Chemostat

Catabolic products from anaerobic fermentation processes are potentially of industrial interest. The volatile fatty acids and alcohols produced can be used as building blocks in chemical processes or applied directly as substrates in a mixed culture process to produce bioplastics. Development of such applications requires a predictable and controllable product spectrum of the fermentation process. The aim of the research described in this paper was (i) to investigate the product spectrum of an open mixed culture fermentation (MCF) process as a function of the pH, using glucose as substrate, and (ii) to relate the product spectrum obtained to generalized biochemical and thermodynamic considerations. A chemostat was operated under carbon and energy limitation in order to investigate the pH effect on the product spectrum in a MCF process. A transition from CO2/H2 production at lower pH values to formate production at higher pH values was observed. The ratio of CO2/H2 versus formate production was found to be related to the thermodynamics of formate dehydrogenation to CO2/H2. This transition was associated with a shift in the catabolic products, from butyrate and acetate to ethanol and acetate, likely due to a decrease in the oxidation state of the electron carriers in the cell. The product spectrum of the MCF process as a function of the pH could largely be explained using general biochemical considerations. Biotechnol. Bioeng. 2007; 98: 69–79. © 2007 Wiley Periodicals, Inc.

The asymptotic behaviour of a model of a tri-trophic food chain in the chemostat is analysed in detail. The Monod growth model is used for all trophic levels, yielding a non-linear dynamical system of four ordinary differential equations. Mass conservation makes it possible to reduce the dimension by 1 for the study of the asymptotic dynamic behaviour. The intersections of the orbits with a Poincaré plane, after the transient has died out, yield a two-dimensional Poincaré next-return map. When chaotic behaviour occurs, all image points of this next-return map appear to lie close to a single curve in the intersection plane. This motivated the study of a one-dimensional bi-modal, non-invertible map of which the graph resembles this curve. We will show that the bifurcation structure of the food chain model can be understood in terms of the local and global bifurcations of this one-dimensional map. Homoclinic and heteroclinic connecting orbits and their global bifurcations are discussed...

Catabolic products from anaerobic fermentation processes are potentially of industrial interest. The volatile fatty acids and alcohols produced can be used as building blocks in chemical processes or applied directly as substrates in a mixed culture process to produce bioplastics. Development of such applications requires a predictable and controllable product spectrum of the fermentation process. The aim of the research described in this paper was (i) to investigate the product spectrum of an open mixed culture fermentation (MCF) process as a function of the pH, using glucose as substrate, and (ii) to relate the product spectrum obtained to generalized biochemical and thermodynamic considerations. A chemostat was operated under carbon and energy limitation in order to investigate the pH effect on the product spectrum in a MCF process. A transition from CO2/H2 production at lower pH values to formate production at higher pH values was observed. The ratio of CO2/H2 versus formate production was found to be related to the thermodynamics of formate dehydrogenation to CO2/H2. This transition was associated with a shift in the catabolic products, from butyrate and acetate to ethanol and acetate, likely due to a decrease in the oxidation state of the electron carriers in the cell. The product spectrum of the MCF process as a function of the pH could largely be explained using general biochemical considerations. Biotechnol. Bioeng. 2007; 98: 69–79. © 2007 Wiley Periodicals, Inc.

We show that the chemostat model with two species having different but close break-even concentrations exhibits a slow–fast dynamics. Considering small perturbations about the dilution rate for which break-even concentrations are identical, we use the Fenichel theory to show the coexistence of species for large times. Then we determine the reduced dynamics, which is non-trivial and characterized by the slopes