Analytic Mathematical Model for Concentration Profile in a Parallel Plate Electrolyzer with Variable Current Density

Abstract

The parallel plate electrolyzer is of interest in electrochemical applications. However, the modelling of an electrolyzer often involves numerical integration or use of infinite series that is computationally expensive. Using some simplifying assumptions, a novel analytical solution to the governing equation could be obtained using a similarity transformation. To obtain the solution, a mathematical limit evaluation is required rather than a simple substitution, resulting in a novel transcendental function that describes the constants of integration. However, the constants of integration could be excellently approximated by a rational function, with the coefficients obtainable by solving equations for special cases or linear regression. The quadratic and quartic regression were found to give a better fit. It is also demonstrated that the general solution reduces to constant current density and surface concentration under special cases. Using this approach, a simple mathematical model was developed to approximate the solutions that often require cumbersome numerical methods such as the finite element method.