Dielectrophoresis of nanoparticles

A numerical scheme based on the distributed Lagrange multiplier method (DLM) is used to study the motion of nano-sized particles of dielectric suspensions subjected to uniform and nonuniform electric fields. Particles are subjected to both electrostatic and hydrodynamic forces, as well as Brownian motion. The results of the simulations presented in this paper show that uniform electric fields the evolution of the particle structures depends on the ratio of electrostatic particle-particle interactions and Brownian forces. When this ratio is of the order of 100 or greater, particles form stable chains and columns, whereas when it is of the order of 10 or smaller the particle distribution is random. For the nonuniform electric field cases considered in this paper, the relative magnitude of Brownian forces is in the range such that it does not influence the eventual collection of particles by dielectrophoresis and the particular locations where the particles are collected. However, Brownian motion is observed to influence the transient particle trajectories. The deviation of the particle trajectories compared to those determined by the electrostatic and hydrodynamic forces alone is characterized by the ratio of Brownian and dielectrophoretic forces.     

Brownian Motion and Large Electric Polarizabilities Facilitate Dielectrophoretic Capture of Sub-200 nm Gold Nanoparticles in Water

Dielectrophoresis can move small particles using the force resulting from their polarization in a divergent electric field. In liquids, it has most often been applied to micrometric objects such as biological cells or latex microspheres. For smaller particles, the dielectrophoretic force becomes very small and the phenomenon is furthermore perturbed by Brownian motion. Whereas dielectrophoresis has been used for assembly of superstructures of nanoparticles and for the detection of proteins and nucleic acids, the mechanisms underlying DEP of such small objects require further study. This work presents measurements of the alternating-current (AC) dielectrophoretic response of gold nanoparticles of less than 200 nm diameter in water. An original dark-field digital video-microscopic method was developed and used in combination with a microfluidic device containing transparent thin-film electrodes. It was found that the dielectrophoretic force is only effective in a small zone very close to the tip of the electrodes, and that Brownian motion actually facilitates transport of particles towards this zone. Moreover, the fact that particles as small as 80 nm are still efficiently captured in our device is not only due to Brownian transport but also to an effective polarizability that is larger than what would be expected on basis of current theory for a sphere in a dielectric medium.     

Limitations of differential electrophoresis for measuring colloidal forces: a Brownian dynamics study

Differential electrophoresis experiments are often used to measure subpiconewton forces between two spheres of a heterodoublet. The experiments have been interpreted by solving the electrokinetic equations to obtain a simple Stokes law-type equation. However, for nanocolloids, the effects of Brownian motion alter the interpretation: (1) Brownian translation changes the rate of axial separation. (2) Brownian rotation reduces the alignment of the doublet with the applied electric field. (3) Particles can reaggregate by Brownian motion after they break, forming either heterodoublets or homodoublets, and because homodoublets cannot be broken by differential electrophoresis, this effectively terminates the experiment. We tackle points 1 and 2 using Brownian dynamics simulations (BDS) with electrophoresis as an external force, accounting for convective translation and rotation as well as Brownian translation and rotation. Our simulations identify the lower particle size limit of differential electrophoresis to be about 1 microm for desired statistical accuracy. Furthermore, our simulations predict that particles around 10 nm in size and at ambient conditions will break primarily by Brownian motion, with a negligible effect due to the electric field.     

Microdevices for manipulation and accumulation of micro- and nanoparticles by dielectrophoresis

Microfluidic devices with three-dimensional (3-D) arrays of microelectrodes embedded in microchannels have been developed to study dielectrophoretic forces acting on synthetic micro- and nanoparticles. In particular, so-called deflector structures were used to separate particles according to their size and to enable accumulation of a fraction of interest into a small sample volume for further analysis. Particle velocity within the microchannels was measured by video microscopy and the hydrodynamic friction forces exerted on deflected particles were determined according to Stokes law. These results lead to an absolute measure of the dielectrophoretic forces and allowed for a quantitative test of the underlying theory. In summary, the influence of channel height, particle size, buffer composition, electric field, strength and frequency on the dielectrophoretic force and the effectiveness of dielectrophoretic deflection structures were determined. For this purpose, microfluidic devices have been developed comprising pairs of electrodes extending into fluid channels on both top and bottom side of the microfluidic channels. Electrodes were aligned under angles varying from 0 to 75 degrees with respect to the direction of flow. Devices with channel height varying between 5 and 50 microm were manufactured. Fabrication involved a dedicated bonding technology using a mask aligner and UV-curing adhesive. Particles with radius ranging from 250 nm to 12 microm were injected into the channels using aqueous buffer solutions.     

Parasitic trap cancellation using multiple frequency dielectrophoresis, demonstrated by loading cells into cages

This paper presents a method of using multiple frequencies to counteract electric field distortions that interfere with the dielectrophoretic (DEP) manipulation of particles or cells. To demonstrate the technique, simulations were performed for a scenario in which cells were to be loaded into a cage whose walls created parasitic trapping sites that prevented cells from entering it. By employing negative DEP on one electrode in conjunction with positive DEP on another, these traps could be almost completely cancelled. The model predictions were validated experimentally: multiple frequency DEP was used to load many cells into a cage in a matter of seconds in fluid flows of up to 300 microm s(-1), which could not be done with single frequency DEP. Actively cancelling field distortions permits the presence of features that would otherwise be prohibited near regions of dielectrophoretic manipulation, significantly expanding the environments in which dielectrophoresis can be used.     

Brownian dynamics simulations of single-wall carbon nanotube separation by type using dielectrophoresis

We theoretically investigate the separation of individualized metallic and semiconducting single-wall carbon nanotubes (SWNTs) in a dielectrophoretic (DEP) flow device. The SWNT motion is simulated by a Brownian dynamics (BD) algorithm, which includes the translational and rotational effects of hydrodynamic, Brownian, dielectrophoretic, and electrophoretic forces. The device geometry is chosen to be a coaxial cylinder because it yields effective flow throughput, the DEP and flow fields are orthogonal to each other, and all the fields can be described analytically everywhere. We construct a flow-DEP phase map showing different regimes, depending on the relative magnitudes of the forces in play. The BD code is combined with an optimization algorithm that searches for the conditions that maximize the separation performance. The optimization results show that a 99% sorting performance can be achieved with typical SWNT parameters by operating in a region of the phase map where the metallic SWNTs completely orient with the field, whereas the semiconducting SWNTs partially flow-align.     

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.     

Electrokinetic particle entry into microchannels

The fundamental understanding of particle electrokinetics in microchannels is relevant to many applications. To date, however, the majority of previous studies have been limited to particle motion within the area of microchannels. This work presents the first experimental and numerical investigation of electrokinetic particle entry into a microchannel. We find that the particle entry motion can be significantly deviated from the fluid streamline by particle dielectrophoresis at the reservoir-microchannel junction. This negative dielectrophoretic motion is induced by the inherent non-uniform electric field at the junction and is insensitive to the microchannel length. It slows down the entering particles and pushes them toward the center of the microchannel. The consequence is the demonstrated particle deflection, focusing, and trapping phenomena at the reservoir-microchannel junction. Such rich phenomena are studied by tuning the AC component of a DC-biased AC electric field. They are also utilized to implement a selective concentration and continuous separation of particles by size inside the entry reservoir.     

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.     

Accumulation and trapping of hepatitis A virus particles by electrohydrodynamic flow and dielectrophoresis

Hepatitis A virus particles (d = 27 nm) were successfully accumulated and trapped in a microfluidic system by means of a combination of electrohydrodynamic flow and dielectrophoretic forces. Electric fields were generated in a field cage consisting of eight microelectrodes. In addition, high medium conductance (0.3 S/m) resulted in sufficient Joule heating and the corresponding spatial variation of temperature, density, and permittivity to induce electrohydrodynamic flow in the vicinity of the field cage. Flow vortices transport particles toward the center of the field cage, where dielectrophoretic forces cause permanent entrapment and particle aggregation. Spatial distribution of temperature, density, and permittivity as well as resulting flow patterns were modeled numerically and are in good agreement with experimental results. This accumulation scheme might be applicable to sample concentration enhancement in biosensor applications.     

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.     

Electrophoretic size separation of particles in a periodically constricted microchannel

The size separation of Brownian particles with the same free mobility in an electrophoretic microchannel with alternating thick regions and narrow constrictions is studied theoretically. The electrophoretic mobility is field dependent and generally increases with field strength. In weak fields, Brownian diffusion dominates and the migration is controlled by the entrance effect. Therefore, smaller particles migrate faster than larger ones. In strong fields, however, the particle tends to follow electric field lines. Smaller particles are susceptible to Brownian motion and thus influenced by the nonuniform electric field in the well significantly. As a result, larger particles possess higher mobilities. Our simulation results agree with the experimental observations and provide guidance for efficient nanofluidic separation.     

Dynamically controlled dielectrophoresis using resonant tuning

Electrically polarizable micro- and nanoparticles and droplets can be trapped using the gradient electric field of electrodes. But the spatial profile of the resultant dielectrophoretic force is fixed once the electrode structure is defined. To change the force profile, entire complex lab-on-a-chip systems must be re-fabricated with modified electrode structures. To overcome this problem, we propose an approach for the dynamic control of the spatial profile of the dielectrophoretic force by interfacing the trap electrodes with a resistor and an inductor to form a resonant resistor–inductor–capacitor (RLC) circuit. Using a dielectrophoretically trapped water droplet suspended in silicone oil, we show that the resonator amplitude, detuning, and linewidth can be continuously varied by changing the supply voltage, supply frequency, and the circuit resistance to obtain the desired trap depth, range, and stiffness. We show that by proper tuning of the resonator, the trap range can be extended without increasing the supply voltage, thus preventing sensitive samples from exposure to high electric fields at the stable trapping position. Such unprecedented dynamic control of dielectrophoretic forces opens avenues for the tunable active manipulation of sensitive biological and biochemical specimen in droplet microfluidic devices used for single-cell and biochemical reaction analysis.     

Electrohydrodynamics of a drop under nonaxisymmetric electric fields

We consider the electrohydrodynamics of a spherical drop in a nonaxisymmetric electric field, which can be approximated by the sum of a uniform field and a linear straining field. We obtain the analytic solution of the three-dimensional flow fields inside and outside a drop for the Stokes flow regime by using Lamb's general solution and the leaky dielectric model. With the analytic solution, the dielectrophoretic migration velocity of a drop is obtained as a function of the type and the frequency of the imposed electric field. The direction of drop motion is found to be parallel to the dielectrophoretic force. The analytic solution is also used to investigate the characteristics of the interfacial flow under various nonaxisymmetric electric fields. While investigating the interfacial flow, we find a surface vortex structure under certain nonaxisymmetric electric fields, which is found to be related to the chaotic mixing inside the drop. Finally, we consider the chaotic features of three-dimensional flows inside the drop under static nonaxisymmetric electric fields.     

Insulator-based dielectrophoretic focusing and trapping of particles in non-Newtonian fluids

Insulator-based dielectrophoretic (iDEP) microdevices have been limited to work with Newtonian fluids. We report an experimental study of the fluid rheological effects on iDEP focusing and trapping of polystyrene particles in polyethylene oxide, xanthan gum, and polyacrylamide solutions through a constricted microchannel. Particle focusing and trapping in the mildly viscoelastic polyethylene oxide solution are slightly weaker than in the Newtonian buffer. They are, however, significantly improved in the strongly viscoelastic and shear thinning polyacrylamide solution. These observed particle focusing behaviors exhibit a similar trend with respect to electric field, consistent with a revised theoretical analysis for iDEP focusing in non-Newtonian fluids. No apparent focusing of particles is achieved in the xanthan gum solution, though the iDEP trapping can take place under a much larger electric field than the other fluids. This is attributed to the strong shear thinning-induced influences on both the electroosmotic flow and electrokinetic/dielectrophoretic motions.     

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.     

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.     

Aggregation of Charged Particles under Electrophoresis or Gravity at Arbitrary Péclet Numbers

Collision efficiencies are considered for colloidal suspensions of solid spheres moving in a viscous fluid under the influence of electrophoresis or gravity, Brownian motion, and electrostatic and van der Waals forces. The results are compared to those for convection (electrophoresis or gravity) and diffusion (Brownian motion) acting independently. The collision efficiency increases by many orders of magnitude over that predicted by simply adding diffusive and convective efficiencies in a specific parameter regime. This regime occurs when there is a large energy barrier in the interparticle potential, causing a stable region of parameter space if there is no diffusion. Brownian motion alone will only cause small amounts of aggregation under these conditions. However, for electric fields or buoyancy effects which are only slightly too weak to allow particles to overcome the potential barrier, the addition of weak Brownian motion to a system with convection can cause significant numbers of particles to overcome the energy barrier and aggregate. Copyright 2000 Academic Press.     

Force measurements between sub-100 nm colloidal particles

Interparticle forces have been measured between polystyrene latex particles as small as 85 nm in diameter in KCl solutions. A variant of the differential electrophoresis technique, called particle force light scattering (PFLS), was used to measure forces between Brownian, nearly touching particles for diameters from 4500 nm down to 85 nm. The forces, some less than 0.1 pN, matched to within a factor of 2 with predictions from depletion and DLVO theory.     

Trapping of DNA by dielectrophoresis

Under suitable conditions, a DNA molecule in solution will develop a strong electric dipole moment. This induced dipole allows the molecule to be manipulated with field gradients, in a phenomenon known as dielectrophoresis (DEP). Pure dielectrophoretic motion of DNA requires alternate current (AC) electric fields to suppress the electrophoretic effect of the molecules net charge. In this paper, we present two methods for measuring the efficiency of DEP for trapping DNA molecules as well as a set of quantitative measurements of the effects of strand length, buffer composition, and frequency of the applied electric field. A simple configuration of electrodes in combination with a microfluidic flow chamber is shown to increase the concentration of DNA in solution by at least 60-fold. These results should prove useful in designing practical microfluidic devices employing this phenomenon either for separation or concentration of DNA.