Modeling of metal distribution when coating flat metal plates in electroplating baths

Electrolytic metal coating processes are used to protect products from corrosion, decorative surface finish and other purposes. Electroplated coating has an important quantitative characteristic, which is coating thickness. Since the electric field in the electrolyte is not uniform, the coating thickness at different points on the surface of detail is different. An important task here is to apply a more uniform coating. To solve this problem, it is necessary to calculate the distribution of potentials in a galvanic bath from Laplace's equation. The study aims to increase the convergence rate of the numerical procedure in order to solve Laplace's equation with nonlinear boundary conditions by developing a numerical scheme based on Newton's method. Based on a numerical solution of Laplace's equation with nonlinear boundary conditions describing the potential distribution in a galvanic bath, the thickness of the nickel deposition layer on the surface of a flat metal cathode plate was calculated for different sizes of galvanic baths and anode voltages. A feature of the numerical calculation scheme is the use of Newton's method for the approximate solution of the resulting system of nonlinear algebraic equations with a given accuracy. The obtained results show the effectiveness of the applied numerical method: the quadratic convergence rate of Newton's method gives a time gain of 10 times in comparison with one of the best numerical methods for this type of problem.