Properties of the chemostat model with aggregated biomass

Abstract

We revisit the well-known chemostat model, considering that bacteria can be attached together in aggregates or flocs. We distinguish explicitly free and attached compartments in the model and give sufficient conditions for coexistence of these two forms. We then study the case of fast attachment and detachment and shows how it is related to densitydependent growth functions. Finally, we give some insights concerning the cases of multispecific flocs and different removal rates.

Editorial

“…One subset of papers, is concerned with macro-or reactor scale systems, in which biological activity is due to biofilms, but without explicit spatial resolution of the colony scale processes. Explored in these papers are co-existence of floating and aggregated bacterial cells in a chemostat (Rapaport, 2018), the dynamics of pathogen contamination in drinking water distribution networks (Marzooq et al, 2018) and the effect of diffusion limitation and heterogeneity formation induced by microbial colonies embedded in matrices of materials (Aristotelous et al, 2018). A second group examines biofilms on a mesoscale, i.e.…”

Properties of the Chemostat Model with Aggregated Biomass and Distinct Removal Rates

“…These models were inspired by the Freter model [8,9] of the microflora in the large intestine. Another mechanism that promotes the coexistence is the flocculation of the species, see [4,5,7,11,12,27,28]. Attachment and detachment phenomena of bacteria, whether in biofilms on a support [14] or in the form of aggregates or flocs [35] are well known and frequently observed in bacterial growth.…”

“…An interesting property of general model (1.3), and its extension to competing species, is that under the assumption that attachment and detachment velocities are fast compared to the specific growth and disappearance rates, using singular perturbation method, see [5,10,11,27], the flocculation model can be reduced to a model with density-dependent growth function. It is well known that density-dependence of the growth functions promotes the coexistence of species [6,13,21,22,23,24].…”

“…We simply distinguish the total biomass v = (2u 2 + 3u 3 + • • • ) m in flocs and the planktonic biomass u = u 1 m. Therefore, to the term A(•) = au in [11], we must add a term which is proportional to v and which corresponds to the aggregation of flocs with planktonic bacteria to form bigger flocs. For simplicity, we assume that the coefficient of proportionality is also equal to a and we take A(•) = a(u + v) instead of the more general choice A(•) = a u u + a v v. This choice of a linear attachment term was first proposed in [5] and was also considered in [4,12,27,28]. It corresponds to the following flocculation interactions: planktonic bacteria can stick with planktonic bacteria or flocs to form new flocs, with rate a(u + v)u, proportional to both the density of isolated bacteria u and the total biomass density u + v. Moreover, we assume, as in Smoluchowski's modeling, that B(•) = b, that is to say, flocs can split and liberate planktonic bacteria, with rate bv, proportional to their density v. The model takes the form:…”

“…In [15,16,17], the planktonic cell death rate and adherent cell death rate are considered among the Freter model of biofilm formation by adding an anti-microbial agent to the continuously stirred tank reactor. Thus, a significant death rate of isolated and/or attached bacteria could increase the removal rates D u and/or D v up to values larger than the dilution rate D. Therefore the study will not be restricted to the cases [4,5,12,27,28], and the cases…”