The Boundary Layer in a Concentrated, Multicomponent Electrolyte

In this paper, we use the method of matched asymptotic expansions to derive boundary layer equations for a well-stirred, concentrated, multicomponent electrolyte containing a single ion reacting at the electrodes. We have two main objectives. First, we wish to show how the boundary layer approximation, up to now applied mainly to dilute, binary electrolytes or to the case of excess supporting electrolyte, 1 may be systematically generalized. Second, and more important, we show how the generalization leads to equations almost identical with those valid for a dilute, binary electrolyte, for which J. L. Blue 2 has derived an elegant and efficient method of solution. In the general case, the singular perturbation in the boundary layer leads to a set of coupled convective diffusion (CD) equations for the concentrations or, in other words, a vector CD-equation in place of the single, scalar CD-equation for a dilute, binary electrolyte. The vector CD-equation is diagonalized by introducing the eigenvalues and eigenvectors of a reduced diffusivity matrix. The resulting uncoupled, scalar CD-equations can then be solved by Blue's method. The perturbation yields linear CD-equations in the electrolyte, but the strongly nonlinear dependence of the electrode current density on the electrolyte potential and the reactant ion concentration is retained. In fact, the first approximation is simply the so-called "secondary current distribution," the potential satisfying Laplace's equation in 803