https://search.dev.ndltd.org/etd/massey/oai:mro.massey.ac.nz:10179/14483
type: CreativeWork
name: Mathematical analysis of the reaction diffusion processes occuring within a biofilm: submitted as a 3 paper thesis for the degree of Masters of Philosophy in biotechnology at Massey University in New Zealand
description: This thesis investigates the behaviour of the solutions to mass transfer type reaction-diffusion equations within a biological film around a spherical particle, around a rotating cylinder and on a slab. In general these biological films may be found in any biological system and as examples of systems with spherical, cylindrical and slab geometry we examine biofilms in a fluidised bed biofilm reactor, biological growth around a rotating cylinder and on a rotating biological disk contactor. These equations model concentrations of substrates within a single biofilm as a function of position and time. In dimensionless coordinates , these equations have the form = _1_ l (xa-1 QY) - 4/ F(y) a-1 ax ax (P) X for a = 1,2,3 being geometries of a slab, cylinder and sphere respectively and \w-• ti hai-a F(y) may correspond to F0,F1 Fn or Fmm and where ' FO = 1 corresponds to zero order kinetics F1 = y corresponds to first order kinetics Fn =yn corresponds to nth order kinetics where n is an integer and F Y corresponds to Michaelis-Menten reaction kinetics mm 1 + y The dependent variable y corresponds to concentration and the independent variables x and t correspond to distance and time respectively. The model parameters are saturation parameter , which describes the concentration and Thiele modulus <1>, which is the ratio of reaction to diffusion coefficients. The boundary conditions are (a,t)=O and y(1,t)=1 for all time >0 Here a is the internal boundary, a parameter that corresponds in spherical geometries to the ratio of the radius of a support media to the total radius of the bioparticle, in cylindrical geometries to the radius of a cylinder without biofilm to the total radius of the cylinder with biofilm and in slab geometry to be the ratio of the inactive region of diffusion to the thickness of biofilm measured from the centre of the slab. This may vary but for our purposes we shall take it to be a constant. The major part of this thesis is concerned with the solution to …
abstract: This thesis investigates the behaviour of the solutions to mass transfer type reaction-diffusion equations within a biological film around a spherical particle, around a rotating cylinder and on a slab. In general these biological films may be found in any biological system and as examples of systems with spherical, cylindrical and slab geometry we examine biofilms in a fluidised bed biofilm reactor, biological growth around a rotating cylinder and on a rotating biological disk contactor. These equations model concentrations of substrates within a single biofilm as a function of position and time. In dimensionless coordinates , these equations have the form = _1_ l (xa-1 QY) - 4/ F(y) a-1 ax ax (P) X for a = 1,2,3 being geometries of a slab, cylinder and sphere respectively and \w-• ti hai-a F(y) may correspond to F0,F1 Fn or Fmm and where ' FO = 1 corresponds to zero order kinetics F1 = y corresponds to first order kinetics Fn =yn corresponds to nth order kinetics where n is an integer and F Y corresponds to Michaelis-Menten reaction kinetics mm 1 + y The dependent variable y corresponds to concentration and the independent variables x and t correspond to distance and time respectively. The model parameters are saturation parameter , which describes the concentration and Thiele modulus <1>, which is the ratio of reaction to diffusion coefficients. The boundary conditions are (a,t)=O and y(1,t)=1 for all time >0 Here a is the internal boundary, a parameter that corresponds in spherical geometries to the ratio of the radius of a support media to the total radius of the bioparticle, in cylindrical geometries to the radius of a cylinder without biofilm to the total radius of the cylinder with biofilm and in slab geometry to be the ratio of the inactive region of diffusion to the thickness of biofilm measured from the centre of the slab. This may vary but for our purposes we shall take it to be a constant. The major part of this thesis is concerned with the solution to …
author: Parshotam, Aroon A
keywords: Biofilms, Mathematical models
date published: 1988
date modified: 2026-07-27T20:18:16Z
provider: Massey University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Massey University