Diffusion across laminar flow interface

The profiles in Figure 3.37B represent the situation in which a potential is applied that requires equal concentrations of O and R at the electrode surface to satisfy the Nernst equation (i.e., E = Eq R). To fulfill this requirement, the electrode electrolyzes O to R at the rate required to maintain equal concentrations of O and R at the surface. If this potential is maintained, a continuous electrolysis of O to R is necessary to maintain surface concentrations because R diffuses away from the interface across the stagnant layer and is then swept away by the laminar flow. 

Diffusion across an interface. Consider a pond containing pure water. If the air above it is dry, water will evaporate from the surface, especially if the wind is blowing. The air flow will readily be turbulent, so that water vapor can be transported from the pond surface by convection. Now a surfactant is added, enough to produce a monomolecular layer on the pond, and the evaporation rate is markedly reduced. It is often assumed that the surfactant layer provides resistance to evaporation because water cannot readily diffuse through it. However, the layer is very thin (a few nanometers) and can only cause a small resistance to diffusion (see Section 5.3.3). The main explanation of the reduced evaporation must be that the wind over the surface causes a y-gradient, so that the surface can now withstand a tangential stress hence a laminar boundary layer of air will be formed near the surface, and the diffusion of water vapor through the boundary layer (which may be about a millimeter thick) will cause a considerable decrease in transport rate. 

Ferrigno et al. [65] reported the operation of a vanadium redox flow cell without using a membrane or separator. The mixing of anolyte and catho-lyte was prevented by maintaining parallel laminar flows of the electrolytes forced through a Y-shape entrance. The interface between the flow electrolytes plays the role of a separator across which ions diffuse and migrate. 

Although such determination for the molecular diffusivity is very simple, the value obtained should be treated as the first estimate for the molecular diffusivity as in practice the flow of vapor from the liquid interface to the top is usually laminar that is there exists a velocity distribution across the tube which the analysis dealt with here did not take into account. The readers should refer to Whitaker (1991) for detailed exposition of the influence of the velocity profile. 

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