Boundary layers and distance scales

At an electrode surface, the velocity of the solution with respect to the surface will be zero and the concentration of electroactive species will be different from that in the bulk of the solution (zero at the limiting current). The behaviour of an electrochemical system under the influence of a steady flow is therefore governed by two boundary layers SH within which the solution velocity increases until it reaches its limiting value far from the surface and SD, within which the reagent concentration increases until it reaches its bulk solution value. In the case of a modulated flow or modulated motion of the electrode, there is a third distance scale which must be considered, Shm, the boundary layer over which the modulation is damped out. 

When a fluid flow of constant velocity, u, impinges parallel to the edge of a plate, the boundary condition is such that the fluid velocity is zero on the surface of the plate. This results in the formation of a hydrodynamic boundary layer in which the flow velocity parallel to the surface varies with distance normal to the surface. The hydrodynamic boundary layer thickness increases with distance, jc, from the upstream edge of the plate as given by equation (10.5) [7]  

When the flow is constrained to a channel bounded on both faces, then at a sufficient distance from the entry point, xe, the two hydrodynamic boundary layers associated with each wall overlap and the fluid velocity varies parabolically with position across the channel. 

When the concentration boundary layer is sufficiently thin the mass transport problem can be solved under the approximation that the solution velocity within the concentration boundary layer varies linearly with distance away from the surface. This is called the L6v que approximation (8, 9] and is satisfactory under conditions where convection is efficient compared with diffusion. More accurate treatments of mass transfer taking account of the full velocity profile can be obtained numerically [10, 11] but the Ldveque approximation has been shown to be valid for most practical electrodes and solution velocities. Using the L vSque approximation, the local value of the concentration boundary layer thickness, 8k, (determined by equating the calculated flux to the flux that would be obtained according to a Nernstian diffusion layer approximation that is with a linear variation of concentration across the boundary layer) is given by equation (10.6) [12]. 

Although in general the calculation of 8hm for modulation is difficult, a simplistic understanding can be obtained through consideration of the flow pattern above an oscillating infinite plate [13]. The velocity profile u(y,t) parallel to the wall, at a distance y above the wall, is a lagged, damped simple-harmonic motion  

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