Numerical Determination of Potential Distributions and Current Densities in Multi-Electrode Systems

Abstract

Two numerical solution methods of the Laplacian equations, within boundary conditions set by the geometries and electrode reactions of arbitrary cells, are presented. One method is based on the location of current sources on suitable locations in and around the cell. The strength of these sources is a variable. With the solution of the equations of the potential gradients at the boundaries, the strength of the sources is determined, and herewith potentials and current densities. In the second method, the potential distribution is determined by solution of the equations obtained with a finite element discretisation of the cell. Compatibility with the potential dependant boundary conditions at the electrode surfaces is reached, for both methods, with an iteration procedure. Both methods are used for the solution of a problem for which an analytical solution is available. Some conclusions regarding their applicability are drawn, and an example of the use of this method on the problem of the galvanic corrosion for a ship/propeller/sea water system is given.

Experimental Measurement and Computer Simulation of Galvanic Corrosion of Magnesium Coupled to Steel

“…Most of the previous studies have also reported agreement between modeling predictions and experimental measurements for the galvanic current distribution. [45][46][47][48][49][50][51][52] In contrast, Ault and Meany [53] concluded: a) "the deepest pit was not immediately adjacent to the cathodic metals that most mathematical models predict"; b) "the mathematical model only can provide a order of magnitude estimation of galvanic current flow"; and c) "the mathematical model can neither accurately predict long term current distribution nor the magnitude of pitting corrosion". These conclusions are of particular significance for the present study on the galvanic corrosion of magnesium because localized corrosion is often the form of corrosion of magnesium in practical solutions as typified by 5 % NaCl solution.…”

Iterative algorithms for impressed cathodic protection systems

“…Let n be the Newton-Raphson solution at the nth iteration with 0 60 and * be the exact solution of (5)- (8). If…”

“…Let { n } be the Newton-Raphson iterative sequence and * be the exact solution of (5)- (8). If condition (19) is satisÿed, then the Newton-Raphson iteration converges to the exact solution for arbitrary initial value 0 ¡0 and * ¿ · · · ¿ n ¿ n−1 ¿ · · · ¿ 1 (34)…”

“…ÿ-nite di erence method [3; 7], ÿnite element method [8] and boundary element method [4; 6; 9]. A computer code was developed by Zamani [6] speciÿcally for ship building with a boundary element method.…”

Computational Analysis of Flow Properties That Could Cause Pipeline Failure

“…Several researchers have studied the internal corrosion problems of oil pipelines [1,2]. In recent times, more researchers have studied the more recently discovered causes and prevention of corrosion in pipelines [3,4].The study of corrosion enables the user of materials to optimize the service life of such materials.…”