1.4 Cell division 5.3.1.5 Cell diffusion and spreading 5.3.2 Multiple species and substrates (; ; ) 5.3.3 Solution procedure 5.3.4 Applications 5.4 Hybrid model of computational fluid dynamics and cellular automata 5.4.1 Modeling domain and description 5.4.2 Controlling equations 5.4.2.1 Bulk fluid flow and reactive transport 5.4.2.2 Substrate transport 5.4.2.3 Boundary conditions 5.4.2.4 Nonreactive tracer transport 5.4.2.5 Biofilm growth 5.4.2.6 Biomass attachment 5.4.3 Discrete cellular automata for biofilm spreading 5.4.4 Solution procedure 5.4.5 Results 5.5 Summary References Further reading 6. Hybrid lattice Boltzmann continuum–discrete models 6.1 Biofilm growth and development in reactive transport systems 6.1.1 Control equations 6.1.1.1 Bulk fluid flow and reactive transport 6.1.1.2 Biofilm growth 6.1.1.3 Extra biomass transfer 6.1.1.4 Detachment 6.1.1.5 Shrinkage 6.1.1.6 Solving methods 6.2 Hybrid lattice Boltzmann and cellular automaton models 6.2.1 Lattice Boltzmann equation 6.2.2 Hybrid lattice Boltzmann and cellular automaton procedure 6.2.3 Thermal effects 6.2.4 pH effects 6.2.5 Illumination effects 6.2.6 Competition and cooperation 6.2.7 Dimensionless numbers and normalizing 6.3 Hybrid lattice Boltzmann and individual-based models 6.3.1 Controlling equations 6.3.1.1 Lattice Boltzmann model for flow and transport in porous media 6.3.1.2 Reactive transport equations 6.3.2 Individual-based model 6.3.3 Solution methods 6.3.4 Applications 6.4 Summary References Further reading 7. Bioreactor concepts, types, and modeling 7.1 Bioreactor definition and functions 7.1.1 Bioreactor definition 7.1.2 Essential functions and requirements 7.2 Bioreactor types 7.2.1 Classifications of bioreactors according to their operational modes 7.2.1.1 Batch reactors 7.2.1.2 Fed-batch reactors 7.2.1.3 Continuous reactors 7.2.2 Classification according to microorganism immobility 7.2.2.1 Stirred tank reactor 7.2.2.2 Bubble column bioreactors 7.2.2.3 Airlift bioreactors 7.2.2.4 Packed bed 7.2.2.5 Fluidized bed 7.2.2.6 Membrane and hollow fibrous bed 7.2.2.7 Moving bed biofilm reactors 7.2.2.8 Photobioreactors 7.2.2.9 Microbioreactors and miniature bioreactors 7.3 Bioreactor components and control system 7.3.1 Control systems 7.3.1.1 Temperature control 7.3.1.2 pH control 7.3.1.3 Substrate and oxygen concentration control 7.3.2 Main components 7.3.2.1 Vessels 7.3.2.2 Mixing devices 7.3.2.2.1 Mechanically agitated devices 7.3.2.2.2 Spargers 7.3.2.2.3 Baffles 7.3.2.2.4 Static mixer 7.3.2.3 Heat exchanger devices 7.3.2.3.1 Jacket 7.3.2.3.2 Spiral cooling coils 7.3.2.3.3 Double-pipe heat exchangers and shell and tube heat exchangers 7.4 Bioreactor modeling 7.4.1 Kinetic models 7.4.1.1 Mass balances in a bioreactor 7.4.1.2 Reaction rates and biomass growth rates 7.4.1.3 Temperature effects 7.4.1.4 General energy balance 7.4.2 Computational fluid dynamics models 7.4.2.1 Mathematical models 7.4.2.1.1 Bulk fluid flow and reactive transport 7.4.2.1.2 Reactive transport 7.4.2.1.3 Biomass growth 7.4.2.2 Solution procedure of computational fluid dynamics model 7.4.2.3 Applications 7.4.3 Hybrid continuous–discrete models 7.5 Challenges and trends for bioreactor modeling 7.6 Summary