A size-structured model for the nutrient-driven self-cycling fermentation process

Self-cycling fermentation is a computer-aided process used for culturing microorganisms. Applications include sewage treatment and toxic waste cleanup. We consider a model of self-cycling fermentation with nutrient level as the triggering factor. The model is formulated in terms of impulsive ordinary and partial differential equations and refined to include the size of the microorganisms. A threshold is determined in terms of biologically relevant parameters that show that size specific parameters can affect the outcome. The model predicts that either the system fails and the population of microorganisms essentially washes out or, more favourably, the fermentor cycles indefinitely, with one impulse per period, maintaining a positive, though oscillatory, number of cells. However, in any case, the average length and surface area always equilibrate.