Cellular growth in biofilms

In this paper we develop a macroscopic evolutionary equation for the growth of the cellular phase starting from a microscopic description of mass tran sport: and a simple structured model for product formation. The methods of continuum mechanics and volume averaging are used to develop the macroscopi c representation by carefully considering the fluxes of chemical species th at pertain to cell growth. The concept of structured models is extended to include the transport of reacting chemical species at: the microscopic scal e. The resulting macroscopic growth model is similar in form to previously published models for the transport of a single substrate and electron donor and for the production of cellular mass and exopolymer. The method of volu me averaging indicates under what conditions the developed growth model is valid and provides an explicit connection between the relevant microscopic model parameters and their corresponding macroscopic counterparts. (C) 1999 John Wiley & Sons, Inc.