Calculation of Currents of Local Galvanic Cells

Abstract

The current flow for a local electrolytic cell with rectangular anode and cathode is calculated as a function of a polarization parameter, electrolyte thickness and conductivity, anode and cathode size, and zero current potential difference. The total current is obtained from the numerical computation (with error analysis) of a series solution of Laplace's equation assuming a linear polarization relation at the electrode-electrolyte interface. For high values of the polarization parameter and sufficiently thick electrolytes an asymptotic formula obtains for the current approximately proportional to the anodic fraction, as was found by Waber et al. However, in general the cell geometry greatly influences the amount of current flow, especially for anode shapes near to linear rather than near to square. This effect can be greater than an order of magnitude. The calculated results are compared with experimental data obtained by Ogburn and Schlissel and are shown to be in good agreement. Corrosion currents in randomly pitted surfaces may be estimated from the above results.

Engineering Applications of Current and Potential Distributions in Disk Electrode Systems

“…The same is true for the vertical range (see Eq. [41]), in general agreement with the computations of Simmons et al (2) for the effect of electrolyte depth in a related problem.…”

“…The Hankel transform (as used in this paper) of a function V (r), is defined as follows Hv[V(r)] -= gv(p) : r~v(pr)g(r)dr [2] where Jv is the Bessel function of the first kind and of order v, and p is the transformed variable. Mathematical details regarding Hankel transforms may be found elsewhere (13).…”

“…[28] with Eq. [2] and [3], it may be seen that the unknown A (p) may be obtained by application of the Hankel transform inversion formula, giving A(p) = ( JDa ) J,(pa) [29] Combining Eq. [29], [7], and [11], gives the integral representation for the potential field, which, for z ----0, may be solved from the Weber-Schafheitlin integral formulas.…”

“…Advances in the mathematical treatment of current density problems have been made recently through the use of machine computation methods (1,2). Analytic results remain attractive because of their generality, although the mathematical effort for all but the simplest geometries becomes excessive.…”

Mathematical Characterization of Corrosion Currents in Local Electrolytic Cells

“…The mechanism of such corrosion processes, mainly the pitting reaction, has been extensively studied (3)(4)(5). Nevertheless, so far, only two theoretical attempts have been made to characterize quantitatively the corrosion current of local electrolytic cells (6,7).…”