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The Poisson-Nernst-Planck (PNP) diffusional model for the immittance or impedance spectroscopy response of an electrolytic cell in a finite-length situation is extended to a general framework. In this new formalism, the bulk behavior of the mobile charges is governed by a fractional diffusion equation in the presence of a reaction term. The solutions have to satisfy a general boundary condition embodying, in a single expression, most of the surface effects commonly encountered in experimental situations. Among these effects, we specifically consider the charge transfer process from an electrolytic cell to the external circuit and the adsorption-desorption phenomenon at the interfaces. The equations are exactly solved in the small AC signal approximation and are used to obtain an exact expression for the electrical impedance as a funcion of the frequency. The predictions of the model are compared to and found to be in good agreement with the experimental data obtained for an electrolytic solution of CdCl2H2O.

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Heavy metals are commonly regarded as environmentally aggressive and hazardous to human health. Among the different metals, lead plays an important economic role due to its large use in the automotive industry, being an essential component of batteries. Different approaches have been reported in the literature aimed at lead removal, and among them a very successful one considers the use of water hyacinths for sorption-based operation. The modeling of the metal sorption kinetics is a fundamental step towards in-depth studies and proper separation equipment design and optimization. Fractional calculus represents a novel approach and a growing research field for process modeling, which is based on the successful use of derivatives of arbitrary order. This paper reports the modeling of the kinetics of lead sorption by water hyacinths (Eichhornia crassipes) using a fractional calculus. A general procedure on error analysis is also employed to prove the actual fractional nature of the proposed model by the use of parametric variance analysis, which was carried out using two different approaches (with the complete Hessian matrix and with a simplified Hessian matrix). The joint parameter confidence regions were generated, allowing to successfully show the fractional nature of the model and the sorption process.

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