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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.

Electronic displays are nearly ubiquitous in modern society. With the drive to lower power consumption, reflective displays based on reversible electrophoretic deposition of nanoparticles have emerged as a candidate next generation display technology. Understanding the origins of color in these displays is challenging because the color is determined by the transient arrangement of particles in the electric field. In this article, a new technique, based on small angle x-ray scattering, is developed to simultaneously interrogate nanoparticle arrangement and measure color while the display is in operation. Furthermore, a particle-based numerical model of electrophoretic deposition is demonstrated to quantitatively predict transient interparticle distances during operation.

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.

Aqueous droplets acquire charge when they contact electrodes in high voltage electric fields, but the exact mechanism of charge transfer is not understood. Recent work by Elton et al. revealed that electrodes are physically pitted during charge transfer with aqueous droplets. The pits are believed to result when a dielectric breakdown arc occurs as a droplet approaches the electrode and the associated high current density transiently locally melts the electrode, leaving distinct crater-like deformations on the electrode surface. Here we show that the droplet conductivity strongly modulates the pitting morphology but has little effect on the amount of charge transferred. Electron and atomic force microscopy shows that deionized water droplets yield no observable deformations, but as the salt concentration in the droplet increases above 10–3 M, the deformations become increasingly large. The observed intensity of the flash of light released during the dielectric breakdown arc also increases with droplet con...

Extant theories for induced-charge electrokinetics (ICEK) sometimes fail to predict even the correct direction of flow. By combining the recently discovered phenomenon of asymmetric rectified electric fields with a generalized form of ICEK, this long-standing dilemma is explained.

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.

Micron-scale particles suspended in various aqueous electrolytes have been widely observed to aggregate near electrodes in response to oscillatory electric fields, a phenomenon believed to result from electrically induced flows around the particles. Previous work has focused on elucidating the effects of the applied field strength, frequency, and electrolyte type on the aggregation rate of particles, with less attention paid to the ionic strength. Here we demonstrate that an applied field causes micron-scale particles in aqueous NaCl to rapidly aggregate over a wide range of ionic strengths, but with significant differences in aggregation morphology. Optical microscopy observations reveal that at higher ionic strengths (∼1 mM) particles arrange as hexagonally closed-packed (HCP) crystals, but at lower ionic strengths (∼0.05 mM) the particles arrange in randomly closed-packed (RCP) structures. We interpret this behavior in terms of two complementary effects: an increased particle diffusivity at lower ionic strengths due to increased particle height over the electrode and the existence of a deep secondary minimum in the particle pair interaction potential at higher ionic strength that traps particles in close proximity to one another. The results suggest that electrically induced crystallization will readily occur only over a narrow range of ionic strengths.

Aqueous droplets acquire charge when they contact electrodes in high-voltage electric fields. Although many researchers have investigated droplet charging under various conditions, the droplet charges are typically reported simply in terms of a mean and standard deviation. Here, we show that droplets often acquire significantly less charge for a single contact compared to the previous and subsequent contacts. These "low-charge events," which are not observed with charging of metal balls, yield up to a 60% decrease in charge acquired by the droplet and occur regardless of the applied field strength, droplet conductivity, or droplet volume. In all cases examined here, the occurrence of low-charge events to good approximation follows a negative binomial distribution (i.e., a Pascal distribution) with a mean probability of 13%. We further demonstrate that approximately 16% of charging events are characterized by "irregular" Taylor cone dynamics, suggesting that instabilities in the electrically driven deformation of the approaching liquid interface may be responsible for the low-charge events. The results indicate that workers using systems involving droplet charging should take into account the high likelihood of droplets randomly acquiring less charge than expected.

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.

Micrometer-scale particles suspended in NaCl solutions aggregate laterally near the electrode upon application of a low-frequency (∼100 Hz) field, but the same particles suspended in NaOH solutions are instead observed to separate laterally. The underlying mechanism for the electrolyte dependence remains obscure. Recent work by Woehl et al. (PRX, 2015) revealed that, contrary to previous reports, particles suspended in NaOH solutions indeed aggregate under some conditions while simultaneously exhibiting a distinct bifurcation in average height above the electrode. Here we elaborate on this observation by demonstrating the existence of a critical frequency (∼25 Hz) below which particles in NaOH aggregate laterally and above which they separate. The results indicate that the current demarcation of electrolytes as either aggregating or separating is misleading and that the key role of the electrolyte instead is to set the magnitude of a critical frequency at which particles transition between the two behaviors.

The electric charge acquired by aqueous droplets when they contact an electrode is a crucial parameter in experimental and industrial applications where electric fields are used to manipulate droplet motion and coalescence. For unclear reasons, many investigators have found that aqueous droplets acquire significantly more positive than negative charge. Extant techniques for determining the droplet charge typically rely on a hydrodynamic force balance that depends on accurate characterization of the drag forces acting on the droplet. Here we present an alternative methodology for measuring the droplet charge via direct measurement of the electric current. As the droplet approaches the electrode the current is observed to gradually increase, followed by a large pulse when the droplet makes apparent contact. We interpret the transient current signals as the superposition of the natural response of an RLC circuit and an induced current described by the Shockley-Ramo theory. Nonlinear regression of the observed current to the theoretical model allows for the droplet charge to be extracted, independent of any assumptions about the force balance on the droplet. We demonstrate that regression of the current signal yields charge values that are on average within 4% of charges measured via a force balance. We use the chronocoulometric methodology to investigate how the charge varies with the applied potential, and we demonstrate that deionized water droplets contacting planar electrodes acquire on average 69% more positive charge than negative charge.

Colloidal particles adjacent to electrodes have been observed to exhibit drastically different aggregation behavior depending on the identity of the suspending electrolyte. For example, particles suspended in potassium chloride aggregate laterally near the electrode upon application of a low-frequency (∼100 Hz) oscillatory electric field, but the same particles suspended in potassium hydroxide are instead observed to separate. Previous work has interpreted the particle aggregation or separation in terms of various types of electrically induced fluid flow around the particle, but the details remain poorly understood. Here we present experimental evidence that the aggregation rate is highly correlated to both the particle zeta potential and the electric field amplitude, both of which depend on the electrolyte type. Measurement of the aggregation rate in 26 unique electrolyte-particle combinations demonstrates that the aggregation rate decreases with increasing zeta potential magnitude (i.e., particles with a large zeta potential tended to separate regardless of sign). Likewise, direct measurements of the oscillatory electric field in different electrolytes revealed that the aggregation rate was negatively correlated with solution conductivity and thus positively correlated with the field strength. We tested the experimentally measured aggregation rates against a previously developed point dipole model and found that the model fails to capture the observed electrolyte dependence. The results point to the need for more detailed modeling to capture the effect of electrolyte on the zeta potential and solution conductivity to predict fluid flow around colloids near electrodes.

We report that metallic electrodes are physically pitted during charge transfer events with water droplets or other conductive objects moving in strong electric fields (>1 kV/cm). Post situ microscopic inspection of the electrode shows that an individual charge transfer event yields a crater approximately 1-3 μm wide, often with features similar to a splash corona. We interpret the crater formation in terms of localized melting of the electrode via resistive heating concurrent with dielectric breakdown through the surrounding insulating fluid. A scaling analysis indicates that the crater diameter scales as the inverse cube root of the melting point temperature T_{m} of the metal, in accord with measurements on several metals (660 °C≤T_{m}≤3414 °C). The process of crater formation provides a possible explanation for the longstanding difficulty in quantitatively corroborating Maxwell's prediction for the amount of charge acquired by spheres contacting a planar electrode.

Pulsed electric fields (PEF) nonthermally induce cell membrane permeabilization and thereby improve dehydration and extraction efficiencies in food plant materials. Effects of electrical field strength and number of pulses on plant tissue integrity have been studied extensively. Two previous studies on the effect of pulse frequency, however, did not provide a clear view: one study suggested no effect of frequency, while the other found a greater impact on tissue integrity at lower frequency. This study establishes the effect of pulse frequency on integrity of onion tissues. Changes in electrical characteristics, ion leakage, texture parameters, and percent weight loss were quantified for a wide range of pulse frequencies under conditions of fixed field strength and pulse number. Optical microscopy and viable-cell staining provided direct visualization of effects on individual cells. The key finding is that lower frequencies (f1 Hz) cause more damage to tissue integrity than higher frequencies (f = 1 to 5000 Hz). Intriguingly, the optical microscopy observations demonstrate that the speed of intracellular convective motion (that is, cytoplasmic streaming) following PEF application is strongly correlated with PEF frequency. We provide the first in situ visualization of the intracellular consequence of PEF at different frequencies in a plant tissue. We hypothesize that cytoplasmic streaming plays a significant role in moving conductive ionic species from permeabilized cells to the intercellular space between plant cells, making subsequent pulses more efficacious at sufficiently low frequencies. The results suggest that decreasing the pulse frequency in PEF may minimize the number of pulses needed to achieve a desired amount of permeabilization, thus lowering the total energy consumption. Practical Application: PEF cause pores to be formed in plant cell membranes, thereby improve moisture removal and potential extraction of desirable components. This study used in situ microscopic evaluation of onion cells, as they were pulsed with electric fields at different frequencies, to determine whether frequency was an important parameter. We illustrate that membranes were more effectively broken at lower frequencies as compared to higher frequencies. Application of this information will allow for improved design of PEF systems for more energy efficient dehydration or extraction of plant tissues.

Oppositely charged drops have long been assumed to experience an attractive force that favors their coalescence. In this fluid dynamics video we demonstrate the existence of a critical field strength above which oppositely charged drops do not coalesce. We observe that appropriately positioned and oppositely charged drops migrate towards one another in an applied electric field; but whereas the drops coalesce as expected at low field strengths, they are repelled from one another after contact at higher field strengths. Qualitatively, the drops appear to `bounce' off one another. We directly image the transient formation of a meniscus bridge between the bouncing drops., Gallery of fluid motion entry for 2009 APS DFD meeting

Electrohydrodynamic (EHD) flow around a charged spherical colloid near an electrode was studied theoretically and experimentally to understand the nature of long-range particle–particle attraction near electrodes. Numerical computations for finite double-layer thicknesses confirmed the validity of an asymptotic methodology for thin layers. Then the electric potential around the particle was computed analytically in the limit of zero Péclet number and thin double layers for oscillatory electric fields at frequencies where Faradaic reactions are negligible. Streamfunctions for the steady component of the EHD flow were determined with an electro-osmotic slip boundary condition on the electrode surface. Accordingly, it was established how the axisymmetric flow along the electrode is related to the dipole coefficient of the colloidal particle. Under certain conditions, the flow is directed toward the particle and decays as r−4, in accord with observations of long-range particle aggregation. To test the theory, particle-tracking experiments were performed with fluorescent 300 nm particles around 50μm particles over a wide range of electric field strengths and frequencies. Treating the particle surface conductivity as a fitting parameter yields velocities in excellent agreement with the theoretical predictions. The observed frequency dependence, however, differs from the model predictions, suggesting that the effect of convection on the charge distribution is not negligible as assumed in the zero Péclet number limit.

Application of an oscillatory electric field is known to alter the separation distance between micron-scale colloidal particles and an adjacent electrode. This behavior is believed to be partially due to a lift force caused by electrohydrodynamic flow generated around each particle, with previous work focused on identifying a single steady-state “height” of the individual particles over the electrode. Here, we report the existence of a pronounced bifurcation in the particle height in response to low-frequency electric fields. Optical and confocal microscopy observations reveal that application of a ∼100 Hz field induces some of the particles to rapidly move several particle diameters up from the electrode, while the others move closer to the electrode. Statistics compiled from repeated trials demonstrate that the likelihood for a particle to move up follows a binomial distribution, indicating that the height bifurcation is random and does not result from membership in some distinct subpopulation of particles. The fraction of particles that move up increases with increased applied potential and decreased frequency, in a fashion qualitatively consistent with an energy landscape predicated on competition between electrohydrodynamic flow, colloidal interactions, and gravitational forces. Taken together, the results provide evidence for the existence of a deep tertiary minimum in the effective electrode-particle interaction potential at a surprisingly large distance from the electrode.

We report the existence of a critical ionic conductivity below which oppositely charged drops only partially coalesce. The extent of coalescence between dissimilarly sized water drops in oil can be tuned from complete coalescence at low electric field strengths to complete noncoalescence at high field strengths, thus providing external control over the daughter droplet size. Strikingly, the size and charge of the daughter droplet are both independent of the ionic conductivity. We present evidence suggesting the charge transfer is instead strongly influenced by convection associated with the capillary-driven penetration of a vortex into the larger drop, and we demonstrate that the size of the daughter droplet is consistent with a scaling model based on a balance between capillary-driven inertia and electrostatic repulsion.

Pulsed electric fields (PEF) are known to be effective at permeabilizing plant tissues. Prior research has demonstrated that lower pulse frequencies induce higher rates of permeabilization, but the underlying reason for this response is unclear. Intriguingly, recent microscopic observations with onion tissues have also revealed a correlation between PEF frequency and the subsequent speed of intracellular convective motion, i.e., cytoplasmic streaming. In this paper, we investigate the effect of cytoplasmic streaming on the efficacy of plant tissue permeabilization via PEF. Onion tissue samples were treated with Cytochalasin B, a known inhibitor of cytoplasmic streaming, and changes in cellular integrity and viability were measured over a wide range of frequencies and field strengths. We find that at low frequencies (f \ 1 Hz), the absence of cytoplasmic streaming results in a 19% decrease in the conductivity disintegration index compared with control samples. Qualitatively, similar results were observed using a microscopic cell viability assay. The results suggest that at low frequencies convection plays a statistically significant role in distributing more conductive fluid throughout the tissue, making subsequent pulses more efficacious. The key practical implication is that PEF pretreatment at low frequency can increase the rate of tissue permeabilization in dehydration or extraction processes, and that the treatment will be most effective when cytoplasmic streaming is most active, i.e., with freshly prepared plant tissues. V C 2012

The impact of pulsed electric fields (PEF) on cellular integrity and texture of Ranchero and Sabroso onions (Allium cepa L.) was investigated. Electrical properties, ion leakage rate, texture, and amount of enzymatically formed pyruvate were measured before and after PEF treatment for a range of applied field strengths and number of pulses. Critical electric field strengths or thresholds (E(c)) necessary to initiate membrane rupture were different because dissimilar properties were measured. Measurement of electrical characteristics was the most sensitive method and was used to detect the early stage of plasma membrane breakdown, while pyruvate formation by the enzyme alliinase was used to identify tonoplast membrane breakdown. Our results for 100-μs pulses indicate that breakdown of the plasma membrane occurs above E(c)= 67 V/cm for 10 pulses, but breakdown of the tonoplast membrane is above either E(c)= 200 V/cm for 10 pulses or 133 V/cm for 100 pulses. This disparity in field strength suggests there may be 2 critical electrical field strengths: a lower field strength for plasma membrane breakdown and a higher field strength for tonoplast membrane breakdown. Both critical electric field strengths depended on the number of pulses applied. Application of a single pulse at an electric field up to 333 V/cm had no observable effect on any measured properties, while significant differences were observed for n≥10. The minimum electric field strength required to cause a measurable property change decreased with the number of pulses. The results also suggest that PEF treatment may be more efficient if a higher electric field strength is applied for a fewer pulses.

We investigate a new type of behavior whereby small vesicles orbiting around a larger vesicle in a toroidal electrohydrodynamic flow undergo dynamic angular segregation. Application of a low frequency (approximately 50 Hz) electric field induces aggregation of adjacent unilamellar vesicles near the electrode, in a manner similar to that observed with rigid colloidal particles. For polydisperse vesicle suspensions, however, small vesicles (10 microm) are often observed to "orbit" around larger vesicles (20 microm) in a toroidal electrohydrodynamic flow field. While orbiting, the smaller vesicles gradually segregate into well-defined angular cross sections. Viewed from above, the vesicles appear to form dynamic "bands" at prescribed angles, separated by regions devoid of vesicles. We interpret the angular segregation in terms of induced dipolar interactions, and we propose a model based on point dipoles rotating in a cellular flow field. We demonstrate that the model yields a surprisingly diverse range of vesicle trajectories, including many that are qualitatively consistent with the experimental observations.

Electric fields generate transverse flows near electrodes that sweep colloidal particles into densely packed assemblies. We interpret this behavior in terms of electrohydrodynamic motion stemming from distortions of the field by the particles that alter the body force distribution in the electrode charge polarization layer. A scaling analysis shows how the action of the applied electric field generates fluid motion that carries particles toward one another. The resulting fluid velocity is proportional to the square of the applied field and decreases inversely with frequency. Experimental measurements of the particle aggregation rate accord with the electrohydrodynamic theory over a wide range of voltages and frequencies.

Droplets are frequently observed to move as if they were solid rather than liquid, i.e., with no slip at the liquid-liquid interface. This behavior is usually explained in terms of the so-called “stagnant cap” model, in which surfactants accumulate at the trailing edge of the droplet, immobilizing the surface and increasing the observed drag coefficient. Here, we show that the drag coefficient for charged droplets is temporarily reduced by reversing the direction of an electric driving force. Using high speed video, we simultaneously track the velocity and relative interfacial velocity of individual aqueous droplets moving electrophoretically through oil. The observed velocity behavior is highly sensitive to the concentration of surfactant. For sufficiently low or sufficiently high concentration, upon reversal of the electric field the droplet rapidly accelerates in the opposite direction but then decelerates, concurrent with a transient rearrangement of tracer particles on the droplet surface. In contras...

International audience; We demonstrate an electrohydrodynamic ͑EHD technique for separating giant unilamellar vesicles by size in polydisperse suspensions. An oscillatory electric field ͑ϳ30 Hz generates EHD flow around each vesicle close to an electrode. Nearby vesicles are entrained in the flow and the vesicles move toward one another. Upon aggregation, smaller vesicles are pulled underneath the larger vesicles, which ultimately lifts them off of the electrode. A brief spike in the electric field then serves to irreversibly adhere the bottom layer of smaller vesicles to the electrode, and the large vesicles are subsequently removed by flow. We demonstrate that a single application of this technique can remove more than 90% of the smallest vesicles (diameter < 20 µm) from a suspension of electroformed giant lipid vesicles.