Theoretical Investigation of the Phenomenon of Space Charge Breakdown in Electromembrane Systems

Abstract

At present, it is customary to consider the overlimit operating modes of electromembrane systems to be effective, and electroconvection as the main mechanism of overlimiting transfer. The breakdown of the space charge is a negative, “destructive” phenomenon, since after the breakdown the size and number of electroconvective vortices are significantly reduced, which leads to a decrease in mass transfer. Therefore, electromembrane desalination processes must be carried out before space charge breakdown occurs. Thus, the actual problem arises of determining at which potential jumps a breakdown of the space charge occurs at a given concentration of the solution. Electromembrane systems are used for desalination at electrolyte solution concentrations ranging from 1 to 100 mol/m3. In a theoretical study of increasing the efficiency of the desalination process, mathematical modeling is used in the form of a boundary value problem for the system of Nernst–Planck and Poisson (NPP) equations, which refers to “hard” problems that are difficult to solve numerically. This is caused by the appearance of a small parameter at the derivative in the Poisson equation in a dimensionless form, and, correspondingly, a boundary layer at ion-exchange membranes, where concentrations and other characteristics of the desalination process change exponentially. It is for this reason that the numerical study of the boundary value problem is currently obtained for initial concentrations of the order of 0.01 mol/m3. The paper proposes a new numerical–analytical method for solving boundary value problems for the system of Nernst–Planck and Poisson equations for real initial concentrations, using which the phenomenon of space charge breakdown (SCB) in the cross section of the desalination channel in potentiostatic and potentiodynamic modes is studied. The main regularities of the appearance and interaction of charge waves, up to their destruction (breakdown), are established. A simple formula is proposed for engineering calculations of the potential jump depending on the concentration of the solution, at which the breakdown of the space charge begins.