Mathematical modelling of multispecies biofilms for wastewater treatment
This dissertation relates to the applications of a one-dimensional mathematical model for multispecies biofilm formation and growth. The model consists of a system of nonlinear hyperbolic partial differential equations, describing the growth of microbial species in biofilms, and a system of semilinear parabolic partial differential equations, which governs substrate diffusion from the surrounding aqueous phase into the biofilm. Overall, this leads to a free boundary value problem, essentially hyperbolic. In a first study, the analysis and simulations of the attachment phenomena in the initial phase of biofilm growth have been addressed. The resulting mathematical problem has been discussed by using the method of characteristics and the fixed-point theorem has been used to obtain existence, uniqueness and properties of solutions. A second aspect of the thesis deals with the analysis and prediction of population dynamics in multispecies biofilms for wastewater treatment. The model has been applied to simulate the bacterial competition and to evaluate the influence of substrate diffusion on microbial stratification for a nitrifying multispecies biofilm including Anammox bacteria and a sulfate-reducing biofilm. In both cases, specific kinetics equations have been introduced to describe biomass growth and substrate consumption. The method of characteristics has been used for numerical purposes and the mass conservation equation plays a crucial role in checking the accuracy of simulations. The simulation results reveal that the model is able to evaluate properly the effects that boundary conditions exert on bacterial competition. Finally, the biofilm model has been extended to include the colonization phenomenon. The new model is able to take into account the invasion of new species diffusing from bulk liquid to biofilm, still based on a set of nonlinear hyperbolic partial differential equations for what concerns the growth process. Indeed, the biological invasion process of new species into the biofilm has been modeled by a system of nonlinear parabolic partial differential equations. The invasion model has been successfully applied to simulate the invasion of heterotrophic bacteria in a constituted autotrophic biofilm and viceversa.