Current-induced membrane discharge

Efficient Anion-Exchange Membranes with Anti-Scaling Properties Obtained by Surface Modification of Commercial Membranes Using a Polyquaternium-22

Anion-exchange membranes modified with a polyquaternium-22 (PQ-22) polymer were studied for their use in electrodialysis. The use of PQ-22 for modification makes it possible to "replace" weakly basic amino groups on the membrane surface with quaternary amino groups. It was found that the content of quaternary amino groups in PQ-22 is higher than the content of carboxyl groups, which is the reason for the effectiveness of this polymer even when modifying Ralex AHM-PES membranes that initially contain only quaternary amino groups. In the case of membranes containing weakly basic amino groups, the PQ-22 polymer modification efficiency is even higher. The surface charge of the modified MA-41P membrane increased, while the limiting current density on the current-voltage curves increased by more than 1.5 times and the plateau length decreased by 2.5 times. These and other characteristics indicate that the rate of water splitting decreased and the electroconvective mixing at the membrane surface intensified, which was confirmed by direct visualization of vortex structures. Increasing the surface charge of the commercial MA-41P anion-exchange membrane, reducing the rate of water splitting, and enhancing electroconvection leads to mitigated scaling on its surface during electrodialysis.

Electrochemical Methods for Water Purification, Ion Separations, and Energy Conversion

Agricultural development, extensive industrialization, and rapid growth of the global population have inadvertently been accompanied by environmental pollution. Water pollution is exacerbated by the decreasing ability of traditional treatment methods to comply with tightening environmental standards. This review provides a comprehensive description of the principles and applications of electrochemical methods for water purification, ion separations, and energy conversion. Electrochemical methods have attractive features such as compact size, chemical selectivity, broad applicability, and reduced generation of secondary waste. Perhaps the greatest advantage of electrochemical methods, however, is that they remove contaminants directly from the water, while other technologies extract the water from the contaminants, which enables efficient removal of trace pollutants. The review begins with an overview of conventional electrochemical methods, which drive chemical or physical transformations via Faradaic reactions at electrodes, and proceeds to a detailed examination of the two primary mechanisms by which contaminants are separated in nondestructive electrochemical processes, namely electrokinetics and electrosorption. In these sections, special attention is given to emerging methods, such as shock electrodialysis and Faradaic electrosorption. Given the importance of generating clean, renewable energy, which may sometimes be combined with water purification, the review also discusses inverse methods of electrochemical energy conversion based on reverse electrosorption, electrowetting, and electrokinetic phenomena. The review concludes with a discussion of technology comparisons, remaining challenges, and potential innovations for the field such as process intensification and technoeconomic optimization.

Interfacial Resistive Switching by Multiphase Polarization in Ion-Intercalation Nanofilms

Nonvolatile resistive-switching (RS) memories promise to revolutionize hardware architectures with in-memory computing. Recently, ion-interclation materials have attracted increasing attention as potential RS materials for their ion-modulated electronic conductivity. In this Letter, we propose RS by multiphase polarization (MP) of ion-intercalated thin films between ion-blocking electrodes, in which interfacial phase separation triggered by an applied voltage switches the electron-transfer resistance. We develop an electrochemical phase-field model for simulations of coupled ion-electron transport and ion-modulated electron-transfer rates and use it to analyze the MP switching current and time, resistance ratio, and current-voltage response. The model is able to reproduce the complex cyclic voltammograms of lithium titanate (LTO) memristors, which cannot be explained by existing models based on bulk dielectric breakdown. The theory predicts the achievable switching speeds for multiphase ion-intercalation materials and could be used to guide the design of high-performance MP-based RS memories.

Portable Seawater Desalination System for Generating Drinkable Water in Remote Locations

A portable seawater desalination system would be highly desirable to solve water challenges in rural areas and disaster situations. While many reverse osmosis-based portable desalination systems are already available commercially, they are not adequate for providing reliable drinking water in remote locations due to the requirement of high-pressure pumping and repeated maintenance. We demonstrate a field-deployable desalination system with multistage electromembrane processes, composed of two-stage ion concentration polarization and one-stage electrodialysis, to convert brackish water and seawater to drinkable water. A data-driven predictive model is used to optimize the multistage configuration, and the model predictions show good agreement with the experimental results. The portable system desalinates brackish water and seawater (2.5-45 g/L) into drinkable water (defined by WHO guideline), with the energy consumptions of 0.4-4 (brackish water) and 15.6-26.6 W h/L (seawater), respectively. In addition, the process can also reduce suspended solids by at least a factor of 10 from the source water, resulting in crystal clear water (<1 NTU) even from the source water with turbidity higher than 30 NTU (i.e., cloudy seawater by the tide). We built a fully integrated prototype (controller, pumps, and battery) packaged into a portable unit (42 × 33.5 × 19 cm³, 9.25 kg, and 0.33 L/h production rate) controlled by a smartphone, tested for battery-powered field operation. The demonstrated portable desalination system is unprecedented in size, efficiency, and operational flexibility. Therefore, it could address unique water challenges in remote, resource-limited regions of the world.

Electroconvective instability near an ion-selective surface: A mesoscopic lattice Boltzmann study

Direct numerical simulations of electroconvection instability near an ion-selective surface are conducted using a mesoscopic lattice Boltzmann method (LBM). An electrohydrodynamic model of ion transport and fluid flow is presented. We numerically solve the Poisson-Nernst-Planck equations for the electric field and the Navier-Stokes equations for the flow field. The results cover Ohmic, limiting, and overlimiting current regimes, and they are in good agreement with the asymptotic analytical solution for the relationship between current and voltage. The influences of different ion transport mechanisms on the voltage-current relationship are discussed. The results reveal that the electroconvection mechanism is as important as other ion transport mechanisms in electrohydrodynamic flow. By comparing the contribution of different regions in the numerical domain, we find that the flow in the extended space charge layer is dominated by electroconvection. We also study the influences of multiple driving parameters, and the electrohydrodynamic coupling constant plays a dominant role in triggering convective instability. The flow pattern and ion concentration distribution are described in detail. Moreover, the route of flow from steady state to periodic oscillation and then to chaos is discussed.

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.

Current efficiency and selectivity reduction caused by co-ion leakage in electromembrane processes

In electromembrane processes such as electrodialysis (ED) and ion concentration polarization (ICP), the diffusion layers on both diluate and concentrate sides influence permselectivity of the ion-exchange membrane and current utilization. The diffusion layer in the diluate stream, due to lower salinity and higher resistivity, has been regarded as the primary source of energy loss. In contrast, very few studies have focused on the diffusion layer in the concentrate stream. In this paper, we evaluate the influence of hydrodynamic convective flow on the development of diffusion layers on both concentrate and diluate sides, specifically in the ICP desalination process. Interestingly, the higher convective flow in the concentrate side was shown to drastically improve the current utilization drop in high operating current, which has been a recurring challenge in electromembrane processes. We attribute this to the prevention of co-ion leakage into the membrane, confirmed by both experimentation and numerical modeling. This new insight has a clear design implication for optimizing electromembrane processes for higher energy efficiency.

Investigation of ion-exchange membranes by means of chronopotentiometry: A comprehensive review on this highly informative and multipurpose technique

Electrodialysis is mostly used for drinking water production but it has gained applicability in different new fields in recent decades. Membrane characteristics and ion transport properties strongly influence the efficiency of electrodialysis and must be evaluated to avoid an intense energy consumption and ensure long membrane times of usage. To this aim, conducting studies on ion transport across membranes is essential. Several dynamic characterization methods can be employed, among which, chronopotentiometry has shown special relevance because it allows a direct access to the contribution of the potential in different states of the membrane/solution system. The present paper provides a critical review on the use of chronopotentiometry to determine the main membrane transport properties and to evaluate mass transfer phenomena. Properties, such as limiting current density, electrical resistances, plateau length, transport number of counter-ions in the membrane, transition times, and apparent fraction of membrane conductive area have been intensively discussed in the literature and are presented in this review. Some of the phenomena evaluated using this technique are concentration polarization, gravitational convection, electroconvection, water dissociation, and fouling/scaling, all of them also shown herein. Mathematical and experimental studies were considered. New trends in chronopotentiometric studies should include ion-exchange membranes that have been recently developed (presenting anti-fouling, anti-microbial, and monovalent-selective properties) and a deeper discussion on the behaviour of complex solutions that have been often treated by electrodialysis, such as municipal wastewaters. New mathematical models, especially 3D ones, are also expected to be developed in the coming years.

Nanopore-Based Power Generation from Salinity Gradient: Why It Is Not Viable

In recent years, the development of nanopore-based membranes has revitalized the prospect of harvesting salinity gradient (blue) energy. In this study, we systematically analyze the energetic performance of nanopore-based power generation (NPG) at various process scales, beginning with a single nanopore, followed by a multipore membrane coupon, and ending with a full-scale system. We confirm the high power densities attainable by a single nanopore and demonstrate that, at the coupon scale and above, concentration polarization severely hinders the power density of NPG, revealing the common, yet significant, error in linearly extrapolating single-pore performance to multipore membranes. Through our consideration of concentration polarization, we also importantly show that the development of materials with exceptional nanopore properties provides limited enhancement of practical process performance. For a full-scale NPG membrane module, we find an inherent tradeoff between power density and thermodynamic energy efficiency, whereby achieving a high power density sacrifices the energy efficiency. Furthermore, we derive a simple expression for the theoretical maximum energy efficiency of NPG, showing it is solely related to the membrane selectivity (i.e., S²/2). Through this relation, it is apparent that the energy efficiency of NPG is limited to only 50% (for a completely selective membrane, i.e., S = 1), reinforcing our optimistic full-scale simulations which result in a (practical) maximum energy efficiency of 42%. Finally, we assess the net extractable energy of a full-scale NPG system which mixes river water and seawater by including the energy losses from pretreatment and pumping, revealing that the NPG process-both in its current state of development and in the case of highly optimistic performance with minimized external energy losses-is not viable for power generation.

Novel ionic separation mechanisms in electrically driven membrane processes

Electromembrane processes including electrodialysis (ED) and related processes are usually limited by diffusion transport of ions from a bulk solution to ion exchange membranes. The diffusion limited current (DLC) occurs when the concentration at membrane surfaces vanishes and approaches zero. Increasing the applied potential difference above this point has no substantial effect on ion transport and causes operational problems such as low current efficiency, high energy consumption, and mineral scaling. However, it is evident from numerous studies that operating at overlimiting current (OLC) is possible and allows one to enhance the mass transfer of an electromembrane process. While OLC is sometimes possible by electrochemical means, such as water splitting or current induced membrane discharge, it has been found that exotic ion transport mechanisms, such as ion concentration polarization in micro/nanofluidic system, deionization shock waves, and ionic bridges, can provide novel electrokinetic means of achieving OLC. In this paper, these novel ionic separation mechanisms and their role in enhanced current transfer are reviewed in the context of emerging electromembrane processes, such as shock ED and electrodeionization (EDI).

Dynamic analysis of the extended space charge layer using chronopotentiometric measurements

In this paper, we experimentally verified the length (LESC) and the concentration (cESC) of the extended space charge (ESC) layer in front of the electrical double layer (EDL) using the chronopotentiometric measurement and the equivalent circuit model analysis. From the experimentation, the coupled-response of the EDL and the ESC layer was discriminated from the contribution of electro-osmotic flow (EOF). In addition, we derived the potential differences across the ESC (VESC) layer using the circuit model of the ICP layer under rigorous consideration of ESC and EDL. As a result, we obtained that VESC was linearly proportional to the square of the applied current (iapplied). Hence, LESC and cESC were quantitatively provided, where LESC is linear to the iapplied and cESC is constant regardless of iapplied. Thus, this experimentation could not only clarify an essential ICP theory but also guide in ESC-based applications.

Water Desalination by Flow-Electrode Capacitive Deionization in Overlimiting Current Regimes

Since flow-electrodes do not have a maximum allowable charge capacity, a high salt removal rate in flow-electrode capacitive deionization (FCDI) can be achieved theoretically by simply increasing the applied voltage. However, present attempts to run FCDI at high voltages are unsatisfactory because of the instability of the module occurring in the overlimiting current regimes. To implement FCDI in the overlimiting current regimes (namely, OLC-FCDI), in this work, we analyzed the voltage-current (V-I) characteristics of several FCDI units. We confirmed that a continuous, rapid, and stable desalination performance of OLC-FCDI can be attained when the employed FCDI unit possesses a linear V-I characteristic (only one ohmic regime), which is distinct from the three V-I regimes in electrodialysis (ohmic, limiting current, and water splitting regimes) and the two in membrane capacitive deionization (ohmic and water splitting regimes). Notably, the linearV-I characteristic of FCDI requires continuous charge percolation near the boundaries of ion-exchange membranes. Effective methods include increasing the carbon content in the flow-electrodes and introducing electrical (carbon cloth) or ionic (ion-exchange resins) conductive intermediates in the solution compartment, which result in corresponding upgraded FCDI units exhibiting extremely high salt removal rates (>100 mg m^-2 s^-1), good cycling stability, and rapid seawater desalination performance under typical OLC-FCDI operation condition (27-40 g L^-1 NaCl, 500 mA). This study can guide future research of FCDI in terms of flow-electrode preparation and device configuration optimization.

Approximate time-dependent current-voltage relations for currents exceeding the diffusion limit

The time-dependent behavior of one-dimensional ion transport into a permselective medium is theoretically modeled in this work for currents exceeding the diffusion limit. Leveraging the findings of Yariv [E. Yariv, Phys. Rev. E 80, 051201 (2009)10.1103/PhysRevE.80.051201], we derive three separate expressions for the potential drop for short, intermediate, and long times. We show that the potential drop correlates to the time evolution of the space-charge layer adjacent to the permselective interface. Our approximate models show remarkable correspondence to numerical simulations.

Design principles of ion selective nanostructured membranes for the extraction of lithium ions

It is predicted that the continuously increasing demand for the energy-critical element of lithium will soon exceed its availability, rendering it a geopolitically significant resource. The present work critically reviews recent reports on Li⁺ selective membranes. Particular emphasis has been placed on the basic principles of the materials' design for the development of membranes with nanochannels and nanopores with Li⁺ selectivity. Fundamental and practical challenges, as well as prospects for the targeted design of Li⁺ ion-selective membranes are also presented, with the goal of inspiring future critical research efforts in this scientifically and strategically important field.

Theory of active chromatin remodeling.. [DOI: 10.1101/687145] [Citation(s) in RCA: 0] [Impact Index Per Article: 0]

Nucleosome positioning controls the accessible regions of chromatin and plays essential roles in DNA-templated processes. ATP driven remodeling enzymes are known to be crucial for its establishment in vivo, but their non-equilibrium nature has hindered the development of a unified theoretical framework for nucleosome positioning. Using a perturbation theory, we show that the effect of these enzymes can be well approximated by effective equilibrium models with rescaled temperatures and interactions. Numerical simulations support the accuracy of the theory in predicting both kinetic and steady-state quantities, including the effective temperature and the radial distribution function, in biologically relevant regimes. The energy landscape view emerging from our study provides an intuitive understanding for the impact of remodeling enzymes in either reinforcing or overwriting intrinsic signals for nucleosome positioning, and may help improve the accuracy of computational models for its prediction in silico.

Nanoelectrokinetic bufferchannel-less radial preconcentrator and online extractor by tunable ion depletion layer

Among various preconcentration strategies using nanofluidic platforms, a nanoscale electrokinetic phenomenon called ion concentration polarization (ICP) has been extensively utilized due to several advantages such as high preconcentration factor and no need of complex buffer exchange process. However, conventional ICP preconcentrator had difficulties in the recovery of preconcentrated sample and complicated buffer channels. To overcome these, bufferchannel-less radial micro/nanofluidic preconcentrator was developed in this work. Radially arranged microchannel can maximize the micro/nano membrane interface so that the samples were preconcentrated from each microchannel. All of preconcentrated plugs moved toward the center pipette tip and can be easily collected by just pulling out the tip installed at the center reservoir. For a simple and cost-effective fabrication, a commercial printer was used to print the nanoporous membrane as "Nafion-junction device." Various analytes such as polystyrene particle, fluorescent dye, and dsDNA were preconcentrated and extracted with the recovery ratio of 85.5%, 79.0%, and 51.3%, respectively. Furthermore, we used a super inkjet printer to print the silver electrode instead of nanoporous membrane to preconcentrate either type of charged analytes as "printed-electrode device." A Faradaic reaction was used as the main mechanism, and we successfully demonstrated the preconcentration of either negatively or positively charged analytes. The presented bufferchannel-less radial preconcentrator would be utilized as a practical and handy platform for analyzing low-abundant molecules.

Modelling of Ion Transport in Electromembrane Systems: Impacts of Membrane Bulk and Surface Heterogeneity

Artificial charged membranes, similar to the biological membranes, are self-assembled nanostructured materials constructed from macromolecules. The mutual interactions of parts of macromolecules leads to phase separation and appearance of microheterogeneities within the membrane bulk. On the other hand, these interactions also cause spontaneous microheterogeneity on the membrane surface, to which macroheterogeneous structures can be added at the stage of membrane fabrication. Membrane bulk and surface heterogeneity affect essentially the properties and membrane performance in the applications in the field of separation (water desalination, salt concentration, food processing and other), energy production (fuel cells, reverse electrodialysis), chlorine-alkaline electrolysis, medicine and other. We review the models describing ion transport in ion-exchange membranes and electromembrane systems with an emphasis on the role of micro- and macroheterogeneities in and on the membranes. Irreversible thermodynamics approach, “solution-diffusion” and “pore-flow” models, the multiphase models built within the effective-medium approach are examined as the tools for describing ion transport in the membranes. 2D and 3D models involving or not convective transport in electrodialysis cells are presented and analysed. Some examples are given when specially designed surface heterogeneity on the membrane surface results in enhancement of ion transport in intensive current electrodialysis.

Half-Cell Ion Concentration Polarization on Nafion-Coated Electrode

On ion-selective membranes, cation/anion-selective transport under electric field initiates ion concentration polarization (ICP); ion concentration increases at one side of the membrane (ion enrichment), whereas it decreases at the other side (ion depletion). This polarization always occurs as the pair of ion enrichment and ion depletion. Departing from such pair generation, we demonstrate that only half of ICP (either ion enrichment or ion depletion) can be solitary on a Nafion-coated electrode. Current-voltage-time responses and conductance measurement capture this half-cell ICP with qualitative in situ pH/ion concentration visualization. In this half-cell, ion depletion hinders an ion flux, whereas ion enrichment facilitates the flux, so a diode-like current rectification is observed even in high-voltage regime (<±200 V) with a rectification factor up to 500. The results in this work give us deeper understanding about ICP on the electrodes and also open the possibility to use half-cell ICP as a high-voltage ionic diode and related sensing/energy applications.

Multiscale Model for Electrokinetic Transport in Networks of Pores, Part I: Model Derivation

We present an efficient and robust numerical model for the simulation of electrokinetic phenomena in porous media and microstructure networks considering a wide range of applications including energy conversion, deionization, and microfluidic-based lab-on-a-chip systems. Coupling between fluid flow and ion transport in these networks is governed by the Poisson-Nernst-Planck-Stokes equations. These equations describe a wide range of phenomena that can interact in a complex fashion when coupled in networks involving multiple pores with variable properties. Capturing these phenomena by direct simulation of the governing equations in multidimensions is prohibitively expensive. We present here a reduced-order model that treats a network of many pores via solutions to 1D equations. Assuming that each pore in the network is long and thin, we derive a 1D model describing the transport in the pore's longitudinal direction. We take into account the cross-sectional nonuniformity of potential and ion concentration fields in the form of area-averaged coefficients in different flux terms representing fluid flow, electric current, and ion fluxes. These coefficients are obtained from the solutions to the Poisson-Boltzmann equation and are tabulated against dimensionless surface charge and dimensionless thickness of the electric double layer (EDL). Although similar models have been attempted in the past, distinct advantages of the present framework include a fully conservative discretization with zero numerical leakage, fully bounded area-averaged coefficients without any singularity in the limit of infinitely thick EDLs, a flux discretization that exactly preserves equilibrium conditions, and extension to a general network of pores with multiple intersections. In part II of this two-article series, we present a numerical implementation of this model and demonstrate its applications in predicting a wide range of electrokinetic phenomena in microstructures.

Analysis of ionic conductance of carbon nanotubes

We use space-charge (SC) theory (also called the capillary pore model) to describe the ionic conductance, G, of charged carbon nanotubes (CNTs). Based on the reversible adsorption of hydroxyl ions to CNT pore walls, we use a Langmuir isotherm for surface ionization and make calculations as a function of pore size, salt concentration c, and pH. Using realistic values for surface site density and pK, SC theory well describes published experimental data on the conductance of CNTs. At extremely low salt concentration, when the electric potential becomes uniform across the pore, and surface ionization is low, we derive the scaling G∝sqrt[c], while for realistic salt concentrations, SC theory does not lead to a simple power law for G

Enhanced Salt Removal by Unipolar Ion Conduction in Ion Concentration Polarization Desalination

Chloride ion, the majority salt in nature, is ∼52% faster than sodium ion (DNa+ = 1.33, DCl- = 2.03[10(-9)m(2)s(-1)]). Yet, current electrochemical desalination technologies (e.g. electrodialysis) rely on bipolar ion conduction, removing one pair of the cation and the anion simultaneously. Here, we demonstrate that novel ion concentration polarization desalination can enhance salt removal under a given current by implementing unipolar ion conduction: conducting only cations (or anions) with the unipolar ion exchange membrane stack. Combining theoretical analysis, experiment, and numerical modeling, we elucidate that this enhanced salt removal can shift current utilization (ratio between desalted ions and ions conducted through electrodes) and corresponding energy efficiency by the factor ∼(D- - D+)/(D- + D+). Specifically for desalting NaCl, this enhancement of unipolar cation conduction saves power consumption by ∼50% in overlimiting regime, compared with conventional electrodialysis. Recognizing and utilizing differences between unipolar and bipolar ion conductions have significant implications not only on electromembrane desalination, but also energy harvesting applications (e.g. reverse electrodialysis).

Resistance identification and rational process design in Capacitive Deionization

Capacitive Deionization (CDI) is an electrochemical method for water desalination employing porous carbon electrodes. To enhance the performance of CDI, identification of electronic and ionic resistances in the CDI cell is important. In this work, we outline a method to identify these resistances. We illustrate our method by calculating the resistances in a CDI cell with membranes (MCDI) and by using this knowledge to improve the cell design. To identify the resistances, we derive a full-scale MCDI model. This model is validated against experimental data and used to calculate the ionic resistances across the MCDI cell. We present a novel way to measure the electronic resistances in a CDI cell, as well as the spacer channel thickness and porosity after assembly of the MCDI cell. We identify that for inflow salt concentrations of 20 mM the resistance is mainly located in the spacer channel and the external electrical circuit, not in the electrodes. Based on these findings, we show that the carbon electrode thickness can be increased without significantly increasing the energy consumption per mol salt removed, which has the advantage that the desalination time can be lengthened significantly.

Dynamics of microvortices induced by ion concentration polarization

We investigate the coupled dynamics of the local hydrodynamics and global electric response of an electrodialysis system, which consists of an electrolyte solution adjacent to a charge selective membrane under electric forcing. Under a dc electric current, counterions transport through the charged membrane while the passage of co-ions is restricted, thereby developing ion concentration polarization (ICP) or gradients. At sufficiently large currents, simultaneous measurements of voltage drop and flow field reveal several distinct dynamic regimes. Initially, the electrodialysis system displays a steady Ohmic voltage difference (ΔV_{ohm}), followed by a constant voltage jump (ΔV_{c}). Immediately after this voltage increase, microvortices set in and grow both in size and speed with time. After this growth, the resultant voltage levels off around a fixed value. The average vortex size and speed stabilize as well, while the individual vortices become unsteady and dynamic. These quantitative results reveal that microvortices set in with an excess voltage drop (above ΔV_{ohm}+ΔV_{c}) and sustain an approximately constant electrical conductivity, destroying the initial ICP with significantly low viscous dissipation.