Maximum Rate of Soluble Substrate Utilization (k)

The Maximum Rate of Soluble Substrate Utilization coefficient is referred to by the symbol k. This coefficient is used for designing a complete-mix activated-sludge system and has to do with the biomass growth process.
Substrate in biological processes used for wastewater treatment, referres to the organic matter or nutrients in wastewater, that are converted during biological treatment or that may be limiting in biological treatment. (page 550)
In specific circumstances, there will be a certain rate with which the soluble substrate will be depleted by bacteria. At a high substrate concentration, the utilization rate will be high and will be practically even to the maximum rate of soluble substrate utilization

For designing a complete-mix activated-sludge system, where these coefficients come in handy, please take a look at the Summary of the Related Calculators.
More coefficients used for designing a complete-mix activated-sludge system, are gathered in the Table of Coefficients.

source: Metcalf and Eddy page 582