Polarization and interactions of colloidal particles in ac electric fields

Micrometer-sized polystyrene particles form two-dimensional crystals in alternating current (ac) electric fields. The induced dipole-dipole interaction is the dominant force that drives this assembly. We report measurements of forces between colloidal particles in ac electric fields using optical tweezers and find good agreement with the point dipole model. The magnitude of the pair interaction forces depends strongly on the bulk solution conductivity and decreases as the ionic strength increases. The forces also decrease with increasing field frequency. The salt and frequency dependences are consistent with double layer polarization with a characteristic relaxation frequency omega(CD) approximately a(2)/D, where a is the particle radius and D is the ion diffusivity. This enables us to reinterpret the order-disorder transition reported for micrometer-sized polystyrene particles [Lumsdon et al., Langmuir 20, 2108 (2004)], including the dependence on particle size, frequency, and ionic strength. These results provide a rational framework for identifying assembly conditions of colloidal particles in ac fields over a wide range of parameters.     

Accumulation and filtering of nanoparticles in microchannels using electrohydrodynamically induced vortical flows

We present an approach for the accumulation and filtering of nano- and microparticles in microfluidic devices that is based on the generation of electric traveling waves in the radio-frequency range. Upon application of the electric field via a microelectrode array, complex particle trajectories and particle accumulation are observed in well-defined regions in a microchannel. Through the quantitative mapping of the 3-D flow pattern using two-focus fluorescence cross-correlation spectroscopy, two vortices could be identified as one of the sources of the force field that induces the formation of particle clouds. Dielectrophoretic forces that directly act on the particles are the second source of the force field. A thorough 2-D finite element analysis identifies the electric traveling wave mechanism as the cause for the unexpected flow behavior observed. Based on these findings, strategies are discussed, first, for avoiding the vortices to optimize electrohydrodynamic micropumps and, secondly, for utilizing the vortices in the development of microdevices for efficient particle accumulation, separation, and filtering. Such devices may find numerous biomedical applications when highly diluted nano- and microsuspensions have to be processed.     

Electric birefringence of dispersions of platelets

This paper describes the electro-optic response of a suspension of disk-like colloids. We have considered aqueous suspensions of Gibbsite platelets and measured the electrically induced birefringence in the broad frequency range 10(2)-10(8) Hz. When simply dispersed in an electrolyte solution, these particles orient with their major axis parallel to the electric field at all frequencies. The spectral dependence of their Kerr coefficient features three regimes: an electrokinetic α-relaxation within the kHz range, a conductive Maxwell-Wagner-O'Konski (MWO) relaxation having characteristic frequency in the 1-10 MHz range, and a nonzero high frequency asymptote. We quantitatively analyze the MWO spectral component and the high-frequency asymptote on the basis of a model developed for oblate particles. This analysis enables us to obtain the relevant particle properties: surface conductivity, zeta potential, and intrinsic Gibbsite birefringence. When the particles are dispersed in a mixture that also contains smaller spherical particles that have a charge of the same sign, their electric birefringence becomes negative at low frequency. This anomalous orientation of the platelets is analogous to that observed in mixtures of prolate and spherical particles, and demonstrates the anomalous birefringence as a universal property of suspensions of nonspherical particles when surrounded by smaller charged particles.     

Movement of colloidal particles in two-dimensional electric fields

We characterize the movement of carbon black particles in inhomogeneous, two-dimensional dc electric fields. Motivated by display applications, the particles are suspended in a nonpolar solvent doped with a charge control agent. The two-dimensional fields are generated between strip electrodes on a glass slide spaced 120 microm apart with field strengths up to 10(4) V/m. Such fields are insufficient to drive either electrohydrodynamic instabilities or natural convection due to ohmic heating, but they move the particles between the electrodes in about 30 s. In the center region between the strip electrodes, the particles move by electrophoresis; that is, the particle velocity is proportional to the electric field. However, when imposing a constant-potential or constant-current boundary condition at the electrodes to derive the electrical field, the electrophoretic mobility calculated from the measured particle velocities is outside the range of mobilities predicted from the theory of O'Brien and White. Near the electrodes the particles either speed up or slow down, depending on the polarity of the electrode, and these changes in velocity cannot be explained simply by electrophoresis in a spatially varying electric field. We suggest that this anomalous motion arises from electrohydrodynamic flows originating from the interaction between the space charge of the polarized layers above the electrodes and the electric field. Approximate calculations indicate such flows could be sufficiently strong to explain the anomalous trajectories near the edges of the electrodes.     

Electro-optic characteristics of aqueous beta-FeOOH particles

This paper presents a detailed analysis of the electro-optic behavior of suspensions of noninteracting monodisperse beta-FeOOH particles. The electro-optic parameters are determined for aqueous suspensions of the oxide particles and the influences of surface charge and Debye layer thickness are verified. Since the conventional method of frequency analysis is inconsistent in the low-frequency range, new electro-optic parameters are introduced to define the frequency variation of the effects. Electric polarizability is determined with precision to a constant, and its relative variations are followed. As reported for other oxides, electric polarizability correlates with charge variations in the diffuse part of the particle surface electric layer, and its relaxation frequency increases with surface charge density, indicating a Maxwell-Wagner type of surface polarization. The alternating component of the responses yields particle relaxation frequency and the phase shift of the responses at this frequency. For all studied samples the phase shift at particle relaxation frequency is 45 degrees. The relative changes in the steady component of the responses in the low-frequency range are followed by field intensity curves at characteristic frequencies of the samples. Electrophoretic rotation is the process consistent with our data for the low-frequency effect. The results show that it is enhanced by the combined actions of low or slowly relaxing polarizability and significant electrophoretic mobility.     

In situ conductance measurements for alignments of silica particles under alternating electric fields

The alignments of silica particles formed in sinusoidal electrical fields of 1 kHz were assessed using an optical microscope with measuring the electric conductance of a silica dispersion between two Pt electrodes in a vitreous silica glass cell. We confirmed that the electric conductance of the silica dispersion between the two electrodes in the cell reflected the surface conductance of the silica particles settling at the bottom of the cell. More interestingly, we observed that the electric conductance of the silica dispersion in the cell increased when pearl chains of the silica particle were formed along the direction of the electric field. However, no clear change in the electric conductance of the dispersion was observed at higher electric field strengths where a transition from pearl chains to zigzag band patterns and circulating movements of the silica particles in the zigzag bands formed.     

Anomalous low-frequency electro-optic behavior of ferric oxide particles in the presence of poly(ethylene oxide)

Electro-optic techniques were used to investigate the influence of poly(ethylene oxide) (PEO) on the surface electric state of positively charged oxide particles. The variations in particle electrophoretic mobility of beta-FeOOH particles in the presence of PEO indicate significant changes in the surface electric state of the particles in the concentration interval of PEO 10(-2)-10(-1) g dm(-3). The electro-optic results for the same conditions were unexpected: no significant difference is observed in the value and the relaxation frequency of particle electric polarizability in the frequency domain of the alpha-relaxation (detected in the kilohertz range); particle rotational relaxation time also remains unchanged; considerable changes are detected only in the relaxation interval of particle rotation (detected in the hertz range). The obtained results reject the possibility of the formation on the particle surface of a thick polymer layer. A thin adsorption layer cannot explain the significant decrease in particle electrophoretic mobility. The variations in electrophoretic mobility are well correlated with the effects in the domain of particle rotation. A possible explanation of the observed effects is proposed, based on our previous investigations of the effects in the low-frequency domain. The presented results demonstrate that the important information on the electrokinetic charge distribution is not found in the domain of the alpha-dispersion, but in the domain of particle rotation.     

Nonlinear electrophoresis of dielectric particles in Newtonian fluids

In classical electrokinetics, the electrophoretic velocity of a dielectric particle is a linear function of the applied electric field. Theoretical studies have predicted the onset of nonlinear electrophoresis at high electric fields because of the nonuniform surface conduction over the curved particle. However, experimental studies have been left behind and are insufficient for a fundamental understanding of the parametric effects on nonlinear electrophoresis. We present in this work a systematic experimental study of the effects of buffer concentration, particle size, and particle zeta potential on the electrophoretic velocity of polystyrene particles in a straight rectangular microchannel for electric fields of up to 3 kV/cm. The measured nonlinear electrophoretic particle velocity is found to exhibit a 2(±0.5)-order dependence on the applied electric field, which appears to be within the theoretically predicted 3- and 3/2-order dependences for low and high electric fields, respectively. Moreover, the obtained nonlinear electrophoretic particle mobility increases with decreasing buffer concentration (for the same particle) and particle size (for particles with similar zeta potentials) or increasing particle zeta potential (for particles with similar sizes). These observations are all consistent with the theoretical predictions for high electric fields.     

Controlled microparticle manipulation employing low frequency alternating electric fields in an array of insulators

Low frequency alternating current insulator-based dielectrophoresis is a novel technique that allows for highly controlled manipulation of particles. By varying the shape of an AC voltage applied across a microchannel containing an array of insulating cylindrical structures it was possible to concentrate and immobilize microparticles in bands; and then, move the bands of particles to a different location. Mathematical modeling was performed to analyze the distribution of the electric field and electric field gradient as function of the shape of the AC applied potential, employing frequencies in the 0.2-1.25 Hz range. Three different signals were tested: sinusoidal, half sinusoidal and sawtooth. Experimental results demonstrated that this novel dielectrophoretic mode allows highly controlled particle manipulation.     

A novel particle separation method based on induced‐charge electro‐osmotic flow and polarizability of dielectric particles

A new microfluidic method of particle separation was proposed and studied theoretically in this paper. This method is based on the induced charge electro‐osmotic flow (ICEOF) and polarizability of dielectric particles. In this method, a pair of metal plates is embedded on the side channel walls to create a region of circulating flows under applied electric field. When a dielectric particle enters this region, the vortices produced by ICEOF around the particle will interact with the circulating flows produced by the metal plates. Such hydrodynamic interaction influences the particle's trajectory, and may result in the particle being trapped in the flow circulating zone or passing through this flow circulating zone. Because the hydrodynamic interaction is sensitive to the applied electric field, and the polarizability and the size of the particles, separation of different particles can be realized by controlling these parameters. Comparing with electrophoresis and dielectrophoresis methods, this strategy presented in this paper is simple and sensitive.     

Dielectrophoretic assembly of metallodielectric Janus particles in AC electric fields

"Janus" particles with two hemispheres of different polarizability or charge demonstrate a multitude of interesting effects in external electric fields. We reported earlier how particles with one metallic hemisphere and one dielectric hemisphere self-propel in low-frequency alternating current (AC) electric fields. Here, we demonstrate the assembly of such Janus particles driven by AC electric fields at frequencies above 10 kHz. We investigated the relation between field-induced dielectrophoretic force, field distribution, and structure of the assemblies. The phase space for electric field intensity and frequency was explored for particle concentrations large enough to form a monolayer on a glass surface between two gold electrodes. A rich variety of metallodielectric particle structures and dynamics were uncovered, which are very different from those obtained from directed assembly of plain dielectric or plain conductive particles under the action of fields of similar frequency and intensity. The metallodielectric particles assemble into new types of chain structures, where the metallized halves of neighboring particles align into lanes along the direction of the electric field, while the dielectric halves face in alternating direction. The staggered chains may assemble in various orientations to form different types of two-dimensional metallodielectric crystals. The experimental results on the formation of staggered chains are interpreted by means of numerical simulations of the electric energy of the system. The assembly of Janus metallodielectric particles may find applications in liquid-borne microcircuits and materials with directional electric and heat transfer.     

Steady electro-optic characteristics of noninteracting colloidal particles

In previous papers on the electro-optic effects of beta-FeOOH particles we proposed a new procedure for analysis of the low frequency behavior of charged particles. The procedure is based on comparison of characteristic field intensity curves on an appropriate scale and helps to test the dependence of the slow effects on particle surface electric polarizability (relaxing in the kilohertz domain). The results stimulated us to test the applicability of the method to other samples and to reconsider the literature data on the electro-optic behavior of charged colloids in the hydrodynamic domain. The aim of the present paper is to demonstrate on a series of samples similar features of the electro-optic responses of charged particles in the relaxation interval of particle rotation. The analysis leads to a new hypothesis for explanation of the complicated low frequency behavior of charged particles. The superposition of two slow effects (linear and quadratic with field intensity), relaxing in the relaxation interval of particle rotation, can explain the complicated frequency curves in this domain. One of the slow effects is observed for all polarizable particles. It is of negative sign and displays the features of an induced dipole effect dependent on the "kilohertz" induced moment. It corresponds to a slow stage of the surface polarization process related to electrokinetic charge. The linear slow effect shows permanent dipole like behavior and appears only at certain ionic content of the medium. It shows no direct dependence on counterion mobility and on the "kilohertz" induced moment and is probably due to surface charge nonuniformity.     

Dynamic electrophoretic mobility of spherical colloidal particles in salt-free concentrated suspensions

In this contribution, the dynamic electrophoretic mobility of spherical colloidal particles in a salt-free concentrated suspension subjected to an oscillating electric field is studied theoretically using a cell model approach. Previous calculations focusing the analysis on cases of very low or very high particle surface charge are analyzed and extended to arbitrary conditions regarding particle surface charge, particle radius, volume fraction, counterion properties, and frequency of the applied electric field (sub-GHz range). Because no limit is imposed on the volume fractions of solids considered, the overlap of double layers of adjacent particles is accounted for. Our results display not only the so-called counterion condensation effect for high particle charge, previously described in the literature, but also its relative influence on the dynamic electrophoretic mobility throughout the whole frequency spectrum. Furthermore, we observe a competition between different relaxation processes related to the complex electric dipole moment induced on the particles by the field, as well as the influence of particle inertia at the high-frequency range. In addition, the influences of volume fraction, particle charge, particle radius, and ionic drag coefficient on the dynamic electrophoretic mobility as a function of frequency are extensively analyzed.     

Control of particle alignment in water by an alternating electric field

We attempted to align a large number of silica particles dispersed in aqueous solution by controlling the alternating electric field between the two electrodes (400 microm apart). Relatively large particles (9.9 microm) were found to align forming strings in the direction parallel to the electric field while relatively small particles (2.0 and 4.9 microm) were observed to align making stripes in the direction perpendicular to the field. The number of stripes formed by particles between the electrodes increased with increasing frequency of the alternating field. This peculiar perpendicular particle alignment appeared when the contribution to particle alignment of electroosmotic flow exceeded that of dielectric polarization and the osmotic flow was found to be stronger around the particles than in the vicinity of the electrode surface.     

Electrodeless direct current dielectrophoresis using reconfigurable field-shaping oil barriers

We demonstrate dielectrophoretic (DEP) potential wells using pairs of insulating oil menisci to shape the DC electric field. These oil menisci are arranged in a configuration similar to the quadrupolar electrodes, typically used in DEP, and are shown to produce similar field gradients. While the one-pair well produces a focusing effect on particles in flow, the two-pair well results in creating spatial traps against crossflows. Uncharged polystyrene particles were used to map the DEP force fields and the experimental observations were compared against the field profiles obtained by numerically solving Maxwell's equations. We demonstrate trapping of a single particle due to negative DEP against a pressure-driven crossflow. This can be easily extended to trap and hold cells and other objects against flow for a longer time. We also show the results of particle trapping experiments performed to observe the effect of adjusting the oil menisci and the gap between two pairs of menisci in a four-menisci configuration on the nature of the DEP well formed at the center. A design parameter, Theta, capturing the dimensions of the DEP energy well, is defined and simulations exploring the effects of different geometric features on Theta are presented.     

Cellular spin resonance inversion by ion-induced dipoles

Cellular spin resonance (CSR ) or electrorotation is the spinning of cells or other particulate matter in rotating electric fields. The spin rate of the (bio)particle varies markedly with the applied frequency and often is seen to have rather sharp maxima as the frequency is varied. In certain frequency ranges, living cells often are observed to undergo a striking inversion of their spin rate and then spin counter-clockwise (CCW ) while the direction of rotation of the applied electric field is clockwise (CW ). The CSR spectra are presumably due to dipolar interactions with the applied field, as are the spectra obtained by straightforward dielectrophoresis (DEP ) techniques. The two spectra, however, differ radically in the low frequency ranges (below about 1 MHz). It is our objective to explain this apparently anomalous behavior. We believe that the anomaly appears primarily because one is comparing rotational with translational force responses. In the DEP techniques, the simpler translational force arising from the comparative polarizability of cell versus medium (water) gives a straightforward measure of the differential polarizability owing to volume and surface effects pro forma. In the CSR techniques the spin rate reflects the torque on the cells and hence emphasizes polarization at the outer periphery of the cells rather than that of the average overall polarizability. The problem is considered in terms of a living or dead cell rotating with an angular velocity Ω in a fluid medium of viscosity η when it is subject to an electric field rotating at angular frequency ω. It is observed in many experiments that Ω ? ω, and also that the sign of Ω for the same cell can change from CW to CCW and back to CW as the applied frequency ω of the CW electric field is increased. Moreover, the sign and magnitude of the CSR spectra differ for living and dead cells. All of these experimental results can be explained quantitatively by using Maxwell's equations and the dielectric properties of a lossy dielectric sphere in an ionically conductive dielectric fluid.     

Observations of the near-wall accumulation of suspended particles due to shear and electroosmotic flow in opposite directions

On the basis of previous studies, the particles in a dilute (volume fractions φ_∞ < 4 × 10^–3) suspension in combined Poiseuille and electroosmotic “counterflow” at flow Reynolds numbers Re ≤ 1 accumulate, then assemble into structures called “bands,” within ∼6 μm of the channel wall. The experimental studies presented here use a small fraction of tracer particles labeled with a different fluorophore from the majority “bulk” particles to visualize the dynamics of individual particles in a φ_∞ = 1.7 × 10^–3 suspension. The results at two different near-wall shear rates and three electric field magnitudes E show that the near-wall particles are concentrated about 150-fold when the bands start to form, and are then concentrated about 200-fold to a maximum near-wall volume fraction of ∼0.34. The growth in the near-wall particles during this accumulation stage appears to be exponential. This near-wall particle accumulation is presumably driven by a wall-normal “lift” force. The observations of how the particles accumulate near the wall are compared with recent analyses that predict that suspended particles subject to shear flow and a dc electric field at small particle Reynolds numbers experience such a lift force. A simple model that assumes that the particles are subject to this lift force and Stokes drag suggests that the force driving particles toward the wall, of O(10^–17 N), is consistent with the time scales for particle accumulation observed in the experiments.     

Near-wall velocities of particles suspended in shear flow and a streamwise electric field

Particles with a diameter of ∼0.5 µm in a dilute (volume fractions φ_∞ < 4 × 10⁻³) suspension assemble into highly elongated structures called “bands” under certain conditions in combined Poiseuille and electroosmotic flows in opposite directions through microchannels at particle-based Reynolds numbers Re_p < < 1. The particles are first concentrated near, then form “bands” within ∼6 µm of, the channel wall. The experiments described here examine the near-wall dynamics of individual “tracer” particles during the initial concentration, or accumulation, of particles, and the steady-state stage when the particles have formed relatively stable bands at different near-wall shear rates and electric field magnitudes. Surprisingly, the near-wall upstream particle velocities are found to be consistently greater in magnitude than the expected values based on the particles being convected by the superposition of both flows and subject to electrophoresis, which is in the same direction as the Poiseuille flow. However, the particle velocities scale linearly with the change in electric field magnitude, suggesting that the particle dynamics are dominated by linear electrokinetic phenomena. If this discrepancy with theory is only due to changes in particle electrophoresis, electrophoresis is significantly reduced to values as small as 20%–50% of the Smoluchowski relation, or well below previous model predictions, even for high particle potentials.     

Dielectrophoretic choking phenomenon in a converging‐diverging microchannel for Janus particles

The dielectrophoretic (DEP) choking phenomenon is revisited for Janus particles that are transported electrokinetically through a microchannel constriction by a direct‐current (DC) electric field. The negative DEP force that would block a particle with a diameter significantly smaller than that of the constriction at its inlet is seen to be relaxed by the rotation of the Janus particle in a direction that minimizes the magnitude of the DEP force. This allows the particle to pass through the constriction completely. An arbitrary Lagrangian‐Eulerian (ALE) numerical method is used to solve the nonlinearly coupled electric field, flow field, and moving particle, and the DEP force is calculated by the Maxwell stress tensor (MST) method. The results show how Janus particles with non‐uniform surface potentials overcome the DEP force and present new conditions for the DEP choking by a parametric study. Particle transportation through microchannel constrictions is ubiquitous, and particle surface properties are more likely to be non‐uniform than not in practical applications. This study provides new insights of importance for non‐uniform particles transported electrokinetically in a microdevice.     

Electro-optic characteristics of optically interacting beta-FeOOH particles

In this article the influence of multiple light scattering on the basic electro-optic parameters of optically dense colloidal particles is analyzed. The model system is an aqueous suspension of monodisperse ellipsoidal beta-FeOOH particles that displays large electric light scattering variations, including sign reversal, at very low particle volume fractions (two orders of magnitude below the critical concentration of particle electric interactions). The scaling method permits the relative variations in particle electric polarizability to be followed and its relaxation frequency to be determined. Particle rotational relaxation frequency and the phase shift of the responses at this frequency are obtained by the alternating component of the effects. Characteristic field intensity curves in the low-frequency range are used to follow the relative changes induced by the slow electrokinetic effect. The experimental results show that, despite the drastic variations in the effects with volume fraction, the basic electro-optic parameters are independent of multiple scattering and can be adequately determined for any particle concentration, excluding a narrow range in the vicinity of the electro-optic sign reversal. The investigation demonstrates that the dependence of the frequency behavior of aqueous beta-FeOOH on particle volume fraction reported in the literature is due not to optical interactions but to variation of particle surface electric state in the process of dilution.