Electro-Kinetic Instability in a Laminar Boundary Layer Next to an Ion Exchange Membrane

Abstract

The electro-kinetic instability in a pressure driven shear flow near an ion exchange membrane is considered. The electrochemical system, through which an electrical potential drop is applied, consists in a polarization layer in contact with the membrane and a bulk. The numerical investigation contained two aspects: analysis of the instability modes and description of the Lagrangian transport of fluid and ions. Regarding the first aspect, the modes were analyzed as a function of the potential drop. The analysis revealed how the spatial distribution of forces controls the dynamics of vortex association and dissociation. In particular, the birth of a counter-clockwise vortex between two clockwise vortices, and the initiation of clusters constituting one or two envelopes wrapping a vortex group, were examined. In regards to the second aspect, the trajectories were computed with the fourth order Runge Kutta scheme for the time integration and with the biquadratric upstream scheme for the spatial and time interpolation of the fluid velocity and the ion flux. The results for the periodic mode showed two kinds of trajectories: the trochoidal motion and the longitudinal one coupled with a periodic transverse motion. For the aperiodic modes, other mechanisms appeared, such as ejection from the mixing layer, trapping by a growing vortex or merging vortices. The analysis of the local velocity field, the vortices’ shape, the spatial distribution of the forces and the ion flux components explained these trajectories.

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

“…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.…”

“…Electroconvection in ED channels with forced fluid flow was investigated by M.Kh. Urtenov et al [19,41] and R. Kwak et al [17,42], R. Abu-Rjal et al [27], P. Magnico [33]. In such channels, the concentration is distributed unevenly along the length of the channel: as the solution moves between the membranes, the electrolyte concentration decreases and the thickness of the diffusion layer increases.…”

“…This movement of the vortices causes current density fluctuations on the CVC [19]. As the potential drop increases, the size of the vortices increases; at a certain potential drop (V cr2 on Figure 3) single vortices transform into large vortex complexes consisting of several vortices rotating in opposite directions [19,33]. As a result, the amplitude of the current density oscillations (or potential drop) increases and oscillations become chaotic [19].…”

“…As a result, the amplitude of the current density oscillations (or potential drop) increases and oscillations become chaotic [19]. P. Magnico investigated the role of electroconvective vortices in the fluid motion using the Lagrangian approach [33]. In this way, trajectories were constructed that reflect the ejection from the mixing layer, trapping by a growing vortex or merging vortices.…”

“…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.…”