Separating the EPS in a biofilm : models and simulations of movement of the EPS within

Abstract

In this dissertation two models are investigated for describing movement of different components within a biofilm. The first model uses a single fluid three component formulation of the biofilm to model the movement within the biofilm in 1D. This is done using a system partial differential equations to model the expansion or contraction of the biofilm in order for the three components to reach an ideal concentration. The model is further refined to include separate velocities for each component as well as using zeroth order kinetics for the growth. In order to solve this system of partial differential equations a finite difference method with an upwind scheme was used to solve the system numerically. The second model is an energy based approach done in both 1D and 2D. An energy, in the case the Flory-Huggins free energy density, is used to describe the interactions of different components within the biofilm. The Cahn-Hilliard equation with the Flory-Huggins free energy density is used to model the separation of the biofilm into two phases. A brief derivation of both the Flory-Huggins equation and the Cahn-Hilliard equation is given using a lattice model and thermodynamic properties. The Flory-Huggins equation is modified slightly for simplicity. A movement energy is also added to the Flory-Huggins equation in order to allow the polymers within the biofilm to move around the domain. In the 1D case the numerical solution was found using finite differences with an upwind scheme similar to the first model. The 2D case is more difficult to solve due to the extra dimension. Due to this the projection method was used to solve part of the system of equations and finite difference using central difference instead of upwind is used to solve the rest.