Abstract Weak turbulent mixing processes increase the effective exchange rate of a passive additive between a small element of fluid and its surroundings. An approximate mean Green's function, controlled by molecular and turbulent diffusion, is used to estimate this exchange rate at high Schmidt numbers for a fully-developed turbulent flow near a rigid interface. The calculations show that turbulent mixing decreases the magnitude of the diffusive and retarding contributions to the turbulent flux and that this leads to a net decrease in the mass transfer rate.