The terminal effect associated with resistive electrodes is modeled analytically for Tafel kinetics. The results are presented as a simple expression for the current density variation as a function of the Tafel slope and system parameters. The current density variation is shown to be especially sensitive to the length of the electrode. The general analytical relationship is compared to that for linear kinetics and applied specifically to electrodeposition on thinly coated metallized fibers.Because metals are much more conductive than electrolytes, the ohmic resistance within electrodes is often ignored in electrochemical cell modeling. However, this effect is important in a wide variety of electrochemical systems, including the following: (i) Large, thin gap cells in which the current density within the electrodes is much greater than that in the electrolyte, and the current in the electrode must travel a much greater distance than in the electrolyte. (ii) Cells for fiber, wire, or sheet plating. In these, the electrode, or at least the conductive portion of it, may be very thin, particularly with an initial electroless or vacuum-deposited metallic layer. (iii) Cells with nonmetallic electrodes, such as electrowinning cells with carbon electrodes or batteries with semiconducting compounds.In cases such as these, the ohmic resistance within the electrode may be quite large. This leads to a nonuniform potential distribution within the electrode and thus to a nonuniform current distribution: the current density near the lead or terminal to the electrode, where there is less ohmic resistance, becomes larger than the current density far from the lead. This effect of electrode resistance on current distribution is known as the terminal effect.Tobias and Wijsman (1) examined the terminal effect for linear kinetics and derived an analytical solution for the current distribution. However, many electrochemical processes, such as electroplating, typically occur under Tafel or Butler-Volmer kinetics. Alkire and Varjian (2) numerically determined the current distribution at a resistive electrode under Butler-Volmer kinetics. These authors also incorporated mass transfer limitations in a later work (3). But theirs were numerical results which were published only for application to a specific process (wire plating) and which are not readily accessible for general development or application to other processes. In addition, the dimensionless groups these authors specified were insufficient to define the kinetic parameters they employed; thus it is impossible to reproduce their results or to compare them with other models. Therefore, an analytical solution incorporating nonlinear kinetics would be useful in determining current distributions under a wide range of conditions. Rousar et al. (4) and Scott (5) determined the two-dimensional current distribution in cells with resistive electrodes. Their analyses are limited, however, to specific electrode geometries subject only to linear kinetics. Vaaler (6) used a resistive network gr...

The effects of the detailed structure of porous electrodes on their macroscopic and microscopic current and potential distributions have been quantitatively analyzed. An analytical expression has been derived for the macroscopic pore resistance in terms of a constriction factor which can be related to the pore microstructure and takes the place of an empirical tortuosity. The model has been verified by comparing its predictions to results from numerical computations and experiment. Analysis of the current and concentration distributions within localized micropores indicates that the microporous area is fully accessible to charge and mass transfer. Thus the kinetics of interfacial processes is determined primarily by the micropore structure, while the ohmic and mass transport limitations throughout the volume of the electrode are imposed prineipally by the resistance of the macropores.Electrochemical cells are often restricted in the current density which may be practically applied. Where kinetic limitations may be significant, or where it is desirable to use the full volume of an electrode for electrochemical reactions, porous electrodes with their high surface areas are generally used to allow for the application of higher currents and greater utilization of reactants. Such is the case for many battery electrodes in which fast kinetics and large extents of reaction are required. The efficiency of utilization and associated voltage losses are intimately linked to the current and potential distributions within the porous structure.Most available models only consider the macroscopic structure of the electrode and assume it to be a superposition of homogeneous phases. Euler and Nonnemacher (1) developed a model to determine the current distributions within porous electrodes under linear kinetics. Newman and Tobias (2) extended this model to apply for Tafel kinetics, both with and without mass-transfer limitations. These authors treated the pore structure as a superposition of continuous phases without regard to the structural details within the electrode. This approach has been adapted by many workers in models for specific porous electrodes, such as nickel oxide electrodes (3, 4), gas-fed electrodes (5), and halogen electrodes for zinc-halogen batteries (6-8).White et al. (9) examined an effect of pore size distribution; they related this to gas-contacted area in gas-fed electrodes. These constitute only a few more recent examples; a more extensive review is provided by Newman and Tiedemann (10).Most of the authors cited above followed the precedent of Ref.(1, 2) by assuming that the electrode consists of a superposition of continuous phases. They did not attempt to relate the model parameters, particularly the tortuosity and specific area, to the structural characteristics of the pores. A numerical study based on a random network model by Kramer and Tomkiewicz (11) suggests that such relations can be found, since their results were found to agree qualitatively with those of a single-pore model. The purpose of our...

Fluid flow, mass transfer, and ohmic resistance are analyzed in through‐hole plating of multilayer printed circuit boards. The analysis indicates that in holes with high aspect ratios plated under practical conditions, the ohmic rather than the mass transport resistance imposes the critical limitation on the current density at which through‐holes may be uniformly plated. An ohmically limited current density is quantitatively identified as a function of the hole dimensions, the conductivity, and the deposition kinetics. It is shown that the ohmic limitation is highly sensitive to the hole dimensions, especially its length. The maximum current density which provides deposits of acceptable uniformity can be increased by increasing the electrolyte conductivity, the electrode polarization, or by modifying the hole geometry.

At gas evolving electrodes, the bubble curtain at the electrode surface contributes to the voltaic inefficiencies of the electrolyzer. Consequently, the structure of the bubble curtain and its effect on electrolyte resistivity is of practical importance. In order to predict the resistance of the bubble curtain several models have been suggested in the literature. Threedimensional models provide an adequate prediction of the resistance of dilute bubble curtains with monolayer gas voidages less than 0.55. This paper proposes a two-dimensional constriction model of a dense bubble curtain which is modified to account for a three-dimensional dispersed phase within the monolayer. The resulting mathematical expression behaves properly in the limits of voidage and its prediction agrees well with the limited available data.

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