Session A11: Electrokinetic Flows: Concentration Polarization and Instability

From electroconvective vortices to current hot spots on ion selective membranes subject to concentration polarization

Electroconvective instabilities near ion-selective surfaces have been shown to greatly enhance ion transport and play a significant role in a wide range of applications in electrochemistry. When the driving voltage exceeds a threshold, electroconvection becomes chaotic and leads to intermittent spikes of current density on the ion-selective surface. We present an investigation of this phenomenon by considering a canonical setting consisting of a symmetric binary electrolyte next to a flat, ion-selective membrane subject to an external driving voltage. By tracking individual rolls of vortices, we reveal the common mechanism under which the three-way coupled fluid dynamics, ion transport, and electrostatic effects lead to advective displacement of ion concentration field, sustained vortices and vortex migration, and current hot spots on the membrane.   

The Equivalent Electrokinetic Circuit Model of Ion Concentration Polarization Layer: Electrical Double Layer, Extended Space Charge and Electro-convection

The first direct chronopotentiometric measurement was provided to distinguish the potential difference through the extended space charge (ESC) layer which is formed with the electrical double layer (EDL) near a perm-selective membrane. From this experimental result, the linear relationship was obtained between the resistance of ESC and the applied current density. Furthermore, we observed the step-wise distributions of relaxation time at the limiting current regime, confirming the existence of ESC capacitance other than EDL’s. In addition, we proposed the equivalent electrokinetic circuit model inside ion concentration polarization (ICP) layer under rigorous consideration of EDL, ESC and electro-convection (EC). In order to elucidate the voltage configuration in chronopotentiometric measurement, the EC component was considered as the “dependent voltage source” which is serially connected to the ESC layer. This model successfully described the charging behavior of the ESC layer with or without EC, where both cases determined each relaxation time, respectively. Finally, we quantitatively verified their values utilizing the Poisson-Nernst-Planck equations. Therefore, this unified circuit model would provide a key insight of ICP system and potential energy-efficient applications.   

Micro/nanofluidic Diode using Asymmetric Ion Concentration Polarization Layer

Recent developments of ion concentration polarization (ICP) theory would suggest that an over-limiting conductance (OLC) of the device is subject to the morphology of ICP layer and a micro-structure is able to alter the morphology. In this study, we demonstrated an ion rectification resulted only from asymmetric microscale structures, while conventional nanofluidic diode applications have usually employed a nanoscale asymmetry which requires sophisticate and expensive fabrication processes. We designed two dead-end microchannels incorporated with the nanoporous membrane. The difference in width of the microchannels was designed to yield asymmetry to the device. Cyclic voltammetry measurement was conducted to investigate the OLC behaviors on both forward and reverse bias. The diodic characteristics on I-V responses were observed at various ratio of the different microchannel width. In addition, we experimentally verified the logarithmical linearity between the ratios and the rectification ratios of OLC. This quantitative analysis would guide the further application utilizing microscale asymmetric diode device that now can be realized with minimum fabrication endeavors.   

Spontaneous water filtration of bio-inspired membrane

Water is one of the most important elements for plants, because it is essential for various metabolic activities. Thus, water management systems of vascular plants, such as water collection and water filtration have been optimized through a long history. In this view point, bio-inspired technologies can be developed by mimicking the nature's strategies for the survival of the fittest. However, most of the underlying biophysical features of the optimized water management systems remain unsolved In this study, the biophysical characteristics of water filtration phenomena in the roots of mangrove are experimentally investigated. To understand water-filtration features of the mangrove, the morphological structures of its roots are analyzed. The electrokinetic properties of the root surface are also examined. Based on the quantitatively analyzed information, filtration of sodium ions in the roots are visualized. Motivated by this mechanism, spontaneous desalination mechanism in the root of mangrove is proposed by combining the electrokinetics and hydrodynamic transportation of ions. This study would be helpful for understanding the water-filtration mechanism of the roots of mangrove and developing a new bio-inspired desalination technology.   

Hydrodynamic Model of Desalination by ``Overlimiting'' Electrodialysis with Electroconvective Vortices

In 1968, Sonin and Probstein developed a hydrodynamic theory of desalination by electrodialysis (Desalination, 5, 293-329, 1968). Under a laminar flow between ion exchange membranes, linear ion concentration gradients are developed near the membranes by ion concentration polarization (ICP) in Ohmic-limiting current regimes. This linear ICP determines the relations between current, voltage, and desalting performance. Here, we revisit the hydrodynamic model with nonlinear ICP phenomenon at overlimiting currents. In this regime, electroconvective vortices on the membrane induce flat and extremely low concentration zones. Based on the previous prediction of the vortex height under shear flow (Kwak et al., PRL, 110, 114501, 2013), we verify that the height directly represents the amount of the removed salt because there is almost no ion in the vortices. Next, from the mass continuity of ions, the amount of the removed salts is equal to the ion flux through the membrane (i.e. current); as a result, we can develop the relations between current, voltage, and salt removal. Lastly, from these relations, power consumption and desalination cost can be calculated to find the optimal operating condition of overlimiting electrodialysis.   

Controlling turbulent drag across electrolytes using electric fields

Controlling friction is a crucial problem in engineering science. Using direct numerical simulation, we investigate the phenomenology of turbulent Couette flows in electrolytes sheared by charged surfaces. We show how the presence of large shear rates affects the structure, dynamics and stress generation in the electrical double layer. The constant injection of energy from the sheared boundaries drives the double layer far from thermodynamic equilibrium, thus placing conventional statistical physical intuitions on a more tenuous footing. Critically, we uncover regimes where friction associated with turbulent dissipation could be controlled by applying an electric field. The implications of our results on chaotic electrokinetic flows and the non-equilibrium electrical double layer in other electrokinetic settings will also be discussed.   

Electrokinetic Fingering In Hele-Shaw Cells

Large scale flow problems in porous media, such as those encountered in underground oil reservoirs, are typically described by the Darcy’s law. However, it is well known that many underground rock formations contain surface groups and minerals that dissociate in the presence of water. Convection of these charges by the pressure driven flow can then set up streaming current and streaming potential that affects the flow. Furthermore, electric fields that are often used to enhance oil recovery, e.g. by reducing the oil's viscosity through electro-thermal heating, drive electro-osmotic flows that could set up very large pressure in small pores. The full description of fluid flow thus requires a solution to the fully coupled electrokinetic problem. In their seminal work, Saffman and Taylor showed that the moving interface between two immiscible fluids in a porous medium becomes unstable if pushed by the low-viscosity fluid. Here we report on the role of electrokinetic phenomena on stability of these viscous fronts in Hele-Shaw cells by using analytic as well as numerical approaches. Interestingly, we find that the instability could be suppressed if the right physical conditions are met or otherwise enhanced, leading to greater mixing of two fluids.   

Energy harvesting through charged nanochannels using external flows of different salt concentrations

Renewable electricity may be generated by mixing of two solutions of different salt concentrations through charged nanochannels or pores, by leveraging ion-selective effect of the nano-confinements. We numerically investigate such a continuous power generation system using reverse electrodialysis (RED) with external flows. In the simulation model, two reservoirs are connected using a nanochannel of constant surface charge density. Solutions of high and low concentrations flow through the two reservoirs at a constant velocity. We examine the effects of (salt) concentration gradients and nanochannel dimensions on the power generation. Moreover, the effect of external flow velocity on the process is analyzed. Our results show that the maximum surface charge density, open circuit voltage, channel resistance, and energy conversion efficiency of the process are significantly affected by the difference of the high and low concentrations and the nanochannel dimension ratio.   

Coherent structures of electrokinetic instability in microflows

Electrokinetic instabilities occur in fluid flow where gradients in electrical properties of fluids, such as conductivity and permittivity, lead to a destabilizing body force. We present an experimental investigation of electrokinetic instability (EKI) in a microchannel flow with orthogonal conductivity gradient and electric field, using time-resolved visualization of a passive fluorescent scalar. This particular EKI has applications in rapid mixing at low Reynolds number in microchannels. Previous studies have shown that such EKI can be characterized by the electric Rayleigh number ($Ra_e$) which is the ratio of diffusive and electroviscous time scales. However, these studies were limited to temporal power spectra and time-delay phase maps of fluorescence data at a single spatial location. In the current work, we use dynamic mode decomposition (DMD) of time-resolved snapshots of EKI to investigate the spatio-temporal coherent structures of EKI for a wide range of $Ra_e$. Our analysis yields spatial variation of modes in EKI along with their corresponding temporal frequencies. We show that EK instability with orthogonal conductivity-gradient and electric field can be characterized by transverse and longitudinal coherent structures which depend strongly on $Ra_e$.