Mass transfer versus kinetic control of uptake across solid‐water boundaries

We present general nondimensional solutions for uptake across a solid‐water boundary, considering the combined influences of mass transfer flux limitation and uptake reaction kinetics. Mass transfer processes are represented by a general mass transfer velocity. Reaction kinetics are represented by first‐order and Monod models. Mathematical solutions are well approximated by standard mass transfer models for low values of the derived nondimensional mass transfer velocity and by standard kinetic models for high values. Approximate limiting values of the nondimensional mass transfer velocity are defined for mass transfer control and kinetic control. The intermediate region, where both mass transfer and kinetics influence the solution, is relatively broad for first‐order kinetics and Monod kinetics in oligotrophic environments. Both limits decrease as concentration increases in the Monod solution, such that under increasingly eutrophic conditions mass transfer control becomes less important, the intermediate range shrinks, and kinetic control becomes an increasingly good approximation. Example calculations using data from experimental ecosystems indicate that boundary nutrient uptake was mass transfer controlled or intermediate under oligotrophic conditions. Nutrient pulses applied to the systems caused temporary eutrophication, which resulted in temporary kinetic control.