DIFFUSION AND REACTION IN BIOFILMS

In the development of models for diffusion and reaction in biofilms, o ne often begins with the assumption that the biofilm is a continuum. T his approach leads to equations for which the domain of validity is no t clearly defined, and it provides no theoretical foundation for the p rediction of the effective coefficients that appear in the postulated equations. In this paper we treat the intracellular phase and the extr acellular phase as continua and use the method of volume averaging to develop the spatially smoothed transport equations for diffusion and r eaction in biofilms. This allows us to identify three regimes in which the spatially smoothed transport equations take on special forms. The first of these is the one-equation model that is valid when the princ iple of local mass equilibrium is satisfied; the second is the two-equ ation model that is not constrained by the principle of local mass equ ilibrium; and the third is a pseudo one-equation model. The latter occ urs when the reaction in the intracellular phase can be treated as ins tantaneous. Constraints that identify the domain of validity of these three models are given. (C) 1997 Elsevier Science Ltd.