rate is defined as the flow of medium per unit of time, F, over the volume V of culture in the bioreactor Maximal growth rate and critical dilution rate Specific growth rate μ is inversely related to the time it takes the biomass to double, called doubling time td, by: Therefore, the doubling time td becomes a function of dilution rate D in steady state: Each microorganism growing on a particular substrate has a maximal specific growth rate μmax (the rate of growth observed if growth is limited by internal constraints rather than external nutrients). If a dilution rate is chosen that is higher than μmax, the cells cannot grow at a rate as fast as the rate with which they are being removed so the culture will not be able to sustain itself in the bioreactor, and will wash out. However, since the concentration of the limiting nutrient in the chemostat cannot exceed the concentration in the feed, the specific growth rate that the cells can reach in the chemostat is usually slightly lower than the maximal specific growth rate because specific growth rate usually increases with nutrient concentration as described by the kinetics of the Monod equation. The highest specific growth' rates (μmax) cells can attain is equal to the critical dilution rate (D'c): where S is the substrate or nutrient concentration in the chemostat and K''S is the half-saturation constant (this equation assumes Monod kinetics). Applications Research Chemostats in research are used for investigations in cell biology, as a source for large volumes of uniform cells or protein. The chemostat is often used to gather steady state data about an organism in order to generate a mathematical model relating to its metabolic processes. Chemostats are also used as microcosms in ecology and evolutionary biology. In the one case, mutation/selection is a nuisance, in the other case, it is the desired process under study. Chemostats can also be used to enrich for specific types of bacterial mutants in culture such as auxotrophs or those that are resistant to antibiotics or bacteriophages for further scientific study. Variations in the dilution rate permit the study of the metabolic strategies pursued by the organisms at different growth rates. Competition for single and multiple resources, the evolution of resource acquisition and utilization pathways, cross-feeding/symbiosis, antagonism, predation, and competition among predators have all been studied in ecology and evolutionary biology using chemostats. Industry