Electrokinetic instability near charge-selective hydrophobic surfaces

Influence of Electroconvection on Chronopotentiograms of an Anion-Exchange Membrane in Solutions of Weak Polybasic Acid Salts

Visualization of electroconvective (EC) vortices at the undulated surface of an AMX anion-exchange membrane (Astom, Osaka, Japan) was carried out in parallel with the measurement of chronopotentiograms. Weak polybasic acid salts, including 0.02 M solutions of tartaric (NaHT), phosphoric (NaH₂PO₄), and citric (NaH₂Cit) acids salts, and NaCl were investigated. It was shown that, for a given current density normalized to the theoretical limiting current calculated by the Leveque equation (i/i_lim^theor), EC vortex zone thickness, d_EC, decreases in the order NaCl > NaHT > NaH₂PO₄ > NaH₂Cit. This order is inverse to the increase in the intensity of proton generation in the membrane systems under study. The higher the intensity of proton generation, the lower the electroconvection. This is due to the fact that protons released into the depleted solution reduce the space charge density, which is the driver of EC. In all studied systems, a region in chronopotentiograms between the rapid growth of the potential drop and the attainment of its stationary values corresponds to the appearance of EC vortex clusters. The amplitude of the potential drop oscillations in the chronopotentiograms is proportional to the size of the observed vortex clusters.

Scaling laws of electroconvective flow with finite vortex height near permselective membranes

In a steady state, the linear scaling laws are confirmed between the intensity characteristics of electroconvective (EC) vortex (including the vortex height and electroosmotic slip velocity) and the applied voltage for the nonshear EC flow with finite vortex height near permselective membranes. This finding in the nonshear EC flow is different from the shear EC flow [Kwak et al., Phys. Rev. Lett. 110, 114501 (2013)10.1103/PhysRevLett.110.114501] and indicates that the local concentration gradient has a significant improvement in the analysis of slip velocity. Further, our study reveals that the EC vortex is mainly driven by the second peak effect of the Coulomb thrust in the extended space-charge layer, and the linear scaling law exhibited by the Coulomb thrust is an essential reason for the linear scaling laws of vortex intensity. The scaling laws proposed in this paper are supported by our direct numerical simulation data and previous experimental observations [Rubinstein et al., Phys. Rev. Lett. 101, 236101 (2008)10.1103/PhysRevLett.101.236101].

The Development of Electroconvection at the Surface of a Heterogeneous Cation-Exchange Membrane Modified with Perfluorosulfonic Acid Polymer Film Containing Titanium Oxide

One way to enhance mass transfer and reduce fouling in wastewater electrodialysis is stimulation of electroconvective mixing of the solution adjoining membranes by modifying their surfaces. Several samples were prepared by casting the perfluorosulfonic acid (PFSA) polymer film doped with TiO₂ nanoparticles onto the surface of the heterogeneous cation-exchange membrane MK-40. It is found that changes in surface characteristics conditioned by such modification lead to an increase in the limiting current density due to the stimulation of electroconvection, which develops according to the mechanism of electroosmosis of the first kind. The greatest increase in the current compared to the pristine membrane can be obtained by modification with the film being 20 μm thick and containing 3 wt% of TiO₂. The sample containing 6 wt% of TiO₂ provides higher mass transfer in overlimiting current modes due to the development of nonequilibrium electroconvection. A 1.5-fold increase in the thickness of the modifying film reduces the positive effect of introducing TiO₂ nanoparticles due to (1) partial shielding of the nanoparticles on the surface of the modified membrane; (2) a decrease in the tangential component of the electric force, which affects the development of electroconvection.

Shear electroconvective instability in electrodialysis channel under extreme depletion and its scaling laws

The electroconvective instability (ECI) in an electrodialysis channel under a strong electric field is studied here. The phenomenon of ECI with extreme depletion (ECI-HD) is reported; that is, the overlapping vortices cause the extreme depletion zone to propagate in the horizontal direction. Using scaling theory and direct numerical simulation, we indicate a series of features under the ECI-HD. The decrease in ion transport rate with voltage in ECI-HD is different from the enhancement in the ECI with moderate depletion (ECI-MD), which results in a unique peak in the voltage-current curve. More importantly, we reveal that the ECI is regulated by a scaling factor consisting of the electric field, hydrodynamic coupling coefficient, and Péclet number. For the ECI-HD, the scaling factor has an opposite effect on the vortex size and overlimiting current as that on the ECI-MD. The extreme depletion zone of the ECI-HD also has an uncommon diffusion self-similar dynamics. These unique scaling laws allow one to establish the quantitative bridge between the ion concentration, electric field, and vortex size by the overlimiting current.

How Electrical Heterogeneity Parameters of Ion-Exchange Membrane Surface Affect the Mass Transfer and Water Splitting Rate in Electrodialysis

Electrodialysis (ED) has been demonstrated as an effective membrane method for desalination, concentration, and separation. Electroconvection (EC) is a phenomenon which can essentially increase the mass transfer rate and reduce the undesirable water splitting effect. Efforts by a number of researchers are ongoing to create conditions for developing EC, in particular, through the formation of electrical heterogeneity on the membrane surface. We attempt, for the first time, to optimize the parameters of surface electrical heterogeneity for ion-exchange membranes used in a laboratory ED cell. Thirteen different patterns on the surface of two Neosepta anion-exchange membranes, AMX and AMX-Sb, were tested. Low-conductive fluoropolymer spots were formed on the membrane surface using the electrospinning technique. Spots in the form of squares, rectangles, and circles with different sizes and distances between them were applied. We found that the spots' shape did not have a visible effect. The best effect, i.e., the maximum mass transfer rate and the minimum water splitting rate, was found when the spots' size was close to that of the diffusion layer thickness, δ (about 250 μm in the experimental conditions), and the distance between the spots was slightly larger than δ, such that the fraction of the screened surface was about 20%.

Mathematical Modeling of the Effect of Water Splitting on Ion Transfer in the Depleted Diffusion Layer Near an Ion-Exchange Membrane

Water splitting (WS) and electroconvection (EC) are the main phenomena affecting ion transfer through ion-exchange membranes in intensive current regimes of electrodialysis. While EC enhances ion transport, WS, in most cases, is an undesirable effect reducing current efficiency and causing precipitation of sparingly soluble compounds. A mathematical description of the transfer of salt ions and H⁺ (OH⁻) ions generated in WS is presented. The model is based on the Nernst–Planck and Poisson equations; it takes into account deviation from local electroneutrality in the depleted diffusion boundary layer (DBL). The current transported by water ions is given as a parameter. Numerical and semi-analytical solutions are developed. The analytical solution is found by dividing the depleted DBL into three zones: the electroneutral region, the extended space charge region (SCR), and the quasi-equilibrium zone near the membrane surface. There is an excellent agreement between two solutions when calculating the concentration of all four ions, electric field, and potential drop across the depleted DBL. The treatment of experimental partial current–voltage curves shows that under the same current density, the surface space charge density at the anion-exchange membrane is lower than that at the cation-exchange membrane. This explains the negative effect of WS, which partially suppresses EC and reduces salt ion transfer. The restrictions of the analytical solution, namely, the local chemical equilibrium assumption, are discussed.

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

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.

Competition between diffusion and electroconvection at an ion-selective surface in intensive current regimes

Considering diffusion near a solid surface and simplifying the shape of concentration profile in diffusion-dominated layer allowed Nernst and Brunner to propose their famous equation for calculating the solute diffusion flux. Intensive (overlimiting) currents generate electroconvection (EC), which is a recently discovered interfacial phenomenon produced by the action of an external electric field on the electric space charge formed near an ion-selective interface. EC microscale vortices effectively mix the depleted solution layer that allows the reduction of diffusion transport limitations. Enhancement of ion transport by EC is important in membrane separation, nano-microfluidics, analytical chemistry, electrode kinetics and some other fields. This paper presents a review of the actual understanding of the transport mechanisms in intensive current regimes, where the role of diffusion declines in the profit of EC. We analyse recent publications devoted to explore the properties of different zones of the diffusion layer. Visualization of concentration profile and fluid current lines are considered as well as mathematical modelling of the overlimiting transfer.

Thermoelectroconvection near charge-selective surfaces

A new kind of instability caused by Joule heating near charge-selective surfaces (permselective membranes, electrodes, or systems of micro- and nanochannels) is investigated theoretically using a model based on the Rubinstein-Zaltzman approach. A simple relation is derived for the marginal stability curves: Joule heating can either destabilize or stabilize the steady state, depending on the location of the space charge region relative to the gravity vector. For the destabilizing case, the short-wave Rubinstein-Zaltzman instability is replaced by a long-wave thermal instability. The physical mechanism of the thermal instability is found to be very different from Rayleigh-Bénard convection, and is based on a nonuniform distribution of the electrical conductivity in the electrolyte. The study is complemented by numerical investigations both of linear and nonlinear instabilities near a charge-selective surface. There is a good qualitative agreement with the analytics. A possible explanation of the discrepancy between the experimental data and our previous theoretical voltage-current characteristics is highlighted.

Equilibrium electroconvective instability

Since its prediction 15 years ago, hydrodynamic instability in concentration polarization at a charge-selective interface has been attributed to nonequilibrium electro-osmosis related to the extended space charge which develops at the limiting current. This attribution had a double basis. On the one hand, it has been recognized that neither equilibrium electro-osmosis nor bulk electroconvection can yield instability for a perfectly charge-selective solid. On the other hand, it has been shown that nonequilibrium electro-osmosis can. The first theoretical studies in which electro-osmotic instability was predicted and analyzed employed the assumption of perfect charge selectivity for the sake of simplicity and so did the subsequent studies of various time-dependent and nonlinear features of electro-osmotic instability. In this Letter, we show that relaxing the assumption of perfect charge selectivity (tantamount to fixing the electrochemical potential of counterions in the solid) allows for the equilibrium electroconvective instability. In addition, we suggest a simple experimental test for determining the true, either equilibrium or nonequilibrium, origin of instability in concentration polarization.