Nernst diffusion layer thickness, rotating

The dependence of the limiting current density on the rate of stirring was first established in 1904 by Nernst (N2) and Brunner (Blla). They interpreted this dependence using the stagnant layer concept first proposed by Noyes and Whitney. The thickness of this layer ( Nernst diffusion layer thickness ) was correlated simply with the speed of the stirring impeller or rotated electrode tip. 

The experimental data show that two electrons per O2 are transported through the Nernst layer in the rotating disk experiments. Consequently, reaction (LXIII) would need to proceed sufficiently fast to be essentially complete within a distance small compared to the Nernst diffusion layer thickness. Thermodynamics imposes an upper limit on the 2 concentration adjacent to the electrode, using the value of Enhe = -0.30 V for the 02-02 couple (see Figure 1). At a potential, for example, of jEnhe = —0.80 the upper... 

Volt mmetiy. Diffusional effects, as embodied in equation 1, can be avoided by simply stirring the solution or rotating the electrode, eg, using the rotating disk electrode (RDE) at high rpm (3,7). The resultant concentration profiles then appear as shown in Figure 5. A time-independent Nernst diffusion layer having a thickness dictated by the laws of hydrodynamics is estabUshed. For the RDE,... 

In hydrodynamic systems Planar diffusion to a uniformly accessible electrode, e.g. for rotating disk electrodes (hypothetical Nernst model with S = diffusion layer thickness)... 

It has already been noted that the flux of material to the rotating disc electrode is uniform over the whole surface, and it is therefore possible to discuss the mass transport processes in a single direction, that perpendicular to the surface (i.e. the z direction). Furthermore, it has been noted that the velocity of movement of the solution towards the surface, is zero at the surface and, close to the surface, proportional to Hence, even in the real situation it is apparent that the importance of convection drops rapidly as the surface is approached. In the Nernst diffusion layer model this trend is exaggerated, and one assumes a boundary layer, thickness 6, wherein the solution is totally stagnant and transport is only by diffusion. On the other hand, outside this layer convection is strong enough for the concentration of all species to be held at their bulk value. This effective concentration profile must, however, lead to the same diffusional flux to the surface (and hence current density) as it found in the real system. 

It is also clear from the previous section that the rate of convective diffusion to the disc is strongly dependent on the rotation rate of the disc, but this is readily taken into account in the Nernst diffusion layer model by noting that the stagnant layer thickness will decrease as the rotation rate is increased. In fact, a quantitative relationship has been deduced [3], i.e. 

The thickness of the Nernst layer increases with the square root of time until natural - convection sets in, after which it remains constant. In the presence of forced convection (stirring, electrode rotation) (see also Prandtl boundary layer), the Nernst-layer thickness depends on the degree of convection that can be controlled e.g., by controlling the rotation speed of a -> rotating disk electrode. See also - diffusion layer. See also Fick s law. 

This can be illustrated in the example of a mechanical stirring device (forced convection) when used for homogenising the liquid electrolyte, mainly away from the zones that are next to the interfaces. The same case applies to analytical chemistry when a rotating disc electrode is involved or when a system is installed in industrial electrolysers in order to force the circulation of the electrolyte. By following a simplified model called the Nernst model one can define the thickness of the diffusion layer (often denoted by 5)... 

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