Transient Diffusion to Electrodes of Large Size

Under transient conditions the concentration distribution depends not only on the coordinate but also on time. The relevant functions can be found by considering the linear diffusion occurring along the x-axis in a volume element (iU bounded by the two planes S which are a distance dx apart (Fig. 11.1) it is obvious that dV=S dx. The rate of concentration change dcj/dt in this volume is given by the ratio of -S dJj (the 

Solutions for a number of typical cases are reported below. To simplify our task we use the assumption that reactant migration is not observed (a large excess of foreign electrolyte), that the diffusion coefficients Dj do not depend on concentration, and that for the reactant v = 1. (The subscript j is dropped in what follows.) 

At time t = 0 an electric current of constant strength begins to flow in the system. At this time the uniform initial concentration distribution is still not disturbed, and everywhere in the solution, even close to the electrode surface, the concentration is the same as the bulk concentration Cyj. Hence, the first boundary condition (for any value of jc) is given by 

According to Eq. (4.47), the current density is related to the concentration gradient at the surface. Since the current density is constant, the gradient will be also constant and at all times t. 

The solution of differential equation (11.1) with boundary conditions (11.2) and (11.3) is 

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