Concentrating colloids with electric field gradients. II. Phase transitions and crystal buckling of long-ranged repulsive charged spheres in an electric bottle

We explored the usefulness of electric field gradients for the manipulation of the particle concentration in suspensions of charged colloids, which have long-ranged repulsive interactions. In particular, we studied the compression obtained by "negative" dielectrophoresis, which drives the particles to the regions of lowest field strength, thus preventing unwanted structural changes by induced dipole-dipole interactions. We used several sample cell layouts and suspension compositions, with a different range of the interparticle repulsions. For these systems, we obtained sufficient compression to observe a transition from the initial fluid phase to a random hexagonal close-packed crystal, as well as a body-centered cubic crystal. The heterogeneous dielectrophoretic crystallization mechanism involved an intriguing "pluglike" motion of the crystal, similar to what we have previously reported for hard-sphere suspensions. In this way, remarkably large single crystals were formed of several millimeters wide and a couple of centimeters long. Moreover, we found that these crystals could be compressed to such an extent that it led to an anisotropic deformation ("buckling") and, upon subsequent relaxation, a reorientation of the lattice, while stacking errors disappeared. These striking differences with the compressed hard-sphere crystals that we studied before [M. E. Leunissen et al., J. Chem. Phys. 128, 164508 (2008).] are likely due to the smaller elastic moduli of the present lower-density soft-sphere crystals.     

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.     

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.     

Two-dimensional crystallization of microspheres by a coplanar AC electric field

The particle-field and particle-particle interactions induced by alternating electric fields can be conveniently used for on-chip assembly of colloidal crystals. Two coplanar electrodes with a millimeter-sized gap between them are used here to assemble two-dimensional crystals from suspensions of either latex or silica microspheres. When an AC voltage is applied, the particles accumulate and crystallize on the surface between the electrodes. Light diffraction and microscopic observations demonstrate that the hexagonal crystal is always oriented with one axis along the direction of the field. The particles disassemble when the field is turned off, and the process can be repeated many times. The diffraction patterns from all consecutively formed crystals are identical. This assembly is driven by forces that depend on the electric field gradient, and a model is proposed involving a combination of dielectrophoresis and induced dipole chaining. The organization of large two-dimensional crystals allows characterization of the electrostatic interactions in the particle ensembles. The process can be controlled via the field strength, the frequency, and the viscosity of the liquid media. It could be used to make rudimentary optical switches or to separate mixtures of particles of different sizes.     

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.     

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.     

Microfluidic system for dielectrophoretic separation based on a trapezoidal electrode array

This paper presents a novel microfluidic device for dielectrophoretic separation based on a trapezoidal electrode array (TEA). In this method, particles with different dielectric properties are separated by the device composed of the TEA for the dielectrophoretic deflection of particles under negative dielectrophoresis (DEP) and poly(dimethylsiloxane)(PDMS) microfluidic channel with a sinuous and expanded region. Polystyrene microparticles are exposed to an electric field generated from the TEA in the microfluidic channel and are dielectrophoretically focused to make all of them line up to one sidewall. When these particles arrive at the region of another TEA for dielectrophoretic separation, they are separated having different positions along the perpendicular direction to the fluid flow due to their different dielectrophoretic velocities. To evaluate the separation process and performance, both the effect of the flow rate on dielectrophoretic focusing and the influence of the number of trapezoidal electrodes on dielectrophoretic separation are investigated. Now that this method utilizes the TEA as a source of negative DEP, non-specific particle adhering to the electrode surface can be prevented; conventional separation approaches depending on the positive DEP force suffer from this problem. In addition, since various particle types are continuously separated, this method can be easily applicable to the separation and analysis of various dielectric particles with high particle recovery and selectivity.     

Multi-particle interaction in AC electric field driven by dielectrophoresis force

When the dielectrophoresis technology is used to manipulate micron-sized particles, the interaction between particles should not be ignored because of the particle-particle interaction. Especially, when multiple particles (number of particles is above 2) are simultaneously manipulated, the interaction between neighboring particles will affect the results of the manipulation. This research investigates the interaction of particles caused dielectrophoresis effect by the Arbitrary Lagrangian-Eulerian (ALE) method based on the hypothesis of the thin layer of the electric double layer at the microscale. The mathematics model can be solved simultaneously by the finite element method for the AC electric field, the flow field around the suspended particles and the particle mechanics at the micrometer scale. In this study, the particle conductivity and the direction of the electric field are investigated, we find that particle conductivity and electric field direction pose an impact on particle movement, and the research reveal the law of microparticle dielectrophoresis movement, which could offer theoretical and technology support to profoundly understand the precise manipulation of particles in microfluidic chips by the dielectrophoresis effect.     

Dielectrophoresis of an inhomogeneous colloidal particle under an inhomogeneous field: a first-principles approach

In reality, colloidal particles often possess an arbitrary inhomogeneity profile. We present a first-principles approach to dielectrophoresis of such an inhomogeneous colloidal particle under an inhomogeneous field of an oscillating electric dipole moment. For numerical simulations, we treat the inhomogeneous particle as a specific graded one with a physically motivated dielectric model and conductivity profile. We find that both multipolar interactions and spatial fluctuations inside the particle can affect the dielectrophoretic spectrum of the particle significantly.     

Protein manipulation with insulator-based dielectrophoresis and direct current electric fields

The present study demonstrates the manipulation of protein particles employing insulator-based dielectrophoresis (iDEP) and direct current (d.c.) electric fields. Fluorescently labeled bovine serum albumin (BSA) protein particles were concentrated inside a microchannel that contained an array of glass cylindrical insulating structures. d.c. electric fields were applied and the dielectrophoretic response of the particles was observed as a function of the suspending medium conductivity (25, 50 and 100muS/cm) and pH (8 and 9). It was shown that the magnitude of the applied electric field (700-1600V/cm) and suspending medium properties have a strong effect on the dielectrophoretic response of the protein particles. The results presented here are the first report on protein manipulation employing d.c.-iDEP.     

Control and modeling of the dielectrophoretic assembly of on-chip nanoparticle wires

Suspensions of metallic nanoparticles in water were assembled via the action of an alternating electric field (dielectrophoresis) into wires of micrometer thickness. Two modes of microwire assembly, one through the bulk of the suspension and one as half-cylinders on the glass surface between the electrodes, were identified. The operating conditions responsible for the two assembly modes were recognized. The control of the process parameters allows making, for example, straight single connectors or massively parallel arrays of microwires on the surface of the chip, which can be extracted in dry form. The microwire assembly process was modeled using finite element electrostatic calculations. The direction of growth can be guided by introducing conductive islands or particles in the suspension. The experiments, supported by electrostatic calculations, show that the wires grow in the direction of highest field intensity, "automatically" making electrical connections to the objects between the electrodes. The results point the way to controlled dielectrophoretic assembly of nanoparticles into on-chip electrical connectors, switches, and networks.     

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.     

Negative dielectrophoresis-based particle separation by size in a serpentine microchannel

Dielectrophoresis has been widely used to focus, trap, concentrate, and sort particles in microfluidic devices. This work demonstrates a continuous separation of particles by size in a serpentine microchannel using negative dielectrophoresis. Depending on the magnitude of the turn-induced dielectrophoretic force, particles travelling electrokinetically through a serpentine channel either migrate toward the centerline or bounce between the two sidewalls. These distinctive focusing and bouncing phenomena are utilized to implement a dielectrophoretic separation of 1 and 3 μm polystyrene particles under a DC-biased AC electric field of 880 V/cm on average. The particle separation process in the entire microchannel is simulated by a numerical model.     

Electrothermal flow effects in insulating (electrodeless) dielectrophoresis systems

We simulate electrothermally induced flow in polymeric, insulator-based dielectrophoresis (iDEP) systems with DC-offset, AC electric fields at finite thermal Péclet number, and we identify key regimes where electrothermal (ET) effects enhance particle deflection and trapping. We study a single, two-dimensional constriction in channel depth with parametric variations in electric field, channel geometry, fluid conductivity, particle electrophoretic (EP) mobility, and channel electroosmotic (EO) mobility. We report the effects of increasing particle EP mobility, channel EO mobility, and AC and DC field magnitudes on the mean constriction temperature and particle behavior. Specifically, we quantify particle deflection and trapping, referring to the deviation of particles from their pathlines due to dielectrophoresis as they pass a constriction and the stagnation of particles due to negative dielectrophoresis near a constriction, respectively. This work includes the coupling between fluid, heat, and electromagnetic phenomena via temperature-dependent physical parameters. Results indicate that the temperature distribution depends strongly on the fluid conductivity and electric field magnitude, and particle deflection and trapping depend strongly on the channel geometry. Electrothermal (ET) effects perturb the EO flow field, creating vorticity near the channel constriction and enhancing the deflection and trapping effects. ET effects alter particle deflection and trapping responses in insulator-based dielectrophoresis devices, especially at intermediate device aspect ratios (2 ≤ r ≤ 7) in solutions of higher conductivity (σ m ≥ 1 × 10(-3)S/m). The impact of ET effects on particle deflection and trapping are diminished when particle EP mobility or channel EO mobility is high. In almost all cases, ET effects enhance negative dielectrophoretic particle deflection and trapping phenomena.     

Characterization and optimization of liquid electrodes for lateral dielectrophoresis

Using the concept of insulator-based "electrodeless" dielectrophoresis, we present a novel geometry for shaping electric fields to achieve lateral deviation of particles in liquid flows. The field is generated by lateral planar metal electrodes and is guided along access channels to the active area in the main channel. The equipotential surfaces at the apertures of the access channels behave as vertical "liquid" electrodes injecting the current into the main channel. The field between a pair of adjacent liquid electrodes generates the lateral dielectrophoretic force necessary for particle manipulation. We use this force for high-speed deviation of particles. By adding a second pair of liquid electrodes, we focus a particle stream. The position of the focused stream can be swept across the channel by adjusting the ratio of the voltages applied to the two pairs. Based on conformal mapping, we provide an analytical model for estimating the potential at the liquid electrodes and the field distribution in the main channel. We show that the simulated particle trajectories agree with observations. Finally, we show that the model can be used to optimize the device geometry in different applications.     

Solid Separation from a Mixed Suspension through Electric‐Field‐Enhanced Crystallization

When applied to a pure component suspension in an apolar solvent, a strong inhomogeneous electric field induces particle movement, and the particles are collected at the surface of one of the two electrodes. This new phenomenon was used to separately isolate two organic crystalline compounds, phenazine and caffeine, from their suspension in 1,4‐dioxane. First, crystals of both compounds were collected at different electrodes under the influence of an electric field. Subsequent cooling crystallization enabled the immobilization and growth of the particles on the electrodes, which were separately collected after the experiment with purities greater than 91 %. This method can be further developed into a technique for crystal separation and recovery in complex multicomponent suspensions of industrial processes.     

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.     

Lateral separation of colloids or cells by dielectrophoresis augmented by AC electroosmosis

Colloidal particles and biological cells are patterned and separated laterally adjacent to a micropatterned electrode array by applying AC electric fields that are principally oriented normally to the electrode array. This is demonstrated for yeast cells, red blood cells, and colloidal polystyrene particles of different sizes and zeta-potentials. The separation mechanism is observed experimentally to depend on the applied field frequency and voltage. At high frequencies, particles position themselves in a manner that is consistent with dielectrophoresis, while at low frequencies, the positioning is explained in terms of a strong coupling between gravity, the vertical component of the dielectrophoretic force, and the Stokes drag on particles induced by AC electroosmotic flow. Compared to high frequency dielectrophoretic separations, the low frequency separations are faster and require lower applied voltages. Furthermore, the AC electroosmosis coupling with dielectrophoresis may enable cell separations that are not feasible based on dielectrophoresis alone.     

Three-dimensional arrangements of polystyrene latex particles with a hyperbolic quadruple electrode system

An attempt was made to arrange polystyrene latex particles (2, 5, and 10 microm in diameter) dispersed in aqueous media making use of their dielectrophoresis and electrophoresis with a hyperbolic quadruple electrode system. Application of a high-frequency ac field enabled the particles to arrange themselves between the electrodes forming a particle monolayer due to the negative dielectrophoretic force. Simultaneous application of high-frequency ac and dc fields caused the particles to gather in the region surrounded by the electrodes to form particle multilayers. Appropriate choice of the way of applying an electric field thus allowed the reversible control of particle arrangements (monolayer, multilayer, dispersion). Reapplication of an ac field to the particle layers produced highly dense particle multilayers.     

Insulator-based dielectrophoresis for the selective concentration and separation of live bacteria in water

Insulator-based dielectrophoresis (iDEP) was utilized to separate and concentrate selectively mixtures of two species of live bacteria simultaneously. Four species of bacteria were studied: the Gram-negative Escherichia coli and the Gram-positive Bacillus subtilis, B. cereus, and B. megaterium. Under an applied direct current (DC) electric field all the bacterial species exhibited negative dielectrophoretic behavior. The dielectrophoretic separations were carried out in a glass microchannel containing an array of insulating posts. The insulating posts in the microchannel produced nonuniformities in the electric field applied along the channel. Mixtures of two species of bacteria were introduced into the microchannel and the electric field was applied. The bacterial species exhibited different dielectrophoretic mobilities under the influence of the nonuniform field. From these experiments a trapping order was established with E. coli trapping at the weakest applied electric field, while the Bacillus species were trapped at different characteristic threshold fields. At stronger applied electric fields, the two different species of bacteria in the microchannel were dielectrophoretically trapped into two spatially distinct bands. The results showed that iDEP has the potential to selectively concentrate and separate different species of bacteria.