Analysis and simulations of the initial phase in multispecies biofilm formation

The work presents a mathematical modelling approach to study dynamic competition during the attachment phenomena in the initial phase of biolm growth. Biofilm development is described by a set nonlinear hyperbolic partial dierential equations. Diffusion of substrates through biolm is modeled by a set of semilinear parabolic partial differential equations. The two sets of equations are mutually connected. The resulting mathematical problem is a free boundary value problem, which is essentially hyperpolic. A characteristic-like method is introduced to convert differential equations to integral equations. Fixed-point theorem is used to obtain existence, uniqueness and properties of solutions. The model has been applied to the biological competition of heterotrophic-autotrophic bacteria in a multi-specie biolm. The eects of dierent attachment rates on the biolm dynamic performances predicting biolm thickness, volume fractions of bacterial species and substrate concentration trends have been investigated. The simulations show that the dierent attachment rates infuence biolm thickness, of course. However, the volume fractions of bacterial species mainly depend on biolm internal dynamics and substrate concentration trends. The bulk concentrations of microbial species play a relative important role only in the outermost layers of biolm.