A General Description of Detachment for Multidimensional Modelling of Biofilms Joao de Bivar Xavier, Cristian Picioreanu, Mark C.M. van Loosdrecht Department of Biotechnology, Delft University of Technology, Julianalaan 67, 2628 BC Delft, The Netherlands; telephone: þ31 (0)15 2781551; fax: þ31 (0)15 2782355; e-mail: j.xavier@tnw.tudelft.nl Received 3 January 2005; accepted 9 March 2005 Published online 25 May 2005 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/bit.20544 Abstract: A general method for describing biomass detachment in multidimensional biofilm modelling is introduced. Biomass losses from processes acting on the entire surface of the biofilm, such as erosion, are modelled using a continuous detachment speed function F det . Discrete detachment events, i.e. sloughing, are implicitly derived from simulations. The method is flexible to allow F det to take several forms, including expressions depen- dent on any state variables such as the local biofilm density. This methodology for biomass detachment was integrated with multidimensional (2D and 3D) particle- based multispecies biofilm models by using a novel application of the level set method. Application of the method is illustrated by trends in the dynamics of biofilms structure and activity derived from simulations performed on a simple model considering uniform biomass (case study I) and a model discriminating bio- mass composition in heterotrophic active mass, extra- cellular polymeric substances (EPS) and inert mass (case study II). Results from case study I demonstrate the effect of applied detachment forces as a fundamental factor influencing steady-state biofilm activity and struc- ture. Trends from experimental observations reported in literature were correctly described. For example, simula- tion results indicated that biomass sloughing is reduced when erosion forces are increased. Case study II illustrates the application of the detachment methodology to systems with non-uniform biomass composition. Simula- tions carried out at different bulk concentrations of substrate show changes in biofilm structure (in terms of shape, density and spatial distribution of biomass com- ponents) and activity (in terms of oxygen and substrate consumption) as a consequence of either oxygen-limited or substrate-limited growth. ß 2005 Wiley Periodicals, Inc. Keywords: biofilm; detachment; erosion; sloughing; individual-based modelling; EPS; level set INTRODUCTION Biomass detachment, i.e. the interphase transport of bio- mass particles from an attached microbial film to the fluid compartment bathing the film (Stewart, 1993), is often the primary process balancing biofilm growth in biofilm reactors (Van Loosdrecht et al., 1995). Detachment determines the steady state accumulation of the biofilm and the average solids retention time (SRT) of the system and is a key parameter influencing biofilm composition and activity (Morgenroth and Wilderer, 1999, 2000). Hence, knowledge and control of biomass detachment is of chief importance in the operation of a biofilm reactor (Tijhuis et al., 1996). Biomass detachment in biofilms may be caused by a diversity of mechanisms including erosion, sloughing, abrasion, predator grazing and human intervention (Bryers, 1988). However, in spite of the diverse causes of detachment, for modelling purposes a simple description using overall detachment rates may be sufficient to explain experimental observations (Stewart, 1993). Wanner and Gujer (1986) included a generic detachment description in their multi- species one-dimensional (1D) biofilm model, later imple- mented in the AQUASIM software (Reichert, 1994). This approach describes detachment using a detachment velocity, i.e. the speed at which the biofilm front retracts as a con- sequence of biomass detachment, allowing almost any function of time (or other relevant physical quantity) to be used as the detachment function. Applications of this approach include for example the interpretation of experi- mental biofilm results (Horn et al., 2003) and a theoretical study on the influence of detachment mechanisms on com- petition in biofilms (Morgenroth and Wilderer, 2000). Apart from the processes involved in detachment, a large number of processes are involved in biofilm formation (Characklis and Marshall, 1990). Therefore, mathematical modelling of biofilm activity is a highly complex task. 1D approaches, such as the model of Wanner and Gujer, simplify this task by restricting the variation of the state variables to a single direction perpendicular to the surface of the solid carrier (often called the ‘‘vertical’’ direction). This is a valid simplification when vertical gradients are orders of magni- tude higher than those in the directions parallel to the carrier surface (Wanner and Gujer, 1986), the ‘‘horizontal’’ direc- tions. Since this applies to most biofilm systems, dynamic multispecies 1D biofilm models are sufficient for the majority of practical purposes (Van Loosdrecht et al., 2002). However, 1D models are not able to describe the dynamics of biofilm ß 2005 Wiley Periodicals, Inc. Correspondence to: Joao de Bivar Xavier Contract grant sponsor: F.C.T./M.C.T.E.S., Portugal Contract grant number: SFRH/BPD/11485/2002