Formula for calculating the theoretical current-voltage characteristic of the 3D desalination channel EDA

The current-voltage characteristic is one of the most significant characteristics of salt ion transport in membrane systems. To date, there are only experimental studies of current-voltage characteristics that show complex, unsteady, unstable behavior. This is one of the reasons why there are no studies of theoretical current-voltage characteristics, another reason is mathematical and computational difficulties. In this article is derived using the Gauss-Ostrogradskii law and analyzes the formula for calculating the theoretical current-voltage characteristic for a three-dimensional desalination channel of an electrodialysis apparatus in a potentiodynamic mode. It’s shown that this formula is stable with respect to rounding errors in spatial variables, while maintaining the complex non-stationary behavior of the current-voltage characteristic over time. To apply the formulas, it is necessary to calculate the local current density using a mathematical model of the transport of binary salt ions in a three-dimensional desalination channel of an electrodialysis apparatus (EDA), taking into account electroconvection. The main regularities of changes in the current-voltage characteristic are established. It is shown that it qualitatively coincides with the experimental current-voltage characteristic. A small quantitative difference can be explained by the fact that the mathematical model does not take into account the dissociation/recombination reaction of water, gravitational convection and other transport mechanisms and requires separate further studies.

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