Mathematical modelling and approximate solutions for microbiological processes in biofilm through homotopy-based methods

Approximate analytical solutions were determined for a mathematical model of a microbiological process in flat biofilms. Approximation methods based on a homotopy concept were used, namely: Homotopy Perturbation Method (HPM), Homotopy Analysis Method (HAM) and Optimal Homotopy Analysis Method (OHAM). Monod and Haldane kinetic models were taken into consideration. Some unknown properties of these methods are presented. It was show that third-order approximation by HAM is more accurate than the method by Abbas and Eberl (2011) and Valdes-Parada et al. (2005). Additionally, the former is the same as for second-order HAM approximation. The accuracy of homotopy-based approximations is considerably influenced by external mass transfer resistances, expressed by the Biot number. The methods are especially useful for modelling bioreactors in which biofilm thicknesses are relatively small and coefficients of mass transfer from liquid to biofilm are large. (C) 2018 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.