The biomass productivity of the CSTR (Rcstr), defined as the cell output per reactor volume, is calculated as

In the Monod model, imax is the maximum specific growth rate of the organism, and KS, called the saturation constant, is inversely proportional to the cell's affinity for the substrate. The value of KS is typically quite low (1 to 5 mg/L for Escherichia coli on glucose), which means thati ^ 1max when S > 10KS and that i only becomes a strong function of the substrate concentration when S < 10KS.

Note that the maximum specific growth rate of the organism limits the extent to which the dilution rate can be increased.

This threshold dilution rate is called the critical dilution rate (DC), and increasing the dilution rate beyond DC results in "washout"; cells are removed from the vessel at a rate faster than their growth rate. This can limit the productivity of the simple CSTR and motivates cell retention or recycle strategies that enable operation at higher throughputs.

Rearranging the growth model to solve for the substrate concentration in the vessel gives

At dilution rates above DC, cells have been washed out of the vessel, and the substrate concentration equals the inlet concentration (SO). By substituting equation 7 into equa-

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