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Résumé :
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A simple biofilm model was developed to simulate the competition between two microorganisms for a common inhibitory substrate. The following assumptions were made for the simulations: (1) the biofilm has a uniform thickness and is composed of 5 segments, (2) growth of two microorganisms A and B which utilize the common substrate is expressed by the Haldane kinetics with a spatial limitation term and is independent of the other microorganism in the biofilm reactor, and (3) diffusion of the substrate, movement of the microorganisms, and continuous loss of the biomass by shearing are expressed by Fick's Law-type equations. The qualitative behavior of the biofilm reactor is characterized by five regions, I-V, depending on the operation conditions, the substrate concentration in feed, and the dilution rate. In region I, both microorganisms are washed out of the biofilm reactor. In region II, microorganism B is washed out, and in region III, microorganism A is washed out of the biofilm. In region IV, both microorganisms coexist with one another. In region V, both microorganisms coexist with a sustained oscillatory behavior. Convergence to regions I-V depends on the initial conditions. In regions II-V, washout of either or both microorganisms is also observed with initial conditions too far away.
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