An innovative type of biofilm model is derived by combining an individual description of microbial particles with a continuum representation of the biofilm matrix. This hybrid model retains the advantages of each approach, while providing a more realistic description of the temporal development of biofilm structure in two or three spatial dimensions. The general model derivation takes into account any possible number of soluble components. These are substrates and metabolic products, which diffuse and react in the biofilm within individual microbial cells. The cells grow, divide, and produce extracellular polymeric substances (EPS) in a multispecies model setting. The EPS matrix is described by a continuum representation as incompressible viscous fluid, which can expand and retract due to generation and consumption processes. The cells move due to a pushing mechanism between cells in colonies and by an advective mechanism supported by the EPS dynamics. Detachment of both cells and EPS follows a continuum approach, whereas cells attach in discrete events. Two case studies are presented for model illustration. Biofilm consolidation is explained by shrinking due to EPS and cell degradation processes. This mechanism describes formation of a denser layer of cells in the biofilm depth and occurrence of an irregularly shaped biofilm surface under nutrient limiting conditions. Micro-colony formation is investigated by growth of autotrophic microbial colonies in an EPS matrix produced by heterotrophic cells. Size and shape of colonies of ammonia and nitrite-oxidizing bacteria (NOB) are comparatively studied in a standard biofilm and in biofilms aerated from a membrane side.

Mathematical models are useful tools to optimize the performance of granular sludge reactors. In these models, typically a uniform granule size is assumed for the whole reactor, even though in reality the granules follow a size distribution and the granule size as such affects the process performance. This study assesses the effect of the granule size distribution on the performance of a granular sludge reactor in which autotrophic nitrogen removal is realized through one-stage partial nitritation-anammox. A comparison is made between different approaches to deal with particle size distributions in one-dimensional biofilm models, from the use of a single characteristic diameter to applying a multiple compartment model. The results show a clear impact on the conversion efficiency of the way in which particle size distribution is modeled, resulting from the effect of the granule size on the competition between nitrite oxidizing and anammox bacteria and from the interaction between granules of different sizes in terms of the exchange of solutes. Whereas the use of a uniform granule size is sufficient in case only the overall reactor behavior needs to be assessed, taking into account the detailed granule size distribution is required to study the solute exchange between particles of different sizes. For the latter purpose, the application of the widespread software package Aquasim is limited and the development of dedicated software applications is required.

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