Mathematical Modeling of Biofilm on Activated Carbon

A mathematical description for the kinetics of biofilm on activated carbon (BFAC model) is derived. The model incorporates film transfer, biodegradation, and adsorption of a substrate, as well as biofilm growth. The modeling problem is uniquely characterized, because it involves diffusion across a moving boundary, diffusion with nonlinear reaction, and diffusion in layered media. The detailed derivation and solution procedure are developed to account for the unique features of the model. The BFAC model is solved with a global orthogonal collocation method (GOCM), which not only provides an efficient solution for the substrate concentration but also allows easy computation of the other key quantities, such as substrate fluxes.