Mass transfer in annuli for both fully developed laminar and turbulent flow conditions has been studied with respect to available experimental data. It is shown that prediction of the Sherwood number for the inner annular wall based on the hypothesis of coincidence of the zero shear stress position for laminar and turbulent flows leads to serious error in the case of small radius ratio. Also it is shown that in contrast with plain tubes the curvature in small radius ratio annuli should be taken into account for the case of small Reynolds numbers. In consequence, the well-known Leveque equation can be used for the calculation of the mass transfer coefficient in annuli only under certain conditions. Possibilities of electrodiffusion diagnostics for the precise determination of the zero shear stress position in annuli are discussed.