Dielectrophoresis of nanosized particle

The theory of dielectrophoresis is constructed with allowance for electroosmotic perturbances. Changes in the flow regime of electrolyte in the diffuse part of electrical double layer under the action of quadratic (with respect to external field) electric forces are considered. The expression for low-frequency limit of the dielectrophoretic velocity of a spherical particle, which is valid at the arbitrary thickness of electrical double layer and fairly small value of ζ-potential (< 50 mV), is derived. It is shown that electroosmotic perturbances appeared to be rather significant for nanosized particles and their dielectrophoretic velocity under the effect of electroosmotic perturbances changes by several times.     

On hybrid electroosmotic kinetics for field‐effect‐reconfigurable nanoparticle trapping in a four‐terminal spiral microelectrode array

Induced‐charge electroosmosis (ICEO) has attracted tremendous popularity for driving fluid motion from the microfluidic community since the last decade, while less attention has been paid to ICEO‐based nanoparticle manipulation. We propose herein a unique concept of hybrid electroosmotic kinetics (HEK) in terms of bi‐phase ICEO (BICEO) actuated in a four‐terminal spiral electrode array, for effective electrokinetic enrichment of fluorescent polystyrene nanoparticles on ideally polarizable metal strips. First, by alternating the applied AC voltage waves between consecutive discrete terminals, the flow stagnation lines where the sample nanoparticles aggregate can be switched in time between two different distribution modes. Second, we innovatively introduce the idea of AC field‐effect flow control on BICEO; by altering the combination of gating voltage sequence, not only the number of circulative particle trapping lines is doubled, but the collecting locations can be flexibly reconfigured as well. Third, hydrodynamic streaming of DC‐biased BICEO is tested in our device design, wherein the global linear electroosmosis dominates BICEO contributed from both AC and DC components, resulting in a reduction of particle enrichment area, while with a sharp increase in sample transport speed inside the bulk phase. The flow field associated with HEK is predicted using a linear asymptotic analysis under Debye–Huckel limit, with the simulation results in qualitative agreement with in‐lab observations of nanoparticle trapping by exploiting a series of improved ICEO techniques. This work provides an affordable and field‐deployable platform for real‐time nanoparticle trapping in the context of dilute electrolyte.     

AC electrokinetics of conducting microparticles: A review

This paper reviews both theory and experimental observation of the AC electrokinetic properties of conducting microparticles suspended in an aqueous electrolyte. Applied AC electric fields interact with the induced charge in the electrical double layer at the metal particle–electrolyte interface. In general, particle motion is governed by both the electric field interacting with the induced dipole on the particle and also the induced-charge electro-osmotic (ICEO) flow around the particle. The importance of the RC time for charging the double layer is highlighted. Experimental measurements of the AC electrokinetic behaviour of conducting particles (dielectrophoresis, electro-rotation and electro-orientation) are compared with theory, providing a comprehensive review of the relative importance of particle motion due to forces on the induced dipole compared with motion arising from induced-charge electro-osmotic flow. In addition, the electric-field driven assembly of conducting particles is reviewed in relation to their AC electrokinetic properties and behaviour.     

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.     

Transient phoretic migration of a permselective colloidal particle

We quantify the phoretic migration of a spherical cation-permselective colloidal particle immersed in a binary electrolyte under a time-dependent electric field. We invoke the thin-Debye-layer approximation, where the size of ionic Debye layer enveloping the particle is much smaller than the particle radius. The imposed electric field generates ion concentration gradients, or concentration polarization, in the bulk (electroneutral) electrolyte outside the Debye layer. The bulk ion concentration polarization--and consequently the particle's phoretic velocity--evolves on the time scale for ion diffusion around the particle, which can be on the order of milliseconds for typical colloidal dimensions. Notably, concentration polarization arises here solely due to the permselectivity of the particle; it does not require non-uniform ionic transport in the Debye layer (i.e., surface conduction). Thus, the phoretic transport of a permselective particle is significantly different to that of a inert, dielectric particle, since surface conduction is necessary to achieve bulk concentration polarization in the (more commonly studied) latter case. Calculations are presented for a permselective particle under oscillatory (ac) and suddenly applied electric fields. In the former case, the particle velocity possesses frequency-dependent components in phase and out of phase with the driving field; in the latter case, the particle approaches its terminal velocity with a long-time (algebraic) tail.     

Effect of double-layer polarization on the forces that act on a nanosized cylindrical particle in an ac electrical field

The polarization of, the forces acting on, and the electroosmotic flow field around a cylindrical particle of radius a* and uniform zeta potential zeta* submerged in an electrolyte solution and subjected to alternating electric fields are computed by solving the Poisson-Nernst-Planck (PNP) equations (the standard model). The dipole coefficient and the electrostatic and hydrodynamic forces are calculated as functions of the electric field's frequency, the solute concentration, and the particle's surface charge. The calculations are not restricted to small Debye screening lengths (lambdaD*). At relatively low frequencies, the polarization coefficient is nearly frequency-independent. As the frequency increases above D*/a*(2), where D* is the effective diffusion coefficient, the polarization coefficient initially increases, attains a maximum, and then decreases to an asymptotic value (when the frequency exceeds (1+Du)D*/lambdaD(*2), where Du is the Dukhin number). At low frequencies, when (lambdaD*/a*)(2)e(|zeta*F*/(2R*T*)|) < 1, the PNP calculations are in excellent agreement with the predictions of the Dukhin-Shilov (DS) low-frequency theory. At high frequencies, when lambda D*/a* < 1, the PNP calculations are in excellent agreement with the Maxwell-Wagner-O'Konski (MWO) theory.     

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.     

DC-dielectrophoretic separation of microparticles using an oil droplet obstacle

A new dielectrophoretic particle separation method is demonstrated and examined in the following experimental study. Current electrodeless dielectrophoretic (DEP) separation techniques utilize insulating solid obstacles in a DC or low-frequency AC field, while this novel method employs an oil droplet acting as an insulating hurdle between two electrodes. When particles move in a non-uniform DC field locally formed by the droplet, they are exposed to a negative DEP force linearly dependent on their volume, which allows the particle separation by size. Since the size of the droplet can be dynamically changed, the electric field gradient, and hence DEP force, becomes easily controllable and adjustable to various separation parameters. By adjusting the droplet size, particles of three different diameter sizes, 1 microm, 5.7 microm and 15.7 microm, were successfully separated in a PDMS microfluidic chip, under applied field strength in the range from 80 V cm-1 to 240 V cm-1. A very effective separation was realized at the low field strength, since the electric field gradient was proved to be a more significant parameter for particle discrimination than the applied voltage. By utilizing low strength fields and adaptable field gradient, this method can also be applied to the separation of biological samples that are generally very sensitive to high electric potential.     

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.     

Separation of erythrocytes and latex beads by dielectrophoretic levitation and hyperlayer field-flow fractionation.

A model system consisting of a mixture of latex beads and erythrocytes has been investigated to demonstrate the practical feasibility of particle separation by means of the combined application of negative dielectrophoresis and hyperlayer field-flow fractionation. The dielectrophoretic levitation of latex beads is demonstrated by energizing interdigitated electrodes, of widths and separation ranging from 5 to 40 μm, with AC signals of 0–10 V (rms) in the frequency range 1 kHz–10 MHz. Maximum levitation was attained at 1 MHz, at which frequency levitation is relatively independent of the suspending medium conductivity. Levitation was also independent of particle size, but dependent on particle density and dielectric properties. At 1 MHz the erythrocytes were attracted to the electrodes by positive dielectrophoresis, and so could be separated from the latex beads by fluid flow. The electric field and field gradient above the electrodes were also computer modelled, and this information was used to design the electrode and chamber geometries for optimum DEP-field-flow fractionation.     

Force acting on a dielectric particle in a concentration gradient by ionic concentration polarization under an externally applied DC electric field

There is a concentration-polarization (CP) force acting on a particle submerged in an electrolyte solution with a concentration (conductivity) gradient under an externally applied DC electric field. This force originates from the two mechanisms: (i) gradient of electrohydrodynamic pressure around the particle developed by the Coulombic force acting on induced free charges by the concentration polarization, and (ii) dielectric force due to nonuniform electric field induced by the conductivity gradient. A perturbation analysis is performed for the electric field, the concentration field, and the hydrodynamic field, under the assumptions of creeping flow and small concentration gradient. The leading order component of this force acting on a dielectric spherical particle is obtained by integrating the Maxwell and the hydrodynamic stress tensors. The analytical results are validated by comparing the surface pressure and the skin friction to those of a numerical analysis. The CP force is proportional to square of the applied electric field, effective for electrically neutral particles, and always directs towards the region of higher ionic concentration. The magnitude of the CP force is compared to that of the electrophoretic and the conventional dielectrophoretic forces.     

Combined AC‐electrokinetic effects: Theoretical considerations on a three‐axial ellipsoidal model

AC fields induce charges at the structural interfaces of particles or biological cells. The interaction of these charges with the field generates frequency‐dependent forces that are the basis for AC‐electrokinetic effects such as dielectrophoresis (DEP), electrorotation (ROT), electro‐orientation, and electro‐deformation. The effects can be used for the manipulation or dielectric single‐particle spectroscopy. The observation of a particular effect depends on the spatial and temporal field distributions, as well as on the shape and the dielectric and viscoelastic properties of the object. Because the effects are not mutually independent, combined frequency spectra are obtained, for example, discontinuous DEP and ROT spectra with ranges separated by the reorientation of nonspherical objects in the linearly and circularly polarized DEP and ROT fields, respectively. As an example, the AC electrokinetic behavior of a three‐axial ellipsoidal single‐shell model with the geometry of chicken‐red blood cells is considered. The geometric and electric problems were separated using the influential‐radius approach. The obtained finite‐element model can be electrically interpreted by an RC model leading to an expression for the Clausius–Mossotti factor, which permits the derivation of force, torque, and orientation spectra, as well as of equations for the critical frequencies and force plateaus in DEP and of the characteristic frequencies and peak heights in ROT. Expressions for the orientation in linearly and circularly polarized fields, as well as for the reorientation frequencies were also derived. The considerations suggested that the simultaneous registration of various AC‐electrokinetic spectra is a step towards the dielectric fingerprinting of single objects.     

Manipulation and characterization of red blood cells with alternating current fields in microdevices

The motion of a suspension of erythrocytes (red blood cells, RBCs) in response to a high-frequency alternating current (AC) field in a microfluidic device is examined with parallel and orthogonal electrode configurations to delineate the various fundamental driving forces. Cell repulsion from the platinum electrodes due to electrode polarization interacting with cell membrane polarizations is observed to be the strongest force acting on the particles in the first few seconds of field application. We exploit this strong repulsion to concentrate the bioparticles between the microelectrodes to amplify multiparticle aggregation phenomenon and dielectrophoretic (DEP) manipulation in a small and well-characterized region within the microfluidic device. Secondary motions include RBC pearl chain formation along field lines due to particle polarization followed by classical dielectrophoretic motion of the chains across field lines to regions of weaker field. These are driven by far weaker dipole-dipole and field-dipole interactions than the preliminary electrode repulsions. RBC chain length and total aggregated cells are presented for a variety of AC frequencies and are significantly amplified by the electrode repulsion. Motion of particles away from the polarized electrode is found to be species- and age-sensitive and can stand by itself as a promising identification and separation mechanism. In a 0.1 S/m isotonic phosphate buffer saline medium, we observe the largest cell mobilities at an optimal frequency of approximately 1 MHz, corresponding to the inverse diffusion time across the double layer of the cell and across the electrode's polarized layer. This suggests that the dielectric responses of both particles and electrodes in the low MHz frequency range are mostly determined by normal electromigration of ions from the bulk to their interfaces. Sensitivity to RBC age and species suggests that the surface proteins and membrane ion channels can affect the capacitance of the interface to accommodate the ions from the bulk. Such surface ion accumulation and polarization mechanisms are different from the classical dielectric theories. The resonant frequency of electrode polarization at around 1 MHz falls between positive and negative dielectrophoretic resonant frequency peaks - suggesting that the double-layer polarization mechanism is a distinct and potentially important bioparticle manipulation tool.     

Magnetohydrodynamic effects on a charged colloidal sphere with arbitrary double-layer thickness

An analytical study is presented for the magnetohydrodynamic (MHD) effects on a translating and rotating colloidal sphere in an arbitrary electrolyte solution prescribed with a general flow field and a uniform magnetic field at a steady state. The electric double layer surrounding the charged particle may have an arbitrary thickness relative to the particle radius. Through the use of a simple perturbation method, the Stokes equations modified with an electric force term, including the Lorentz force contribution, are dealt by using a generalized reciprocal theorem. Using the equilibrium double-layer potential distribution from solving the linearized Poisson-Boltzmann equation, we obtain closed-form formulas for the translational and angular velocities of the spherical particle induced by the MHD effects to the leading order. It is found that the MHD effects on the particle movement associated with the translation and rotation of the particle and the ambient fluid are monotonically increasing functions of κa, where κ is the Debye screening parameter and a is the particle radius. Any pure rotational Stokes flow of the electrolyte solution in the presence of the magnetic field exerts no MHD effect on the particle directly in the case of a very thick double layer (κa→0). The MHD effect caused by the pure straining flow of the electrolyte solution can drive the particle to rotate, but it makes no contribution to the translation of the particle.     

2-D assembly of colloidal particles on a planar electrode

Electrical voltage externally applied between parallel-plate electrodes can cause colloidal particles located near one of the electrodes to aggregate; thus monodisperse particles can be driven to form hexagonally close-packed arrays which can be useful in the fabrication of photonic materials. The mechanism for lateral motion of particles on the electrode surface is electroosmotic flow driven by the action of the applied electric field acting either on the equilibrium charges in the diffuse layer of the particles (ECEO) or on charge induced by the electric field on the surface of the electrode (ICEO). For steady currents, ECEO dominates whereas ICEO dominates for high-frequency alternating current. For intermediate frequencies (10 Hz to 1 kHz) both mechanisms are active. This critical review attempts to integrate concepts from electrochemistry and colloid chemistry to understand this electrokinetic phenomenon.     

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.     

Continuous dielectrophoretic particle separation via isomotive dielectrophoresis with bifurcating stagnation flow

We present a novel technique for continuous label‐free separation of particles based on their dielectrophoretic crossover frequencies. Our technique relies on our unique microfluidic geometry which performs hydrodynamic focusing, generates a stagnation flow with two outlets, and simultaneously produces an isomotive dielectrophoretic field via wall‐situated electrodes. To perform particle separation, we hydrodynamically focus particles onto stagnation streamlines and use isomotive dielectrophoretic force to nudge the particles off these streamlines and direct them into appropriate outlets. Focusing particles onto stagnation streamlines obviates the need for large forces to be applied to the particles and therefore increases system throughput. The use of isomotive (spatially uniform) dielectrophoretic force increases system reliability. To guide designers, we develop and describe a simple scaling model for the particle separation dynamics of our technique. The model predicts the range of particle sizes that can be separated as well as the processing rate that can be achieved as a function of system design parameters: channel size, flow rate, and applied potential. Finally, as a proof‐of‐principle, we use this technique to separate polystyrene bead and cell mixtures of the same diameters as well as mixtures of both particles with varying diameters.     

Concentrating colloids with electric field gradients. I. Particle transport and growth mechanism of hard-sphere-like crystals in an electric bottle

This work concerns the use of electric field gradients to manipulate the local particle concentration in a hard-sphere-like suspension. Inside a specially designed "electric bottle," we observed our colloids to collect in the regions of lowest field strength ("negative dielectrophoresis"). This allows for the use of larger field gradients and stronger dielectrophoretic forces than in the original electric bottle design, which was based on positive dielectrophoresis [M. T. Sullivan et al., Phys. Rev. Lett. 96, 015703 (2006)]. We used confocal scanning laser microscopy to quantitatively follow the time-dependent change in the particle density and the suspension structure. Within a few days, the dielectrophoretic compression was seen to initiate a heterogeneouslike growth of large single crystals, which took place far out-of-equilibrium. The crystals had a random hexagonal close-packed structure and displayed an intriguing growth mechanism, during which the entire crystal was continuously transported, while growing both on the "high-field" and the "low-field" sides, although at different rates. After switching off the electric field, the compressed crystals were found to relax to a lower packing fraction and melt, at a much slower rate than the crystal growth. Besides revealing the particular (far out-of-equilibrium) crystal growth mechanism in these electric bottles, our observations also shed light on the role of the different particle transport processes in the cell and some of the relevant tuning parameters. This is useful for different types of experiments, for instance, focusing more on melting, homogeneous crystallization, or the glass transition.     

Passivated‐electrode insulator‐based dielectrophoretic separation of heterogeneous cell mixtures

Rapid and accurate purification of various heterogeneous mixtures is a critical step for a multitude of molecular, chemical, and biological applications. Dielectrophoresis has shown to be a promising technique for particle separation due to its exploitation of the intrinsic electrical properties, simple fabrication, and low cost. Here, we present a geometrically novel dielectrophoretic channel design which utilizes an array of localized electric fields to separate a variety of unique particle mixtures into distinct populations. This label‐free device incorporates multiple winding rows with several nonuniform structures on to sidewalls to produce high electric field gradients, enabling high locally generated dielectrophoretic forces. A balance between dielectrophoretic forces and Stokes’ drag is used to effectively isolate each particle population. Mixtures of polystyrene beads (500 nm and 2 μm), breast cancer cells spiked in whole blood, and for the first time, neuron and satellite glial cells were used to study the separation capabilities of the design. We found that our device was able to rapidly separate unique particle populations with over 90% separation yields for each investigated mixture. The unique architecture of the device uses passivated‐electrode insulator‐based dielectrophoresis in an innovative microfluidic device to separate a variety of heterogeneous mixture without particle saturation in the channel.     

Analytical solutions and validation of electric field and dielectrophoretic force in a bio-microfluidic channel

In a microbiological device, cell or particle manipulation and characterization require the use of electric field on different electrodes in several configurations and shapes. To efficiently design microelectrodes within a microfluidic channel for dielectrophoresis focusing, manipulation and characterization of cells, the designer will seek the exact distribution of the electric potential, electric field and hence dielectrophoresis force exerted on the cell within the microdevice. In this paper we describe the approach attaining the analytical solution of the dielectrophoretic force expression within a microchannel with parallel facing same size electrodes present on the two faces of channel substrates, with opposite voltages on the pair electrodes. Simple Fourier series mathematical expressions are derived for electric potential, electric field and dielectric force between two distant finite‐size electrodes. Excellent agreement is found by comparing the analytical results calculated using MATLAB? with numerical ones obtained by Comsol. This analytical result can help the designer to perform simple design parametric analysis. Bio‐microdevices are also designed and fabricated to illustrate the theoretical solution results with the experimental data. Experiments with red blood cells show the dielectrophoretic force contour plots of the analytical data matched to the experimental results.