It is impossible to enumerate all the areas where diffusion plays a crucial role. Numerous studies of diffusion have been made since the observation of brownian motion by Robert Brown in 1827. In the last decades, the development of computers made it possible to carry numerical studies of diffusion. Monte Carlo algorithms are often used to model the random walk of a particle in a given system in order to measure its diffusion coefficient. In the last years, Dr Slater's research group developed an exact calculation method that allows one to compute diffusion coefficients with high precision. This calculation method, even if major modifications were necessary, is the base of the two projects presented in this thesis.
The first project is a sequel of an article published in 2006 by Hickey et al. These authors derived an expression that predicts the diffusion coefficient of a point-like particle in a two-phase system, such as a hydrogel made of gelatin with maltodextrin viscous inclusions. This expression works well for a simple two-phase system but neglects numerous characteristics such hydrogels can present. In this thesis' first project, we modify this expression in order to include the possible interactions between the particle and the gel structure, the interfacial steric effects between phases and the possible incomplete phase separation. We validate these modifications by comparing them with exact numerical calculations.
In preceding studies made by the research group of Dr Slater, it was assumed that the system was quenched, i.e. the obstacles didn't move. However, it is logical to believe that gel fibers inside a real hydrogel are subject to thermal motion and that they vibrate around a mean position. The second project presents a new numerical method allowing one to investigate the effect of obstacles motion on the diffusion of a particle. We vary different parameters such as the vibration frequency compared to the diffusion time scale of the particle, the amplitude of vibration, the obstacle concentration as well as their configuration (periodic or random). This new method is innovative because it makes it possible to study in details the transition of a system from a quenched state (fixed obstacles) to an annealed state (obstacles vibrating much faster than the diffusion time scale of the particle).
| Identifer | oai:union.ndltd.org:uottawa.ca/oai:ruor.uottawa.ca:10393/28126 |
| Date | January 2009 |
| Creators | Kingsburry, Christine |
| Publisher | University of Ottawa (Canada) |
| Source Sets | Université d’Ottawa |
| Language | French |
| Detected Language | English |
| Type | Thesis |
| Format | 78 p. |
Page generated in 0.0018 seconds