Diffusion and reactions in the vicinity of plankton: A refined model for inorganic carbon transport

Inorganic carbon uptake by phytoplankton depletes the immediate cell environment and disturbs the carbonate system equilibrium. Uptake is balanced by both diffusional transport across and chemical reactions within the depleted boundary layer. In this study, we have derived a model that simulates inorganic carbon diffusion and reactions in the vicinity of phytoplankton cells. To allow a general application of the model, the reaction kinetics of the carbonate system are reviewed and temperature- and salinity-dependence of the various rate constants are discussed. A consistency condition for some of the kinetic rates is derived. The effective thickness of the diffusive boundary layer in spherical and planar geometry is discussed. In addition, the effect of cell shape on diffusive transport to phytoplankton is examined and a simple means to account for this effect in model calculations is presented. In a second step, the complete description of the diffusion-reaction system is simplified to consider two special cases in which (1) algal production relies on CO2(aq) as the single source of inorganic carbon, and (2) CO2, HCO3−, or CO32− are utilized independently for organic matter production combined with calcite precipitation. In the size range typical for phytoplankton cells model predictions of these simplified versions are nearly identical to those of the complete model, indicating that the simplified models represent good approximations of the complete diffusion-reaction system.