In this work, we study a model of the chemostat where the species are present in two forms, isolated and aggregated individuals, such as attached bacteria or bacteria in flocks. We show that our general model contains a lot of models that were previously considered in the literature. Assuming that flocculation and deflocculation dynamics is fast compared to the growth of the species, we construct a reduced chemostat-like model in which both the growth functions and the apparent dilution rate depend on the density of the species. We also show that such a model involving monotonic growth rates may exhibit bi-stability, while it may occur in the classical chemostat model, but when the growth rate is non-monotonic.