Scholarly Work - Center for Biofilm Engineering
Permanent URI for this collectionhttps://scholarworks.montana.edu/handle/1/9335
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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 Modeling of biocide action against biofilm(2012-02) Zhang, Tian-YuWe consider the mathematical model of dynamic antimicrobial action against bacterial biofilms. A mixture model is used in which the biofilm consisting of live and dead bacteria is modeled as one fluid component, while the solvent containing biocide is modeled as the other, and each component is represented by its volume fraction. The whole system is assumed to be an incompressible fluid and the velocity is governed by the Navier–Stokes equation. Biocide kills the live bacteria and its transport is governed by an advection–reaction–diffusion equation. Certain biocide also weakens the mechanical cohesiveness of the biofilm and results in biofilm removal under the shear stress of the external flow. Spatial and temporal patterns of antimicrobial action of three different biocides are considered and numerical simulation results by finite difference method are presented.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.