An effective model for flocculating bacteria with density-dependent growth dynamics

We present a model for a biological reactor in which bacteria tend to aggregate in flocs, as encountered in wastewater treatment plants. The influence of this flocculation on the growth dynamics of the bacteria is studied. We argue that a description in terms of a specific growth rate is possible when the flocculation dynamics is much faster than the other processes in the system. An analytical computation shows that in this case, the growth rate is density-dependent, i.e., depends both on the substrate and the biomass density. When the flocculation time scale overlaps with the other time scales present in the system, the notion of specific growth rate becomes problematic. However, we show numerically that a density-dependent growth rate can still accurately describe the system response to certain perturbations.