Boundary layer thickness practical example

In electrochemical reactors, the externally imposed velocity is often low. Therefore, natural convection can exert a substantial influence. As an example, let us consider a vertical parallel plate reactor in which the electrodes are separated by a distance d and let us assume that the electrodes are sufficiently distant from the reactor inlet for the forced laminar flow to be fully developed. Since the reaction occurs only at the electrodes, the concentration profile begins to develop at the leading edges of the electrodes. The thickness of the concentration boundary layer along the length of the electrode is assumed to be much smaller than the distance d between the plates, a condition that is usually satisfied in practice. 

In a hydrodynamically free system the flow of solution may be induced by the boundary conditions, as for example when a solution is fed forcibly into an electrodialysis (ED) cell. This type of flow is known as forced convection. The flow may also result from the action of the volume force entering the right-hand side of (1.6a). This is the so-called natural convection, either gravitational, if it results from the component defined by (1.6c), or electroconvection, if it results from the action of the electric force defined by (1.6d). In most practical situations the dimensionless Peclet number Pe, defined by (1.11b), is large. Accordingly, we distinguish between the bulk of the fluid where the solute transport is entirely dominated by convection, and the boundary diffusion layer, where the transport is electro-diffusion-dominated. Sometimes, as a crude qualitative model, the diffusion layer is replaced by a motionless unstirred layer (the Nemst film) with electrodiffusion assumed to be the only transport mechanism in it. The thickness of the unstirred layer is evaluated as the Peclet number-dependent thickness of the diffusion boundary layer. 

In the above considerations, the O/S interface was taken to be a clear-cut boundary between the oxide and the electrolyte. In reality, however, the outer part of the oxide is likely to be hydrated and penetrated by the electrolyte. Hence, the true O/S interface is likely to be withdrawn from the surface to a sufficient depth such that some oxide is left without any electric field imposed across it. This is especially true of thick porous oxide layers, but it can occur with compact layers as well. For example, Hurlen and Haug35 found a duplex film in acetate solution (pH 7-10), composed of a dry barrier-type part and a thicker hydrated part consisting of A1203 H20. Although the hydrated part becomes thinner with decreasing pH and seems to practically vanish at low pH, even a thickness of less than a nanometer is sufficient for the surface oxide to stay outside the electrochemical double layer. 

This frictionless assumption is often appropriate for very stiff materials where adhesive forces are relatively unimportant, but it is often not the case for softer materials such as elastomers, where adhesive forces play a very important role. In these cases, a full-friction boundary condition, where sliding of the two surfaces is not allowed, is often more appropriate, In many important cases (contact of a very thick, incompressible elastic layer, for example) there is little or no practical difference for these two boundary conditions. Nevertheless, in the discussion that follows, we are careful to indicate that boundary condition (frictionless or full-friction) that formally applies in each case. In all cases we assume that the contacting materials are isotropic and homogeneous, each being characterized by two independent elastic constants. 

---