Two parameters account for the flocculated growth of microbes in biodegradation assays

Microbes in activated sludge tanks mostly occur in flocs rather than in cell suspensions. Flocculation results in a limited supply of substrate to the bacteria inside the flocs, which reduces the biodegradation rate of organic compounds by several orders of magnitude. This article presents a simple two-parameter extension of growth models for cell suspensions to account for the ensuing reduction of the degradation rate. The additional parameters represent floc size at division and diffusion length. The biomass of small flocs initially increases exponentially at a rate equal to that of cell suspensions. After this first phase, the growth rate gradually decreases and finally the radius becomes a linear function of time. At this time flocs are large and have a kernel of dead biomass. This kernel arises when the substrate concentration decreases below the threshold level at which cells are just able to pay their maintenance costs. We deduce an explicit approximative expression for the interdivision time of flocs, and thereby for the growth of flocculated microbial biomass at constant substrate concentrations. The model reveals that the effect of stirring on degradation rates occurs through a reduction of the floc size at division. The results can be applied in realistic biodegradation quantifications in activated sludge tanks as long as substrate concentrations change slowly.