This thesis relates to the mathematical modelling of biofilm in two primary areas: biofilm growth, and the effect of microbial immobilisation in biofilm on environmen- tal contaminant transport in the Earth's subsurface. For biofilm growth we construct a model based on polymer solution theory. Parameter estimates motivate a very different model from two published biofilm models also based on polymer solution theory. Analysis of ID solutions provides an expression for growth rate suitable for comparison with experiment. Stability analysis of spatial perturbations to a growing planar front reveals an interfacial instability mechanism similar to that found in a published theoretical study not based on a specific material model. We derive a stability criterion as a critical external nutrient boundary layer thickness, and for the travelling wave solution we identify the finite perturbation wavenumber selected by the instability. For environmental contaminant transport, we identify dissolution of organic phase contaminants and sorption of hydrocarbons onto solid grains as primary lim- itations on bioavailability. We build a pore scale model including both organic phase dissolution and micro- bial uptake and use it to parameterise pore scale Sherwood and Damkohler numbers with respect to pore Peclet number. We illustrate their relation to effective macro- scopic parameters for varying organic phase size relative to pore size. A simple intraparticle diffusion sorption model is extended by considering an external biofilm layer on the particles. A larger scale model considers contaminant transport in a ID flow through a bed of such particles. A physically reasonable pa- rameter regime is suggested, providing analytical solutions for breakthrough curves.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:589760 |
| Date | January 2011 |
| Creators | Winstanley, Henry Fletcher |
| Contributors | Fowler, Andrew |
| Publisher | University of Oxford |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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