A mechanistic derivation of the Monod bioreaction equation for a limiting nutrient.

We present a quasi-steady state mechanistic derivation of the Monod bioreaction equation based upon a conceptual model involving aqueous phase diffusive transport of substrate towards a spherical microbe; transport of the substrate across its surface membrane; and reaction depleting the substrate within the microbe. The resulting Monod coefficients [Formula: see text] and [Formula: see text] are dependent upon substrate-species pairs and the mass transfer properties of the system. Two substrate transport scenarios are investigated: (1) a constant rate model that is a function of a constant flux across the surface of the microbe; and (2) a linear rate model that is the product of a constant transport velocity and the concentration of substrate in contact with the surface of the microbe.