Antonie van Leeuwenhoek 81: 245–256, 2002. © 2002 Kluwer Academic Publishers. Printed in the Netherlands. 245 Mathematical modelling of biofilm structures M.C.M. van Loosdrecht 1,* , J.J. Heijnen 1 , H. Eberl 2 , J. Kreft 3 & C. Picioreanu 1 1 Kluyverlaboratory for Biotechnology, Delft University of Technology, Julianalaan 67, 2628 BC Delft, The Netherlands; 2 GSF, Inst. For Biomathematics and Biometry, pf 1129, 85758 Neuherberg, Germany; 3 Abteilung Theoretische Biologie, Botanisches Institut der Universität Bonn, Kirschallee 1, D-53115 Bonn, Germany ( * Author for correspondence: E-mail: M.C.M.vanLoosdrecht@TNW.TUDelft.NL) Key words: biofilm, detachment, mathematical model, morphology, transport Abstract The morphology of biofilms received much attention in the last years. Several concepts to explain the development of biofilm structures have been proposed. We believe that biofilm structure formation depends on physical as well as general and specific biological factors. The physical factors (e.g. governing substrate transport) as well as general biological factors such as growth yield and substrate conversion rates are the basic factors governing structure formation. Specific strain dependent factors will modify these, giving a further variation between different biofilm systems. Biofilm formation seems to be primarily dependent on the interaction between mass transport and conversion processes. When a biofilm is strongly diffusion limited it will tend to become a heterogeneous and porous structure. When the conversion is the rate-limiting step, the biofilm will tend to become homogenous and compact. On top of these two processes, detachment processes play a significant role. In systems with a high detachment (or shear) force, detachment will be in the form of erosion, giving smoother biofilms. Systems with a low detachment force tend to give a more porous biofilm and detachment occurs mainly by sloughing. Biofilm structure results from the interplay between these interactions (mass transfer, conversion rates, detachment forces) making it difficult to study systems taking only one of these factors into account. Introduction Biofilms consist of cells immobilised in an organic polymer matrix of microbial origin (Characklis & Marshall 1989). The structure of a biofilm has only recently received more attention. Although it was known in the past that biofilms are not uniform in time or space (Characklis & Marshall 1989), frequently it was assumed that biofilms where homogeneous. With a more detailed analysis of biofilms (Caldwell 1993; Gjaltema 1994; De Beer 1994) it is however apparent that a wide variety of biofilm structures exist. Gjaltema et al. (1994) showed that even in a well-mixed biofilm reactor (rototorque reactor) different types of biofilms could be found. These variations arise from slight differences in shear rates at different surface sites in the reactor and from the fact that even in a hydraulic- ally well mixed system, substrate gradients can occur when the characteristic time for substrate conversion is smaller than the characteristic mixing time (Gjaltema 1994). Biofilm studies are either performed at a mac- roscopic level (i.e. measuring general properties of biofilms formed in a reactor or system) or microscop- ically (i.e. using microscopy and micro-electrodes). A microscopic study has the disadvantage that it is difficult to link it with the overall system dynamics, whereas a macroscopic study is difficult to interpret unless a very well defined experimental system is available. The biofilm airlift suspension reactor (Figure 1, Tijhuis et al. 1996) has proved to be an excellent system for biofilm studies. It is a well-mixed reactor with a very short mixing time and the biofilms are formed on particles homogeneously suspended in the reactor. The latter guarantees that although there are different shear zones in the reactor (as in virtually any reactor), averaged over time, each particle is subjected to the same substrate loading and detachment forces.