Modified expressions for substrate flux into biofilm

Abstract

The present study was carried out to simplify existing biofilm one-dimensional models, which consider a single substrate as the limiting factor. Models of Suidan and Wang (1985) and Sáez and Rittmann (1988, 1992) were selected for the present study. Thus, modified expressions were developed for the first one, while the exact solution of the second one could be obtained. The modified expressions and the exact solution are short, simple, easy to use, and give reliable results in comparison to the original models. In addition, the proposed expressions and solution can be used instead of the graphical solutions, which are commonly used to solve the original models. Applicability of the developed expressions has been demonstrated through an illustrative example. The proposed expressions and the present study may be useful to simplify the description of biofilm in many systems such as completely mixed or fluidized-bed reactor for treatment of water or wastewater as well as the biofilm-activated sludge reactors. Moreover, the exact solution from this study can be used to establish the biofilm kinetics instead of using the curve-matching technique. Key words: biofilm, model, modified expressions, steady state, substrate flux.