Dielectrophoretic focusing of particles in a microchannel constriction using DC‐biased AC flectric fields

This paper presents a fundamental study of particle electrokinetic focusing in a single microchannel constriction. Through both experiments and simulations, we demonstrate that such dielectrophoresis‐induced particle focusing can be implemented in a much smaller magnitude of DC‐biased AC electric fields (10 kV/m in total) as compared to pure DC electric fields (up to 100 kV/m). This is attributed to the increase in the ratio of cross‐stream particle dielectrophoretic velocity to streamwise electrokinetic velocity as only the DC field component contributes to the latter. The effects of the 1 kHz frequency AC to DC electric field ratio on particle trajectories and velocity variations through the microchannel constriction are also examined, which are found to agree with the simulation results.     

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.     

Optical manipulation of charged microparticles in polar fluids

In this study, we report a systematic study of the response of a charged microparticle confined in an optical trap and driven by electric fields. The particle is embedded in a polar fluid, hence, the role of ions and counterions forming a double layer around the electrodes and the particle surface itself has been taken into account. We analyze two different cases: (i) electrodes energized by a step‐wise voltage (DC mode) and (ii) electrodes driven by a sinusoidal voltage (AC mode). The experimental outcomes are analyzed in terms of a model that combines the electric response of the electrolytic cell and the motion of the trapped particle. In particular, for the DC mode we analyze the transient particle motion and correlate it with the electric current flowing in the cell. For the AC mode, the stochastic and deterministic motion of the trapped particle is analyzed either in the frequency domain (power spectral density, PSD) or in the time domain (autocorrelation function). Moreover, we will show how these different approaches (DC and AC modes) allow us, assuming predictable the applied electric field (here generated by plane parallel electrodes), to provide accurate estimation (3%) of the net charge carried by the microparticle. Vice versa, we also demonstrate how, once predetermined the charge, the trapped particle acts as a sensitive probe to reveal locally electric fields generated by arbitrary electrode geometries (in this work, wire‐tip geometry).     

Effects of thermal modulation on tunneling through a fluctuating barrier in presence of bichromatic electromagnetic field

The effects of thermal modulation on the tunneling dynamics of a particle moving in a bistable potential with a fluctuating barrier in the presence of bichromatic electromagnetic field are examined. This study brings to light various interesting features. While rate constant increases steadily with increasing fluctuation strength, a stochastic resonance‐like behavior is exhibited when tunneling rate is plotted as a function of barrier fluctuation frequency. The tunneling rate constant decreases with the increase in the differences of the strength of the two electric fields; on the other hand, it displays a maxima when plotted as a function of the ratio of the frequencies of the two fields. When the rate constant is plotted as a function of temperature, it increases and eventually settles down to a saturation value. We have also studied the effect of the phase difference between the two electric fields on the tunneling behavior in the presence of thermal modulation. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Size-controlled flow synthesis of gold nanoparticles using a segmented flow microfluidic platform

Segmented flow is often used in the synthesis of nanomaterials to achieve narrow particle size distribution. The narrowness of the distribution is commonly attributed to the reduced dispersion associated with segmented flows. On the basis of the analysis of flow fields and the resulting particle size distribution, we demonstrate that it is the slip velocity between the two fluids and internal mixing in the continuous-phase slugs that govern the nature of the particle size distribution. The reduction in the axial dispersion has less impact on particle growth and hence on the particle size distribution. Synthesis of gold nanoparticles from HAuCl(4) with rapid reduction by NaBH(4) serves as a model system. Rapid reduction yields gold nuclei, which grow by agglomeration, and it is controlled by the interaction of the nuclei with local flow. Thus, the difference in the physical properties of the two phases and the inlet flow rates ultimately control the particle growth. Hence, a careful choice of continuous and dispersed phases is necessary to control the nanoparticle size and size distribution.     

Electrically driven flow near a colloidal particle close to an electrode with a Faradaic current

To elucidate the nature of processes involved in electrically driven particle aggregation in steady fields, flows near a charged spherical colloidal particle next to an electrode were studied. Electrical body forces in diffuse layers near the electrode and the particle surface drive an axisymmetric flow with two components. One is electroosmotic flow (EOF) driven by the action of the applied field on the equilibrium diffuse charge layer near the particle. The other is electrohydrodynamic (EHD) flow arising from the action of the applied field on charge induced in the electrode polarization layer. The EOF component is proportional to the current density and the particle surface (zeta) potential, whereas our scaling analysis shows that the EHD component scales as the product of the current density and applied potential. Under certain conditions, both flows are directed toward the particle, and a superposition of flows from two nearby particles provides a mechanism for aggregation. Analytical calculations of the two flow fields in the limits of infinitesimal double layers and slowly varying current indicate that the EOF and EHD flow are of comparable magnitude near the particle whereas in the far field the EHD flow along the electrode is predominant. Moreover, the dependence of EHD flow on the applied potential provides a possible explanation for the increased variability in aggregation velocities observed at higher field strengths.     

Field-flow fractionation of magnetic particles in a cyclic magnetic field

Although magnetic field-flow fractionation (MgFFF) is emerging as a promising technique for characterizing magnetic particles, it still suffers from limitations such as low separation efficiency due to irreversible adsorption of magnetic particles on separation channel. Here we report a novel approach based on the use of a cyclic magnetic field to overcome the particle entrapment in MgFFF. This cyclic field is generated by rotating a magnet on the top of the spiral separation channel so that magnetic and opposing gravitational forces alternately act on the magnetic particles suspended in the fluid flow. As a result, the particles migrate transversely between the channel walls and their adsorption at internal channel surface is prevented due to short residence time which is controlled by the rotation frequency. With recycling of the catch-release process, the particles follow saw-tooth-like downstream migration trajectories and exit the separation channel at velocities corresponding to their sedimentation coefficients. A retention model has been developed on the basis of the combined effects of magnetic, gravitational fields and hydrodynamic flow on particle migration. Two types of core-shell structured magnetic microspheres with diameters of 6.04- and 9.40-μm were synthesized and used as standard particles to test the proposed retention theory under varying conditions. The retention ratios of these two types of particles were measured as a function of magnet rotation frequency, the gap between the magnet and separation channel, carrier flow rate, and sample loading. The data obtained confirm that optimum separation of magnetic particles with improved separation efficiency can be achieved by tuning rotation frequency, magnetic field gradient, and carrier flow rate. In view of the widespread applications of magnetic microspheres in separation of biological molecules, virus, and cells, this new method might be extended to separate magnetically labeled proteins or organisms for multiplex analyte identification and purification.     

Numerical study of a novel induced-charge electrokinetic micro-mixer

A novel micro-mixer based on the induced-charge electrokinetic motion of an electrically conducting particle is proposed and numerically demonstrated in this paper. For most microfluidic applications, it is desired to mix different streams of solutions rapidly in a continuous flow mode. Therefore, in this work, we consider a mixing chamber containing an electrically conducting particle and the mixing chamber is located in the middle of a microchannel. Vortices are generated around the electrically conducting particle in an aqueous solution due to the interaction of the applied electric field and the induced surface charge on the particle. These vortices will enhance significantly the mixing of different solutions around the particle. The effectiveness of mixing the two streams entering the mixing chamber is numerically studied as functions of the applied electric field. Excellent mixing can be achieved in this system under two perpendicularly applied electric fields. The proposed micro-mixer is simple and easy to be fabricated for lab-on-a-chip applications.     

Automated and temperature-controlled micro-PIV measurements enabling long-term-stable microchannel acoustophoresis characterization

We present a platform for micro particle image velocimetry (μPIV), capable of carrying out full-channel, temperature-controlled, long-term-stable, and automated μPIV-measurement of microchannel acoustophoresis with uncertainties below 5% and a spatial resolution in the order of 20 μm. A method to determine optimal μPIV-settings for obtaining high-quality results of the spatially inhomogeneous acoustophoretic velocity fields of large dynamical range is presented. In particular we study the dependence of the results on the μPIV interrogation window size and the number of repeated experiments. The μPIV-method was further verified by comparing it with our previously published particle tracking method. Using the μPIV platform we present a series of high-resolution measurements of the acoustophoretic velocity field as a function of the driving frequency, the driving voltage, and the resonator temperature. Finally, we establish a direct and consistent connection between the obtained acoustophoretic velocity fields, and continuous flow mode acoustophoresis, commonly used in applications.     

kT-scale colloidal interactions in high frequency inhomogeneous AC electric fields. I. Single particles

We report nonintrusive optical microscopy measurements of single micrometer-sized silica and polystyrene colloids in inhomogeneous AC electric fields as a function of field amplitude and frequency. By using a Boltzmann inversion of the time-averaged sampling of single particles within inhomogeneous electric fields, we sensitively measure induced dipole-field interactions on the kT energy scale and fN force scale. Measurements are reported for frequencies when the particle polarizability is greater and less than the medium, as well as the crossover between these conditions when dipole-field interactions vanish. For all cases, the measured interactions are well-described by theoretical potentials by fitting a nondimensional induced dipole-field magnitude. While silica dipole-field magnitudes are well-described by existing electrokinetic models, the polystyrene results suggest an anomalously high surface conductance. Sensitive measurements of dipole-field interactions in this work provide a basis to understand dipole-dipole interactions in particle ensembles in the same measurement geometry in part II.     

Two-particle dynamics on an electrode in ac electric fields

The relative motion between pairs of negatively charged latex particles 9.7 microm in diameter and deposited on an electrode was measured by optical microscopy and image analysis. At an rms field of approximately 30 V cm(-1), the two particles moved toward each other at frequencies below 500 Hz, but they separated at 1000 Hz. In the cases of aggregation, there are several interesting characteristics. First, when the center-to-center separation of a pair was initially 6 particle radii or more apart, a transient 'incubation' period of tens of seconds was observed before the particles began to move toward each other. Second, the two particles never came into contact, rather at long times the pair maintained a stationary gap between them equal to approximately one-half the particle radius. This stationary gap between particles was also observed for the aggregation of clusters of three or more particles. Finally, the rate of approach for a pair of particles decreased as the frequency increased. Larger fields are required to move particles together in ac compared to dc fields; at 30 Hz the ac field must be 130 times greater than the dc field to achieve the same rate of approach. Taking advantage of the qualitative and quantitative differences of the cooperative motion of particles in dc vs. ac fields, one should be able to re-position particles by alternating between these two modes. We demonstrated that the same pair of particles can be brought together at low frequency (100 or 200 Hz) and then separated at high frequency (1000 Hz).     

kT-scale colloidal interactions in high-frequency inhomogeneous AC electric fields. II. Concentrated ensembles

We report nonintrusive optical microscopy measurements of ensembles of polystyrene colloids in inhomogeneous AC electric fields as a function of field frequency and particle size. By using an inverse Monte Carlo (MC) simulation analysis of time-averaged particle microstructures, we sensitively measure induced dipole-dipole interactions on the kT energy scale. Measurements are reported for frequencies when the particle polarizability is greater and less than the medium, as well as the crossover between these conditions when dipole-dipole interactions vanish. By using measured single dipole-field interactions and associated parameters from Part I as input in the inverse analysis, the dipole-dipole interactions in this work are accurately modeled with no adjustable parameters for conditions away from the crossover frequency (i.e., |f(CM)| > 0). As dipolar interactions vanish at the crossover, a single frequency-dependent parameter is introduced to account for microstructures that appear to result from weak AC electro-osmotic flow induced interactions. By connecting quantitative measures of equilibrium microstructures and kT-scale dipole-field and dipole-dipole interactions, our findings provide a basis to understand colloidal assembly in inhomogeneous AC electric fields.     

AC electrohydrodynamic propulsion and rotation of active particles of engineered shape and asymmetry

This review presents the recent progress in the development of active particles driven by alternating-current (AC) electrokinetic effects. These particles propel by asymmetrically dissipating the external energy provided by the fields. An AC field can trigger several electrohydrodynamic mechanisms depending on the field frequency and amplitude, which can also control particle–particle interactions and collective behavior. Recently there has been a strong focus on powering and controlling the motion of self-propelling particles with engineered shape, size, and composition. We introduce a tiered classification of AC field-driven active particles and discuss the fundamental electrohydrodynamic effects acting in individual and multi-particle systems. Finally, we address the limitations and challenges in the current state of AC-field driven engineered particles.     

Dielectric response of a concentrated colloidal suspension in a salt-free medium

In this paper the complex dielectric constant of a concentrated colloidal suspension in a salt-free medium is theoretically evaluated using a cell model approximation. To our knowledge this is the first cell model in the literature addressing the dielectric response of a salt-free concentrated suspension. For this reason, we extensively study the influence of all the parameters relevant for such a dielectric response: the particle surface charge, radius, and volume fraction, the counterion properties, and the frequency of the applied electric field (subgigahertz range). Our results display the so-called counterion condensation effect for high particle charge, previously described in the literature for the electrophoretic mobility, and also the relaxation processes occurring in a wide frequency range and their consequences on the complex electric dipole moment induced on the particles by the oscillating electric field. As we already pointed out in a recent paper regarding the dynamic electrophoretic mobility of a colloidal particle in a salt-free concentrated suspension, the competition between these relaxation processes is decisive for the dielectric response throughout the frequency range of interest. Finally, we examine the dielectric response of highly charged particles in more depth, because some singular electrokinetic behaviors of salt-free suspensions have been reported for such cases that have not been predicted for salt-containing suspensions.     

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.     

Theory for hierarchical assembly with dielectrophoresis and the role of particle anisotropy

Nonuniform electric fields cause polarizable particles to move through an effect known as dielectrophoresis (DEP). Additionally, the particles themselves create nonuniform fields due to their induced dipoles. When the nonuniform field of one particle causes another to move, it represents a path to hierarchical assembly termed mutual DEP (mDEP). Anisotropic particles potentially provide further opportunities for assembly through intense and intricate local field profiles. Here, we construct a theoretical framework for describing anisotropic particles as templates for assembly through mDEP by considering the motion of small nanoparticles near larger anisotropic nanoparticles. Using finite element analysis, we study eight particle shapes and compute their field enhancement and polarizability in an orientation-specific manner. Strikingly, we find a more than tenfold enhancement in the field near certain particle shapes, potentially promoting mDEP. To more directly relate the field intensity to the anticipated assembly outcome, we compute the volume experiencing each field enhancement versus particle shape and orientation. Finally, we provide a framework for predicting how mixtures of two distinct particle species will begin to assemble in a manner that allows for the identification of conditions that kinetically bias assembly toward specific hierarchical outcomes.     

Calculation of the electric polarizability of a charged spherical dielectric particle by the theory of colloidal electrokinetics

Dielectrophoresis (DEP) is increasingly being explored as a means to manipulate or separate colloidal particles. The direction and strength of the DEP force depend strongly on the induced dipole strength, K, of a polarized particle, and predictions of DEP forces require carefully computed values for K. In this paper, we present the calculation of the dipole strength using the full electrokinetic theory of Mangelsdorf and White for both static and oscillating electric fields. The effects of particle zeta potential, radius, Debye length and electrolyte composition on the magnitude and sign of Re(K) are discussed. The full theory model is compared with the extended Maxwell-Wagner (EMW) model and the results show that the EMW model can fail to predict the full Re(K) variation with frequency, even predicting Re(K) with the incorrect sign depending on system parameters. A program for the dipole strength calculation shown in this paper is available from the authors.     

Polarization behavior of polystyrene particles under direct current and low‐frequency (<1 kHz) electric fields in dielectrophoretic systems

The relative polarization behavior of micron and submicron polystyrene particles was investigated under direct current and very low frequency (<1 kHz) alternating current electric fields. Relative polarization of particles with respect to the suspending medium is expressed in terms of the Clausius–Mossotti factor, a parameter of crucial importance in dielectrophoretic‐based operations. Particle relative polarization was studied by employing insulator‐based dielectrophoretic (iDEP) devices. The effects of particle size, medium conductivity, and frequency (10–1000 Hz) of the applied electric potential on particle response were assessed through experiments and mathematical modeling with COMSOL Multiphysics^®. Particles of different sizes (100–1000 nm diameters) were introduced into iDEP devices fabricated from polydimethylsiloxane (PDMS) and their dielectrophoretic responses under direct and alternating current electric fields were recorded and analyzed in the form of images and videos. The results illustrated that particle polarizability and dielectrophoretic response depend greatly on particle size and the frequency of the electric field. Small particles tend to exhibit positive DEP at higher frequencies (200–1000 Hz), while large particles exhibit negative DEP at lower frequencies (20–200 Hz). These differences in relative polarization can be used for the design of iDEP‐based separations and analysis of particle mixtures.     

Effect of direct current dielectrophoresis on the trajectory of a non-conducting colloidal sphere in a bent pore

Dielectrophoresis has shown a wide range of applications in microfluidic devices. Force approximations utilizing the point-dipole method in dielectrophoresis have provided convenient predictions for particle motion by neglecting interactions between the particle and its surrounding electric and flow fields. The validity of this approach, however, is unclear when the particle size is comparable to the characteristic length of the channel and when the particle is in close proximity to the channel wall. To address this issue, we apply an accurate numerical approach based on the boundary-element method (BEM) to solve the coupled electric field, flow, and particle motion. This method can handle much closer particle-wall distances than the other numerical approaches such as the finite-element method. Using the BEM and integrating the Maxwell stress tensor, we simulate an electrokinetic, spherical particle moving within a bent cylindrical pore to investigate how the dielectrophoretic force affects the particle's trajectory. In the simulation, both the particle and the channel wall are non-conducting, and the electric double layers adjacent to the solid surfaces are assumed to be thin with respect to the particle radius and particle-wall gap. The results show that as the particle comes close to the wall, its finite size has an increasingly important effect on its own transient motion and the point-dipole approximation may lead to significant error.     

Enhanced pearl-chain formation by electrokinetic interaction with the bottom surface of vessel

Counterions in an electric double layer (EDL) around a colloidal particle accumulate on one side of the EDL and are deficient on the other side under an electric field, resulting in an imbalance of ionic concentration in the EDL, that is to say, the ionic polarization of EDL. It is well known that the ionic polarization of EDL induces electric dipole moments whereby the alignments of colloidal particles (e.g., pearl chains) are formed under alternating electric fields. In this study, we focus on the effect of the frequency of applied electric fields (100 Hz-1 kHz) on the alignment of silica particles settling at the bottom of a silica glass vessel. In digital imaging analyses for pearl chains of silica particles, it is confirmed that surface distances between two neighboring particles decrease but the number of particles in a pearl chain increases as the frequency of the applied electric field is lowered from 1 kHz to 100 Hz. More interestingly, electrical conductance measurements suggest that the induced ionic polarization of EDL around silica particles at the bottom of the silica vessel is enhanced as the frequency is lowered from 1 kHz to 100 Hz, whereas the ionic polarization around isolated silica particles in uniform dispersions is alleviated by the relaxation of ionic concentration in the EDL as a result of the diffusion of counterions. This curious phenomenon can be explained by considering that the ionic polarization of EDL of silica particles at the bottom of a vessel is affected by the electro-osmosis of the silica surface at the bottom of the vessel.