Model and numerical experiment for calculating the theoretical current-voltage characteristic in electro-membrane systems

Abstract

Abstract This work is devoted to problems of numerical calculation of the theoretical current-voltage characteristics (CVC) and galvanography of electromembrane systems in the potentiometric mode. The purpose of this work is the derivation of the formula for calculating the CVC and galvanography of electromembrane systems in the potentiometric mode, which allows calculating stable relative to random errors and rounding errors in over-limiting current densities. To use the formulas, it is necessary to create a mathematical model for calculating the local current density. In this paper, as this model model is used transport of ions in binary salt in the desalination channel, taking into account electroconvection. The electromembrane systems have been used for water medium preparing in mobile mini systems for generating heat and electrical energy as well as vapour producing. The quality of clean water influences on reliability and life time of these systems, including vapour generator and dam-vapour turbine. The obtained formula in the form of a double integral of the local current density is derived, which allows calculating them steadily with respect to random errors and rounding errors. The formulas allowing considering CVC stably with respect to random errors and rounding errors are obtained, and the physical meaning of these formulas is clarified. The calculation of the theoretical CVC with the use of a mathematical model of ion transfer binary salts given electroconvection and shows that it qualitatively coincides with the experimental current-voltage curves. The quantitative difference can be explained by the fact that the mathematical model does not take into account the reaction of water dissociation / recombination, gravitational convection and other transport mechanisms.