Publications by Colleges and Departments (MSU - Bozeman)
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Item Mathematical model of biofilm induced calcite precipitation(2010-08) Zhang, Tian-Yu; Klapper, IsaacMicrobially modulated carbonate precipitation is a fundamentally important phenomenon of both engineered and natural environments. In this paper, we propose a mixture model for biofilm induced calcite precipitation. The model consists of three phases—calcite, biofilm and solvent—which satisfy conservation of mass and momentum laws with addition of a free energy of mixing. The model also accounts for chemistry, mechanics, thermodynamics, fluid and electrodiffusion transport effects. Numerical simulations qualitatively capturing the dynamics of this process and revealing effects of kinetic parameters and external flow conditions are presented.Item Review of mathematical models for biofilms(2010-06) Wang, Qi; Zhang, Tian-YuIn this paper, we briefly review the progress made in the mathematical modeling of biofilms over the last 30 years. Biofilms constitute a spectrum of dynamical microorganisms, whose interaction with the surrounding environment and thereby induced dynamics dictates the complex properties of the living organism. Modeling of biofilms began with a low dimensional continuum description first based on kinematics and translational diffusions: later, more sophisticated microscopic dynamical mechanisms are introduced leading to the anomalous diffusion and dissipation encountered by various components in biofilms. Recently, biofilm and bulk fluid (or solvent) coupling has been investigated using discrete-continuum, multifluid and single fluid multicomponent models to treat the entire biofilm-bulk-fluid system either as a system consisting of various components whose dynamics exhibits different time scale or as a whole. We classify the models into roughly four classes: low-dimensional continuum models, diffusion limited aggregation models, continuum-discrete models, and fully coupled biofilm-fluid models. We will address some hybrid models that combine the ideas from the above categories and new computational protocols combining the existing computational tools. for cell dynamics coupled with the discrete-continuum biofilm model.Item Reaction-diffusion theory explains hypoxia and heterogeneous growth within microbial biofilms associated with chronic infections(2016-06) Stewart, Philip S.; Zhang, Tian-Yu; Xu, Ruifang; Pitts, Betsey; Walters, Marshall C., III; Roe, Frank L.; Kikhney, Judith; Moter, AnnetteReaction–diffusion models were applied to gain insight into the aspects of biofilm infection and persistence by comparing mathematical simulations with the experimental data from varied bacterial biofilms. These comparisons, including three in vitro systems and two clinical investigations of specimens examined ex vivo, underscored the central importance of concentration gradients of metabolic substrates and the resulting physiological heterogeneity of the microorganisms. Relatively simple one-dimensional and two-dimensional (2D) models captured the: (1) experimentally determined distribution of specific growth rates measured in Pseudomonas aeruginosa cells within sputum from cystic fibrosis patients; (2) pattern of relative growth rate within aggregates of streptococcal biofilm harboured in an endocarditis vegetation; (3) incomplete penetration of oxygen into a Pseudomonas aeruginosa biofilm under conditions of exposure to ambient air and also pure oxygen; (4) localisation of anabolic activity around the periphery of P. aeruginosa cell clusters formed in a flow cell and attribution of this pattern to iron limitation; (5) very low specific growth rates, as small as 0.025 h−1, in the interior of cell clusters within a Klebsiella pneumoniae biofilm in a complex 2D domain of variable cell density.Item Mathematical model of the effect of electrodiffusion on biomineralization(2011-05) Zhang, Tian-Yu; Klapper, IsaacBiofilm-induced mineral precipitation is a fundamentally important phenomenon with many potential applications including carbon sequestration and bioremediation. Based on a mixture model consisting of three phases (calcite, biofilm, and solvent) and also accounting for chemistry, mechanics, thermodynamics, fluid, and electrodiffusive transport effects, we describe the self-induced generation of an electric field due to different diffusivities of different ion species and study the effects of this field on ionic transport and calcite precipitation. Numerical simulations suggest that one of these effects is enhanced precipitation.Item A multicomponent model for biofilm-drug interaction(2011-03) Lindley, B.; Wang, Qi; Zhang, Tian-YuWe developed a tri-component model for the biofilm and solvent mixture, in which the extracellular polymeric substance (EPS) network, bacteria and effective solvent consisting of the solvent, nutrient, drugs, etc., are modeled explicitly. The tri-component mixture is assumed incompressible as a whole, while inter-component mixing, dissipation, and conversion are allowed.A linear stability analysis is conducted on constant equilibria revealing up to two unstable modes corresponding to possible bacterial growth induced by the bacterial and EPS production and dependent upon the regime of the model parameters. A 1-D transient simulation is carried out to investigate the non-linear dynamics of the EPS network, bacteria distribution, drug and nutrient distribution in a channel with and without shear. Finally, the transient biofilm dynamics are studied with respect to a host of diffusive properties of the drug and nutrient present in the biofilm.Item Multicomponent hydrodynamic model for heterogeneous biofilms: Two-dimensional numerical simulations of growth and interaction with flows(2012-03) Lindley, B.; Wang, Qi; Zhang, Tian-YuWe develop a tricomponent (ternary) hydrodynamic model for multiphase flows of biomass and solvent mixtures, which we employ to simulate biofilm. In this model, the three predominant effective components in biofilms, which are the extracellular polymeric substance (EPS) network, the bacteria, and the effective solvent (consisting of the solvent and nutrient, etc.), are modeled explicitly. The tricomponent fluid mixture is assumed incompressible as a whole, while intercomponent mixing, dissipation, and conversion are allowed among the effective components. Bacterial growth and EPS production due to the growing bacterial population are modeled in the biomass transport equations. Bacterial decay due to starvation and natural causes is accounted for in the bacterial population dynamics to capture the possible bacterial population reduction due to the depletion of the nutrient. In the growth regime for biofilms, the mixture behaves like a multiphase viscous fluid, in which the molecular relaxation is negligible in the corresponding time scale. In this regime, the dynamics of biofilm growth in the solvent (water) are simulated using a two-dimensional finite difference solver that we developed, in which the distribution and evolution of the EPS and bacterial volume fractions are investigated. The hydrodynamic interaction between the biomass and the solvent flow field is also simulated in a shear cell environment, demonstrating the spatially and temporally heterogeneous distribution of the EPS and bacteria under shear. This model together with the numerical codes developed provides a predictive tool for studying biomass-flow interaction and other important biochemical interactions in the biofilm and solvent fluid mixture.Item Kinetic theories for biofilms(2012-01) Wang, Qi; Zhang, Tian-YuWe apply the kinetic theory formulation for binary complex fluids to develop a set of hydrodynamic models for the two-phase mixture of biofilms and solvent (water). It is aimed to model nonlinear growth and transport of the biomass in the mixture and the biomass-flow interaction. In the kinetic theory formulation of binary complex fluids, the biomass consisting of EPS (Extracellular Polymeric Substance) polymer networks and bacteria is coarse-grained into an effective fluid component, termed the effective polymer solution; while the other component, termed the effective solvent, is made up of the ensemble of nutrient substrates and the solvent. The mixture is modeled as an incompressible two-phase fluid in which the presence of the effective components are quantified by their respective volume fractions. The kinetic theory framework allows the incorporation of microscopic details of the biomass and its interaction with the coexisting effective solvent. The relative motion of the biomass and the solvent relative to an average velocity is described by binary mixing kinetics along with the intrinsic molecular elasticity of the EPS network strand modeled as an elastic dumbbell. This theory is valid in both the biofilm region which consists of the mixture of the biomass and solvent and the pure solvent region, making it convenient in numerical simulations of the biomass-flow interaction. Steady states and their stability are discussed under a growth condition. Nonlinear solutions of the three models developed in this study in simple shear are calculated and compared numerically in 1-D space.