AbstractPresently empirical expressions, especially the Monod equation, are used to quantitatively relate microbial growth rate to limiting substrate concentration in the solution. In this paper microbial growth is postulated to occur by a mechanism involving a mass transfer or assimilation process. The assimilation process is assumed to be substrate mass transfer limited and hence proportional to the limiting substrate concentration. The ingestion is assumed independent of limiting substrate concentration and only dependent upon internal reaction rates. The quantitative relationship between limiting substrate and microbial growth rate resulting from this mechanism is developed. Under certain limiting conditions this expression is shown to reduce to the Monod equation and under other conditions it reduces to the Lotka‐Volterra relationship. This mechanism is applied to batch and continuous cultures and the results obtained are compared quantitatively with experiment.