The 1D Mathematical Model of the Phenomenon of Space-Charge Breakdown of the Electromembrane System in the Galvanodynamic Mode
For the practice of using electromembrane systems, modes of intensive currents are of particular importance, since their use makes it possible to increase the efficiency of the desalting process. Recently, the phenomenon of a space-charge breakdown during desalination in the intensive current mode has been theoretically described. The local minimum and maximum of the space charge regions of the different signs, formed at the surfaces of the cation-exchange and anion-exchange membranes, shift into the depth of the solution, towards each other, and when space charge regions of different signs meet, a space-charge breakdown occurs, that is, a rapid decrease in the magnitude and size of the extended space charge regions. In this article, for the first time, a theoretical analysis of the space-charge breakdown is carried out in the galvanodynamic mode (widely used in the study and operation of membrane systems), when the current density increases with time at a constant rate. Regularities of changes in the expanded space charge regions are established. An equation for the space-charge breakdown time is derived, from which it follows that the square of the breakdown time is directly proportional to the initial concentration of the solution and the channel width, and inversely proportional to the sweep rate of the current density. This equation shows the limitation of the possibility of increasing the mass transfer efficiency in electromembrane systems by reducing the intermembrane distance or increasing the sweep rate of the current density.