Moderately nonlinear diffuse-charge dynamics under an ac voltage

Impedance-Frequency Response of Closed Electrolytic Cells

The electric AC response of electrolytic cells with DC bias is analyzed solving numerically the Poisson-Nernst-Planck equations and avoiding the commonly used infinite solution approximation. The results show the presence of an additional low-frequency dispersion process associated with the finite spacing of the electrodes. Moreover, we find that the condition of fixed ionic content inside the electrolytic cell has a strong bearing on both the steady-state and the frequency response. For example: the characteristic frequency of the high-frequency dispersion decreases when the DC potential increases and/or the electrode spacing decreases in the closed cell case, while it remains essentially insensitive on these changes for open cells. Finally, approximate analytic expressions for the dependences of the main parameters of both dispersion processes are also presented.

Numerical prediction of transient electrohydrodynamic instabilities under an alternating current electric field and unipolar injection

In this paper, a direct numerical simulation (DNS) of dielectric fluid flow subjected to unipolar injection under an alternating current (AC) electric field is carried out. The effect of frequency f of pulsed direct current (PDC) and AC on the transient evolution of electroconvection and their subcritical bifurcations are investigated in details. Electroconvection under PDC or AC tends to exhibit oscillating flow due to the periodic boundary condition of charge density and potential compared to the direct current (DC) case. The results demonstrate that under the PDC field, the linear criterion T _c decreases with increasing frequency, while the nonlinear stability criterion T _f is hardly affected. Under the AC field, a critical frequency f _c  = 0.0316 is found, which separates electroconvection into two typical flow regimes-periodic flow regime (f < f _c ) and inhibited flow regime (f ≥ f _c )-depending on whether free charges can reach the collector electrode before electric field inversion. AC-electrohydrodynamics (EHD) systems promote various flow patterns with relatively lower voltage regimes than DC-EHD systems. These mechanisms of electroconvection under the PDC/AC field offer unique possibilities for fluid flow control in biological EHD-driven flow and portable EHD applications.

Onset of Nonlinear Electroosmotic Flow under an AC Electric Field

Nonlinearity of electroosmotic flows (EOFs) is ubiquitous and plays a crucial role in ion transport, specimen mixing, electrochemistry reaction, and electric energy storage and utilization. When and how the transition from a linear regime to a nonlinear one occurs is essential for understanding, prohibiting, or utilizing nonlinear EOF. However, due to the lack of reliable experimental instruments with high spatial and temporal resolutions, the investigation of the onset of nonlinear EOF still remains in theory. Herein, we experimentally studied the velocity fluctuations of EOFs driven by an alternating current (AC) electric field via ultrasensitive fluorescent blinking tricks. The linear and nonlinear AC EOFs are successfully identified from both the time trace and energy spectra of velocity fluctuations. The transitional electric field (E_A,C) is determined by both the convection velocity (U) and AC frequency (f_f) as E_A,C ∼ f_f^0.48-0.027U. We hope the current investigation could be essential in the development of both theory and applications of nonlinear EOFs.

Localized X-Ray Photoelectron Impedance Spectroscopy (LoXPIS) for Tapping into Charge-Dynamics of Ionic-Liquid Electrolytes within Energy Storage Devices

Many electrochemical devices are based on the fundamental process of ion migration and accumulation on surfaces. Complex interplay of molecular properties of ions and device dimensions control the entire process...

A perturbation solution to the full Poisson-Nernst-Planck equations yields an asymmetric rectified electric field

We derive a perturbation solution to the one-dimensional Poisson-Nernst-Planck (PNP) equations between parallel electrodes under oscillatory polarization for arbitrary ionic mobilities and valences. Treating the applied potential as the perturbation parameter, we show that the second-order solution yields a nonzero time-average electric field at large distances from the electrodes, corroborating the recent discovery of Asymmetric Rectified Electric Fields (AREFs) via numerical solution to the full nonlinear PNP equations [Hashemi Amrei et al., Phys. Rev. Lett., 2018, 121, 185504]. Importantly, the first-order solution is analytic, while the second-order AREF is semi-analytic and obtained by numerically solving a single linear ordinary differential equation, obviating the need for full numerical solutions to the PNP equations. We demonstrate that at sufficiently high frequencies and electrode spacings the semi-analytical AREF accurately captures both the complicated shape and the magnitude of the AREF, even at large applied potentials.

Ions in an AC Electric Field: Strong Long-Range Repulsion between Oppositely Charged Surfaces

Two oppositely charged surfaces separated by a dielectric medium attract each other. In contrast we observe a strong repulsion between two plates of a capacitor that is filled with an aqueous electrolyte upon application of an alternating potential difference between the plates. This long-range force increases with the ratio of diffusion coefficients of the ions in the medium and reaches a steady state after a few minutes, which is much larger than the millisecond timescale of diffusion across the narrow gap. The repulsive force, an order of magnitude stronger than the electrostatic attraction observed in the same setup in air, results from the increase in osmotic pressure as a consequence of the field-induced excess of cations and anions due to lateral transport from adjacent reservoirs.

Asymmetric rectified electric fields between parallel electrodes: Numerical and scaling analyses

Recent computational and experimental work has established the existence of asymmetric rectified electric fields (AREFs), a type of steady electric field that occurs in liquids in response to an applied oscillatory potential, provided the ions present have different mobilities [Hashemi Amrei et al., Phys. Rev. Lett. 121, 185504 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.185504]. Here we use scaling analyses and numerical calculations to elaborate the nature of one-dimensional AREFs between parallel electrodes. The AREF magnitude is shown to increase quadratically with applied potential at low potentials, increase nonlinearly at intermediate potentials, then increase with a constant rate slower than quadratically at sufficiently high potentials, with no impact at any potential on the spatial structure of the AREF. In contrast, the AREF peak location increases linearly with a frequency-dependent diffusive length scale for all conditions tested, with corresponding decreases in both the magnitude and number of sign changes in the directionality of AREF. Furthermore, both the magnitude and spatial structure of the AREF depend sensitively on the ionic mobilities, valencies, and concentrations, with a potential-dependent peak AREF magnitude occurring at an ionic mobility ratio of D_{-}/D_{+}⪅5. The results are summarized with approximate scaling expressions that will facilitate interpretation of the steady component for oscillatory fields in liquid systems.

Surface forces generated by the action of electric fields across liquid films

We explore the force generation and surface interactions arising when electric fields are applied across fluid films. Using a surface force balance (SFB) we measure directly the force between two electrodes in crossed-cylinder geometry across dielectric and electrolytic fluids. In the case of dielectric films the field between the electrodes exerts a force which can be well explained using classic expressions and with no fitting parameters. However when the electrodes are separated by a film of electrolyte, an alternating electric field induces a force which diverges substantially from the calculated static response of the electrolyte. The magnitude of the force is larger than predicted, and the interaction can switch from attractive to repulsive. Furthermore, the approach to steady state in electrolyte takes place over 102-103 s which is very slow compared to both the charging and viscous timescales of the system. The non-trivial electrolyte response in AC electric fields, measured here directly, is likely to underlie several recent reports of unexpected and bifurcating forces driving colloids in AC fields. Our measurements suggest ways to control colloidal and soft matter using electric fields, as well as providing a direct measure of the length- and time-scales relevant in AC electrochemical and electrokinetic systems.

Extreme Levitation of Colloidal Particles in Response to Oscillatory Electric Fields

Micron-scale colloidal particles suspended in electrolyte solutions have been shown to exhibit a distinct bifurcation in their average height above the electrode in response to oscillatory electric fields. Recent work by Hashemi Amrei et al. ( Phys. Rev. Lett., 2018, 121, 185504) revealed that a steady, long-range asymmetric rectified electric field (AREF) is formed when an oscillatory potential is applied to an electrolyte with unequal ionic mobilities. In this work, we use confocal microscopy to test the hypothesis that a force balance between gravity and an AREF-induced electrophoretic force is responsible for the particle height bifurcation observed in some electrolytes. We demonstrate that at sufficiently low frequencies, particles suspended in electrolytes with large ionic mobility mismatches exhibit extreme levitation away from the electrode surface (up to 50 particle diameters). This levitation height scales approximately as the inverse square root of the frequency for both NaOH and KOH solutions. Moreover, larger particles levitate smaller distances, while the magnitude of the applied field has little effect above a threshold voltage. A force balance between the AREF-induced electrophoresis and gravity reveals saddle node bifurcations in the levitation height with respect to the frequency, voltage, and particle size, yielding stable fixed points above the electrode that accord with the experimental observations. These results point toward a low-energy, non-fouling method for concentrating colloids at specific locations far from the electrodes.

Characterization of Chaotic Electroconvection near Flat Inert Electrodes under Oscillatory Voltages

The onset of electroconvective instability in an aqueous binary electrolyte under external oscillatory electric fields at a single constant frequency is investigated in a 2D parallel flat electrode setup. Direct numerical simulations (DNS) of the Poisson–Nernst–Planck equations coupled with the Navier–Stokes equations at a low Reynolds number are carried out. Previous studies show that direct current (DC) electric field can create electroconvection near ion-selecting membranes in microfluidic devices. In this study, we show that electroconvection can be generated near flat inert electrodes when the applied electric field is oscillatory in time. A range of applied voltage, the oscillation frequency and the ratio of ionic diffusivities is examined to characterize the regime in which electroconvection takes place. Similar to electroconvection under DC voltages, AC electroconvection occurs at sufficiently high applied voltages in units of thermal volts and is characterized by transverse instabilities, physically manifested by an array of counter-rotating vortices near the electrode surfaces. The oscillating external electric field periodically generate and destroy such unsteady vortical structures. As the oscillation frequency is reduced to O(10−1) of the intrinsic resistor–capacitor (RC) frequency of electrolyte, electroconvective instability is considerably amplified. This is accompanied by severe depletion of ionic species outside the thin electric double layer and by vigorous convective transport involving a wide range of scales including those comparable to the distance L between the parallel electrodes. The underlying mechanisms are distinctly nonlinear and multi-dimensional. However, at higher frequencies of order of the RC frequency, the electrolyte response becomes linear, and the present DNS prediction closely resembles those explained by 1D asymptotic studies. Electroconvective instability supports increased electric current across the system. Increasing anion diffusivity results in stronger amplification of electroconvection over all oscillation frequencies examined in this study. Such asymmetry in ionic diffusivity, however, does not yield consistent changes in statistics and energy spectrum at all wall-normal locations and frequencies, implying more complex dynamics and different scaling for electrolytes with unequal diffusivities. Electric current is substantially amplified beyond the ohmic current at high oscillation frequencies. Also, it is found that anion diffusivity higher than cation has stronger impact on smaller-scale motions (≲0.1L).

Role of Stefan-Maxwell fluxes in the dynamics of concentrated electrolytes

This theoretical analysis quantifies the effect of coupled ionic fluxes on the charging dynamics of an electrochemical cell. We consider a model cell consisting of a concentrated, binary electrolyte between parallel, blocking electrodes, under a suddenly applied DC voltage. It is assumed that the magnitude of the applied voltage is small compared to the thermal voltage scale, RT/F, where R is the universal gas constant, T is the temperature and F is the Faraday's constant. We employ the Stefan-Maxwell equations to describe the hydrodynamic coupling of ionic fluxes that arise in concentrated electrolytes. These equations inherently account for asymmetry in the mobilities of the ions in the electrolyte. A modified set of Poisson-Nernst-Planck equations, obtained by incorporating Stefan-Maxwell fluxes into the species balances, are formulated and solved in the limit of weak applied voltages. A long-time asymptotic analysis reveals that the electrolyte dynamics occur on two distinct time scales. The first is a faster "RC" time, τ_RC = κ^-1L/D_E, where κ^-1 is the Debye length, L is the length of the half-cell, and D_E is an effective diffusivity, which characterizes the evolution of charge density at the electrode. The effective diffusivity, D_E, is a function of the ambi-polar diffusivity of the salt, D_a, as well as a cross-diffusivity, D_+-, of the ions. This time scale also dictates the initial exponential decay of current in the external circuit. At times longer than τ_RC, the external current again decays exponentially on a slower, diffusive time scale, τ_D∼L²/D_a, where D_a is the ambi-polar diffusivity of the salt. This diffusive time scale is due to the unequal ion mobilities that result in a non-uniform bulk concentration of the salt during the charging process. Finally, we propose an approach by which our theory may be used to measure the cross-diffusivity in concentrated electrolytes.

Oscillating Electric Fields in Liquids Create a Long-Range Steady Field

We demonstrate that application of an oscillatory electric field to a liquid yields a long-range steady field, provided the ions present have unequal mobilities. The main physics is illustrated by a two-ion harmonic oscillator, yielding an asymmetric rectified field whose time average scales as the square of the applied field strength. Computations of the fully nonlinear electrokinetic model corroborate the two-ion model and further demonstrate that steady fields extend over large distances between two electrodes. Experimental measurements of the levitation height of micron-scale colloids versus applied frequency accord with the numerical predictions. The heretofore unsuspected existence of a long-range steady field helps explain several long-standing questions regarding the behavior of particles and electrically induced fluid flows in response to oscillatory potentials.

A mathematical model for electrical impedance spectroscopy of zwitterionic hydrogels

We report a mathematical model for ion transport and electrical impedance in zwitterionic hydrogels, which possess acidic and basic functional groups that carry a net charge at a pH not equal to the isoelectric point. Such hydrogels can act as an electro-mechanical interface between a relatively hard biosensor and soft tissue in the body. For this application, the electrical impedance of the hydrogel must be characterized to ensure that ion transport to the biosensor is not significantly hindered. The electrical impedance is the ratio of the applied voltage to the measured current. We consider a simple model system, wherein an oscillating voltage is applied across a hydrogel immersed in electrolyte and sandwiched between parallel, blocking electrodes. We employ the Poisson-Nernst-Planck (PNP) equations coupled with acid-base dissociation reactions for the charge on the hydrogel backbone to model the ionic transport across the hydrogel. The electrical impedance is calculated from the numerical solution to the PNP equations and subsequently analyzed via an equivalent circuit model to extract the hydrogel capacitance, resistance, and the capacitance of electrical double layers at the electrode-hydrogel interface. For example, we predict that an increase in pH from the isoelectric point, pH = 6.4 for a model PCBMA hydrogel, to pH = 8 reduces the resistance of the hydrogel by ∼40% and increases the double layer capacitance by ∼250% at an electrolyte concentration of 0.1 mM. The significant impact of charged hydrogel functional groups to the impedance is damped at higher electrolyte concentration.

Ion size effects on the osmotic pressure and electrocapillarity in a nanoslit: Symmetric and asymmetric ion sizes

We analyze the effect of asymmetric finite ion size in nanoconfinement in the view of osmotic pressure and electrocapillarity. When the confinement width becomes comparable with the Debye length, the overlapped electric double layer is significantly deformed by the steric effects. We derive the osmotic pressure from the modified Poisson-Boltzmann equation in a nanoslit to examine the deviation from the ideal osmotic pressure and the repulsive force on the wall considering the asymmetry of ion sizes. Then the electrocapillarity due to the steric effect is investigated under constant potential condition with the flat interface assumption. Later, the deformation by the electrocapillarity is also considered in the first order approximation.