2D Mathematical Modelling of Overlimiting Transfer Enhanced by Electroconvection in Flow-Through Electrodialysis Membrane Cells in Galvanodynamic Mode

Abstract

Flow-through electrodialysis membrane cells are widely used in water purification and the processing of agricultural products (milk, wine, etc.). In the research and operating practice of such systems, a significant place is occupied by a galvanodynamic (or galvanostatic) mode. 2D mathematical modelling of ion transfer in the galvanodynamic mode requires solving the problem of setting the average current density equal to a certain value, while the current density distribution in the system is uneven. This article develops a 2D mathematical model of the overlimiting transfer enhanced by electroconvection in a flow-through electrodialysis cell in the galvanodynamic mode. The model is based on the system of Navier–Stokes, Nernst–Planck, Poisson equations and equations for the electric current stream function. To set the electric mode we use a boundary condition, relating the electric field strength and current density. This approach allows us to describe the formation of the extended space charge region and development of electroconvection at overlimiting currents. For the first time, chronopotentiograms and current–voltage characteristics of the membrane systems are calculated for the galvanodynamic mode taking into account the forced flow and development of electroconvection. The behaviors of the calculated chronopotentiograms and current–voltage characteristic coincide qualitatively with experimental data. The effects of the electrolyte concentration, forced flow velocity and channel size on the mass transfer at overlimiting currents are estimated.

Potentiodynamic and Galvanodynamic Regimes of Mass Transfer in Flow-Through Electrodialysis Membrane Systems: Numerical Simulation of Electroconvection and Current-Voltage Curve

“…where β > 0 is the sweep speed of the current density, t 2 is the point in time at which the regime of increasing current density is replaced by decreasing. The calculations are based on the 2D mathematical models of the overlimiting transfer enhanced by electroconvection in a flow-through ED cell for the PD [19,47] and GD [46] regimes. To simplify the numerical solution, we consider the processes in half of the ED channel at the surface of the cation-exchange membrane (CEM), Figure 4.…”

“…Thus, the formulation of the model for the PD regime includes the system of Equations (3)-(7) and boundary conditions (8), (10)- (21). The average over the channel length current density is calculated as [46]:…”

“…To describe the GD regime, Equations (3)-(6) and boundary conditions (8), (10)- (20) are used similarly to PD regime, but there are two differences. First, at the boundary x = 1, y ∈ [0, l] (solution/membrane interface), instead of condition (21), normal to the membrane surface component of the electric field strength is specified as function of the electric current density [46]:…”

“…Condition (23) was obtained from Equations (4) and (7) [46,49]. Secondly, an additional equation is introduced to determine the distribution of current density, which is required by the boundary condition (23).…”

“…However, approaches based on the local electroneutrality assumption do not allow taking explicitly into account the effect of the SCR, which is formed at the solution/membrane boundary. Recently, these difficulties have been overcome using an approach involving the solution of the Poisson equation with a boundary condition determining the potential gradient through the current density [45,46].…”