Forced convection electrode, solution boundary

Fig. 4. Migration contribution to the limiting current in acidified CuS04 solutions, expressed as the ratio of limiting current (iL) to limiting diffusion current (i ) r = h,so4/(( h,so, + cCuS(>4). "Sulfate refers to complete dissociation of HS04 ions. "bisulfate" to undissociated HS04 ions. Forced convection" refers to steady-state laminar boundary layers, as at a rotating disk or flat plate free convection refers to laminar free convection at a vertical electrode penetration to unsteady-state diffusion in a stagnant solution. [F rom Selman (S8).]...

Forced convection may be effected by stirring the solution, rotating or vibrating electrodes (or both), or working with a flowing solution. Theoretical treatment of forced convection in electrolytic cells is difficult, but is possible under certain assumed boundary conditions. A quantity of interest is the diffusion layer away from the electrode surface, and empirical relationships have been developed for some electrode geometries. Two relationships are summarized below ... 

Conventional electrochemical cells have no such arrangement therefore, spontaneous convection flows, which limit the diffusion front shift, can form in them. One of the simplest models, which can evaluate this phenomenon, was proposed by Nernst. According to it, diffusion takes place in a layer of stagnant solution close to the electrode/solution interface. As mentioned earlier, the thickness of the Nernst layer increases with time until natural convection sets in, after which it remains constant. In the presence of forced convection (stirring, electrode rotation), the Nernst layer thickness depends on the intensity of convection that can be controlled, for example, by controlling the rotation speed of an RDE. Hence, the diffusion front can move only as far as to the boundary of the Nernst-type layer. Then, c x) no longer depends on time and the so-called steady state is reached. 

Lionbashevski et al. (2007) proposed a quantitative model that accounts for the magnetic held effect on electrochemical reactions at planar electrode surfaces, with the uniform or nonuniform held being perpendicular to the surface. The model couples the thickness of the diffusion boundary layer, resulting from the electrochemical process, with the convective hydrodynamic flow of the solution at the electrode interface induced by the magnetic held as a result of the magnetic force action. The model can serve as a background for future development of the problem. 

In a real electrochemical system, convection is usually introduced by such means as rotating electrode, stirring, or other forced circulation. In any case, the electrolyte moves relative to electrode surfaces. Due to the mechanical friction between electrolyte solution and electrode surface, a velocity v(x) variation exists. The velocity of solution flow is generally a constant (vqo) in bulk solution (far from the electrode surface and the wall of solution container) and decreases while approaching the solid surfaces [6]. The solution flow velocity v(x) = 0 at solid surface (x = 0). A hydrodynamic (or Prandtl) boundary layer is defined as [6]... 

---