Transport of dissolved and particulate material in biofilm-lined tubes and channels

Abstract

This dissertation develops two models for biofilm-lined channels. The first model seeks to address the rate at which cells move in or out of the flow in a natural hot spring drainage channel. This is done by building a one- and then two-dimensional partial differential equation model of the stream. The model is parameterized using data gathered at Mushroom Spring in Yellowstone National Park in 2011 and 2012. Using this data, we predict erosion and adhesion rates at steady state in upper and lower regions of the stream. The second model describes the utilization of urea by biofilms in an artificial tube flow reactor. The goal of this model is to determine kinetic parameters for ureolytic biofilms. The model is created by deriving two coupled steady state ordinary differential equations, which are parametrized using experimental data. Once the model is fully described, an inverse problem is formulated and solved using a Markov Chain Monte Carlo method. From this model we obtain first order kinetic parameters for a particular strain of E. coli, and discuss results for Michaelis-Menten kinetics. These two model systems are linked by a set of intersecting elements. First, both models concern biofilm-lined channels. Second, in each model these biofilms are found in a streamflow system in which some component transfers from the flow to the biofilm or vice-versa. Third, both systems are represented by low dimensional mathematical models which seek to summarize complex physical behaviors using broad, summarizing parameters. Fourth, in both scenarios the parameters of interest are estimated by combining experimental measurements and mathematical modeling. Finally, error plays an important role in model efficacy. The effects of error are implicit in the first model, but explicitly analyzed in the second.