Spatial distribution of mechanical forces and ionic flux in electro-kinetic instability near a permselective membrane

Abstract

This paper is devoted to the numerical investigation of electro-kinetic instability in a polarization layer next to a cation-exchange membrane. An analysis of some properties of the electro-kinetic instability is followed by a detailed description of the fluid flow structure and of the spatial distribution of the ionic flux. In this aim, the Stokes-Poisson-Nernst-Planck equation set is solved until the Debye length scale. The results show that the potential threshold of the marginal instability and the current density depend on the logarithm of the concentration at the membrane surface. The size of the stable vortices seems to be an increasing function of the potential drop. The fluid motion is induced by the electric force along the maximum concentration in the extended space charge (ESC) region and by the pressure force in the region around the inner edge of the ESC layer. Two spots of kinetic energy are located in the ESC region and between the vortices. The cationic motion, controlled by the electric field and the convection, presents counter-rotating vortices in the stagnation zone located in the fluid ejection region. The anion transport is also characterized by two independent layers which contain counter-rotating vortices. The first one is in contact with the stationary reservoir. In the second layer against the membrane, the convection, and the electric field control, the transversal motion, the Fickian diffusion, and the convection are dominant in the longitudinal direction. Finally, the longitudinal disequilibrium of potential and pressure along the membrane is analyzed.

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

“…Demekhin et al [28] investigated the hysteresis behavior of ideal smooth ion-exchange membranes and showed the dependence of the hysteresis amplitude on the coupling coefficient between the hydrodynamics and the electrostatics. Hysteretic amplitude calculations observed by Demekhin et al has been confirmed by P. Magnico [32].…”

“…Demekhin et al [15,28,29], S.V. Pham et al [16,30], and K. Druzgalski, E. Karatay et al [18,31], P. Magnico [32,33]. Numerical studies of electroconvection flows generated at an electrically heterogeneous membrane surface were carried out by S. Davidson et al [34], M. Andersen et al [35], V.A.…”

“…The difference in the CVCs of the ion-exchange membrane without a forced flow during the transition between the limiting and overlimiting current regimes at the increasing and decreasing potential drop was theoretically described in [11,16,28,32]. S.V.…”

“…Theoretical studies of transport processes taking into account the formation of the extended SCR and the development of electroconvection in membrane systems were mainly carried out for the PD regime using the equations of Navier-Stokes, Nernst-Planck and Poisson for the electric field potential [14][15][16][17][18][19]28,32,33]. The description of the GD regime caused difficulties associated with the absence of a differential equation for the current density.…”

Dynamic analysis of the extended space charge layer using chronopotentiometric measurements

“…These zones were called the ion depletion zone and the ion enrichment zone, respectively. In order to characterize these zone, numerous theories and experimentations had been conducted such as the possible overlimiting conductance (OLC) mechanisms by instabilities [26][27][28][29][30][31][32], diffusioosmosis [33], electro-osmotic flow (EOF) and surface conduction (SC) [34][35][36][37][38], etc. Most of these studies pointed that all these nonlinear electrokinetic phenomena were stemming from the development of extended space charge (ESC) layer in front of the electrical double layer (EDL) at an overlimiting current regime, predicted by Rubinstein and Zaltzman [39,40].…”