On the determination of mass transfer in a concentration boundary layer

The mass transfer of scalar quantities (e.g., O 2 and nutrients) in aquatic environments is an important and complex process involving diffusion and advection. In a flowing environment, concentration boundary layers (CBL) occur above the surfaces of organisms when they are a sink or source of scalars. In this study, we used an O 2 microsensor to profile the O 2 concentrations in the CBL above photosynthesizing freshwater macrophyte ( Vallisneria americana ) leaves that were oriented parallel to the flow in a recirculating flow chamber at 0.5 and 3.3 cm s −1 . Measured O 2 profiles were nonlinear indicating the effect of higher order processes near the surface. O 2 flux ( J obs ) was estimated from these profiles by two nonlinear techniques, hyperbolic tangent and logarithmic models, and the commonly applied linear model. An integrated measurement of O 2 flux ( J int ) for each leaf was also measured independently in a stirred chamber. Whereas J obs determined from the hyperbolic tangent (0.42 ± 0.04 [mean SE] µmol m −2 s −1 ) and linear (0.31 ± 0.04 µmol m −2 s −1 ) models overestimated and underestimated J int (0.37 ± 0.05 µmol m −2 s −1 ), respectively, and were not velocity dependant, the hyperbolic tangent model provided the best fit ( r 2 = 0.88) compared with the linear model ( r 2 = 0.77). In addition, the slope of the regression against J int (1.08 ± 0.06) was closest to 1.00 (i.e., a “perfect” fit). The logarithmic model varied with velocity and overestimated J obs (0.98 ± 0.22 µmol m −2 s −1 at 0.005 m s −1 and 0.90 ± 0.18 µmol m −2 s −1 at 0.033 m s −1 ). These results were confirmed in an analysis of 21 published O 2 concentration profiles measured next to sediments, microbial biofilms, planktonic algae, and epilithic algae. We would, therefore, recommend the hyperbolic tangent model to estimate mass transfer in a CBL.