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Modelling Uranium Bioreduction by One-Dimensional Biofilms

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Title: Modelling Uranium Bioreduction by One-Dimensional Biofilms
Author: Gaebler, Harry J
Department: Department of Mathematics and Statistics
Program: Mathematics and Statistics
Advisor: Eberl, Hermann J
Abstract: We formulate and study a series of mathematical models that describe the bioreduction of uranium by multispecies biofilms, with an emphasis on the inclusion of thermodynamic rate laws to describe the utilization and production of substrates. The physical system described consists of two bacterial species, namely dissimilatory metal reducing bacteria, which degrade uranium in the presence of hydrogen and acetate, and a syntrophic bacterial species, which degrade propionate and produce hydrogen and acetate. We present three different types of bioreactors and investigate the effects of biological processes and energy requirements on the solution to the models. The models presented consist of (i) a thermodynamically inhibited chemostat model, (ii) a thermodynamically inhibited biofilm reactor model with suspended bacteria, and (iii) a multiscale biofilm growth model in porous media. The chemostat model is studied both as a simplified productive system, where analytical results are obtainable using elementary techniques, and a complex system that is studied numerically and verifies that model behaviour of the simpler system extends to more complex systems. The chemostat model is then extended to include aggregated biomass in the form of bacterial biofilms. This extension requires the inclusion of an embedded two-point boundary value problem to describe the flux of substrates into the biofilm. Stability results of the washout equilibrium are obtainable analytically, but due to the complexity of the model, the interior equilibrium is studied numerically. Analysis of the model provides insight into substrate utilization and production within the biofilm, namely that there is at most one unique point within the biofilm where utilization/production ceases, resulting in a layer of completely inactive biomass. The multiscale biofilm growth model is constructed by compartmentalizing the porous domain and describing a mesoscopic multispecies biofilm model in each compartment. The mesoscopic equations are upscaled to the macroscale, which involves studying how different biological and thermodynamic processes behave in the scaling limit. The resulting macroscopic model is a system of quasilinear hyperbolic balance laws, which are studied numerically.
Date: 2021-07
Rights: Attribution-NonCommercial-NoDerivatives 4.0 International
Related Publications: Gaebler, HJ., Hughes, JM. and Eberl, HJ. Thermodynamic inhibition in a biofilm reactor with suspended bacteria. Bull. Math. Biol. 83 (2), 2021. DOI:10.1007/s11538-020-00840-w

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