Decomposition of the two-dimensional Nernst-Planck-Poisson equations for a ternary electrolyte (Q2254127)

The authors consider some Nernst-Planck-Poisson equations for a ternary electrolyte (in dimensionless form) with regard to the concentration and the flux of ions, the velocity of electrolyte solution flow, the diffusion coefficients, the current density, the electric field strength, and Peclet number. The decomposition method is extended to the two-dimensional Nernst-Planck-Poisson equations for ternary electrolytes. To simplify the system of equations, the partial concentrations are replaced by two total concentrations. To obtain an equation for the electric field strength, is introduced the total current density field. Also, the system of equations is simplified by deriving an equation for total current density field, which is a solenoidal field. The decomposition system of equations is useful for contructing simplified models and using numerical and asymptotic solution methods. As in Ohm's Law, the electric field strength is proportional to the current density. In fact, the model of binary electrolyte transport is a nonstationary transport model in the Ohm law approximation for flow membrane systems.