A method for determining electrophoretic and electroosmotic mobilities using AC and DC electric field particle displacements

We have developed a method for measuring the electrophoretic mobility of submicrometer, fluorescently labeled particles and the electroosmotic mobility of a microchannel. We derive explicit expressions for the unknown electrophoretic and the electroosmotic mobilities as a function of particle displacements resulting from alternating current (AC) and direct current (DC) applied electric fields. Images of particle displacements are captured using an epifluorescent microscope and a CCD camera. A custom image-processing code was developed to determine image streak lengths associated with AC measurements, and a custom particle tracking velocimetry (PTV) code was devised to determine DC particle displacements. Statistical analysis was applied to relate mobility estimates to measured particle displacement distributions.     

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.     

Dielectric spectroscopy and electrophoretic mobility measurements interpreted with the standard electrokinetic model

We report results from complementary electrokinetic measurements-dielectric relaxation and electrophoretic mobility-undertaken to test the applicability of the standard electrokinetic theory with a model system. Dielectric spectra were obtained at frequencies between 1 kHz and 40 MHz with a new, two-electrode cell design [Hollingsworth and Saville, J. Colloid Interface Sci. 257 (2003) 65-76]; mobility data were acquired with an electrophoretic light scattering instrument. Data from the two-electrode cell were collected at different electrode separations and interpreted with newly developed procedures to remove the influence of electrode polarization. Methodology A employs extrapolation to infinite electrode separation to compute the dielectric constant and conductivity as functions of frequency. The contributions from suspended particles are reported in terms of dielectric constant and conductivity increments. Methodology B uses a theoretical model of electrode polarization and the standard electrokinetic model in a nonlinear regression scheme. Results are presented in several forms: frequency-dependent dielectric constant and conductivity increments, frequency-dependent dielectric constants and conductivities, and the complex dipole coefficient. It is shown that the standard model provides a consistent methodology for interpreting particle behavior; zeta-potentials inferred from mobility and dielectric relaxation agree to within experimental error. Moreover, the cell design and interpretation are straightforward and provide relatively simple ways to obtain complementary measurements over a wide frequency range. The results unambiguously show that electrokinetic character of this dispersion follows the standard model.     

Electrokinetics of charged spherical colloidal particles taking into account the effect of ion size constraints

The electrokinetic properties of suspended spherical particles are examined using a modified standard electrokinetic model, which takes into account the finite ion size and considers that the minimum approach distance of ions to the particle surface need not be equal to their effective radius in the bulk solution. We calculate the conductivity increment and the electrophoretic mobility and present a detailed interpretation of the obtained results, based on the analysis of the equilibrium and field-induced ion concentrations, as well as the convective fluid flow in the neighborhood of the particle surface. We show that when charge reversal takes place, the sign of the concentration polarization remains unchanged while the sign of the electrophoretic mobility only changes under favorable circumstances.     

Electrophoresis in a Carreau fluid at arbitrary zeta potentials

The electrophoresis of colloidal particles has been studied extensively in the past. Relevant analyses, however, are focused mainly on the electrophoretic behavior of a particle in a Newtonian fluid. Recent advances in science and technology suggest that the electrophoresis conducted in a non-Newtonian fluid can play a role in practice. Here, the electrophoresis of a concentrated colloidal dispersion in a Carreau fluid is investigated under the conditions of arbitrary electrical potential where the effect of double-layer polarization may be significant. A pseudo-spectral method coupled with a Newton-Raphson iteration scheme is used to solve the governing equations, which describe the electric, the flow, and the concentration fields. The results of numerical simulation reveal that, due to the effect of shear thinning, the electrophoretic mobility for the case of a Carreau fluid is greater than for that of a Newtonian fluid. Also, the higher the surface potential of a particle, the more significant the non-Newtonian nature of a Carreau fluid on its electrophoretic mobility.     

Effects of double-layer polarization and electroosmotic flow on the electrophoresis of an ellipsoid in a spherical cavity

The electrophoresis of a rigid, positively charged ellipsoidal particle at the center of a spherical cavity is investigated theoretically under the conditions where the effects of double-layer polarization and the presence of an electroosmotic flow can be important. The equations governing the problem under consideration and the associated boundary conditions are solved numerically, and the influences of the key parameters on the electrophoretic mobility of the particle are discussed. We show that if the cavity is uncharged, the effect of double-layer polarization yields a local minimum in the electrophoretic mobility as the thickness of the double layer varies. This local minimum disappears if the cavity is also positively charged. In addition to reducing the scaled mobility of an ellipsoid, the presence of the boundary is also capable of influencing the relative magnitudes of the scaled mobility for particles of various shapes. For instance, if the volume of an ellipsoid is fixed, the scaled mobility ranks as prolate > sphere > oblate if the boundary effect is unimportant, but that order is reversed if the boundary effect is important.     

Effects of dielectric gradients-mediated ions partitioning on the electrophoresis of composite soft particles: An analytical theory

In this work, we report original analytical expressions defining the electrophoretic mobility of composite soft particles comprising an inner core and a surrounding polymer shell with differentiated permeabilities to ions from aqueous background electrolyte and to fluid flow developed under applied DC field conditions. The existence of dielectric permittivity gradients operational at the core/shell and shell/solution interfaces is accounted for within the Debye–Hückel approximation and flat plate configuration valid in the thin double layer regime. The proposed electrophoretic mobility expressions, applicable to weakly to moderately charged particles with size well exceeding the Debye layer thickness, involve the relevant parameters describing the particle core/shell structure and the electrohydrodynamic features of the core and shell particle components. It is shown that the analytical expressions reported so far in literature for the mobility of hard (impermeable) or porous particles correspond to asymptotic limits of the more generic results detailed here. The impacts of dielectric-mediated effects of ions partitioning between bulk solution and particle body on the electrophoretic response are further discussed. The obtained expressions pave the way for a refined quantitative, analytical interpretation of electrophoretic mobility data collected on soft (nano)particles (e.g., functionalized dendrimers and multilayered polyelectrolytic particles) or biological cells (e.g., viruses) for which the classical hard core-soft shell representation is not appropriate.     

Dynamic electrophoretic mobility of a concentrated dispersion of particles with a charge-regulated surface at arbitrary potential

The dynamic electrophoretic mobility of a concentrated dispersion of biocolloids such as cells and microorganisms is modeled theoretically. Here, a biological particle is simulated by a particle, the surface of which contains dissociable functional groups. The results derived provide basic theory for the quantification of the surface properties of a biocolloid through an electroacoustic device, which has the merit of making direct measurement on a concentrated dispersion without dilution. Two key parameters are defined to characterize the phenomenon under consideration: the first, A, is associated with the pH of the dispersion, and the second, B, is associated with the equilibrium constant of the dissociation reaction of the functional group. We show that if A is large and/or B is small, the surface potential is high, and the effect of double-layer polarization becomes significant. In this case the dynamic electrophoretic mobility may have a local maximum and a phase lead as the frequency of the applied electric field varies. Due to the hydrodynamic interaction between neighboring particles, the dynamic electrophoretic mobility decreases with the concentration of dispersion.     

Efficient nanoparticle focusing utilizing cascade AC electroosmotic flow

This study presents on-chip continuous accumulation and concentration of nanoscale samples using a cascade alternating current electroosmosis (cACEO) flow. ACEO can generate flow motion caused by ion movement due to interactions between the AC electric field and the induced charge layer on the electrode surface, with the potential to accumulate particles, especially in low-conductive liquid. However, the intrinsic particle diffusive motion, which is sensitive to particle size, is an essential element influencing accumulation efficiency. In this study, an electrode combining chevron and double-gap geometry embedded in a microfluidic channel was developed to perform efficient three-dimensional (3D) nanoparticle focusing using ACEO. The chevron electrode pattern was introduced upstream of the focusing zone to overcome particle accumulation in scattering zones near the channel sidewall. To demonstrate the efficiency of the proposed device for particle accumulation, three nanoparticle types were used: latex, metal, and biomaterial. Continuous 3D concentration of 50-nm polystyrene particles was confirmed. The concentration factor, determined based on image processing, became quite high when 50-nm gold nanoparticles were used. Moreover, nanoparticles with a 20-nm diameter were accumulated using cACEO. Finally, we used the concentrator chip to accumulate 50-nm liposome particles, confirming that the device could also successfully concentrate biomaterials.     

Effect of stress-jump condition on electrophoretic behavior of a spherical dispersion of soft particles

The electrophoresis of a concentrated dispersion of soft particles, where a particle comprises a rigid core and an ion-penetrable membrane layer, is modeled theoretically, taking the effect of double-layer polarization into account. In particular, the influence of a stress-jump condition of the flow field at the membrane layer-liquid interface on the electrophoretic mobility of a particle is investigated. The type of particles considered mimic biocolloids, such as cells and microorganisms, and inorganic colloids covered by an artificial polymer layer such as surfactant molecules. A unit cell model is adopted to simulate the present spherical dispersion, and the governing equations and the associated boundary conditions are solved by a pseudo-spectral method based on Chebyshev polynomials. We show that while the stress-jump condition, characterized by a stress-jump coefficient, can have a significant influence on the mobility of a particle, the associated flow field is not influenced appreciably. Also, the influence of the stress-jump condition on the mobility of a particle depends largely on the nature of the membrane layer, characterized by its friction coefficient.     

Simultane Bestimmung von elektrophoretischer Beweglichkeit und Teilchengröße bei überlagerter Konvektion an Suspensionen und Emulsionen

With AWPS (Amplitude Weighted Phase Structuration), a new signal processing scheme is demonstrated for the simultaneous determination of zeta potentials and particle sizes. It allows the measurements of a small electrophoretic mobility in the presence of large particle diffusion and constant velocity, e. g. due to thermal convection. Laser light scattering techniques instead of the former methods determine electrophoretic velocity more objectively and precisely. The applicability of laser measurement techniques by analysis of the frequency spectrum is limited for particles ?50 nm or very low potentials, because of the broadening of the spectral peak by Brownian motion. In contrast to AWPS a separation of the various kinds of collective motion is not possible. The presented results demonstrate that this separation is of considerable significance in the acquisition of reliable values. Additionally the novel signal processing scheme allows a significant increase in sensitivity and therefore the application of an oscillating field (50–100 Hz) with a very small field strength. The system is feasible for particle sizes in the range of a few nm up to several μm. Its high resolution allows experiments with low fields or with small zeta potentials, even in the critical particles size range of a few nanometers.     

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.     

Nonlinear electrophoresis of dielectric particles in Newtonian fluids

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

Superfast electrophoresis of electron-type conducting particles

The features of concentration polarization caused by electric current through a unipolar conductive particle are considered. The peculiarities of the formation of an induced space charge near a particle with electron-type conductivity are analysed. It has been shown that the theoretical values of electrophoretic velocity for these particles are essentially smaller than those calculated for particles with ion-type conductivity.A new method to observe the superfast electrophoresis is developed. The electrophoretic velocity of graphite and activated carbon particles of different size (diameter, 200–500 μm) displaced in distilled water and electrolyte solutions in strong electric fields (100–500 V cm⁻¹) was measured. It is shown that, in contrast to classical electrophoresis, the electrophoretic mobility of such particles increases with the particle size and the external field strength. The experimental and theoretical results are compared. The discrepancy between theory and experiment is analysed.     

Measuring the electrophoretic mobility of concentrated suspensions in nonaqueous media

We present a new method of measuring the electrophoretic mobility of a particle in a concentrated suspension. The method is used to measure the electrophoretic mobility of PMMA particles (diameter 10 microm) suspended in a mixture of liquid hydrocarbons. The particle volume fraction of the suspension is varied from 0 up to 0.30 and the resulting variation of the electrophoretic mobility is discussed. The suspending liquid is such that its refractive index is very close to that of the particles. Thus the suspension is almost transparent and it is possible to follow through a microscope the motion of one particle. The suspension is subjected to a low-frequency electric field (0.5 Hz). The cell containing the suspension is mounted on a piezoelectric crystal. The displacement that compensates for the particle motion (when the particle image is steady) is determined.     

Electrophoresis of concentrated colloidal dispersions in low-polar solvents

We present a method to accurately measure the electrophoretic mobility of spherical colloids at high volume fractions in real space using confocal laser scanning microscopy (CLSM) and particle tracking. We show that for polymethylmethacrylate (PMMA) particles in a low-polar, density- and refractive-index-matched mixture of cyclohexylbromide and cis-decahydronaphthalene, the electrophoretic mobility decreases nonlinearly with increasing volume fraction. From the electrophoretic mobilities, we calculate the ζ-potential and the particle charge with and without correcting for volume fraction effects. For both cases, we find a decreasing particle charge as a function of volume fraction. This is in accordance with the fact that the charges originate from chemical equilibria that represent so-called weak association and/or dissociation reactions. Finally, as our methodology also provides data on particle self-diffusion in the presence of an electric field, we also analyze the diffusion at different volume fractions and identify a nonlinear decreasing trend for increasing volume fraction.     

Rapid-on-chip determination of dielectric properties of biological cells using imaging techniques in a dielectrophoresis dot microsystem

Dielectrophoresis is a technique whereby polarisable particles are manipulated by non-uniform alternating electric fields. A specific application of this technique is deducing the dielectric properties of cells from analysis of the dielectrophoretic spectrum of that particular cell population. We have developed a new microelectrode geometry consisting of two parallel electrode planes, one of which is patterned with arrays of circular apertures or 'dots'. The radial symmetry of the dots means that the polarisability of the particles within the dot can be directly related to change shifts in light transmission through the dot, and quantified from analysis of digital images. We have validated our system using well-characterised cell types and found a high degree of agreement to published data. Furthermore, we have observed that at high particle concentrations, electrostatic inter-particle repulsion causes spontaneous, rapid particle re-dispersion over the dot volume upon removal of an applied electric field. This allows the automated acquisition of a spectrum of 26 data points in approximately 15 min.     

Influence of boundary on the effect of double-layer polarization and the electrophoretic behavior of soft biocolloids

The electrophoresis of a soft particle comprising a rigid core and a charged porous membrane layer in a narrow space is modeled. This simulates, for example, the capillary electrophoresis of biocolloids such as cells and microorganisms, and biosensor types of device. We show that, in addition to the boundary effect, the effects of double-layer polarization (DLP) and the electroosmotic retardation flow can be significant, yielding interesting electrophoretic behaviors. For example, if the friction coefficient of the membrane layer and/or the boundary is large, then the DLP effect can be offset by the electroosmotic retardation flow, making the particle mobility to decrease with increasing double layer thickness, which is qualitatively consistent with many experimental observations in the literature, but has not been explained clearly in previous analyses. In addition, depending upon the thickness of double layer, the friction of the membrane layer of a particle can either retard or accelerate its movement, an interesting result which has not been reported previously. This work is the first attempt to show solid evidence for the influence of a boundary on the effect of DLP and the electrophoretic behavior of soft particles. The model proposed is verified by the experimental data in the literature. The results of numerical simulation provide valuable information for the design of bio-analytical apparatus such as nanopore-based sensing applications and for the interpretation of relevant experimental data.     

System for <Emphasis Type="Italic">In Situ</Emphasis> Characterization of Nanoparticles Synthesized in a Thermal Plasma Process

We have designed a particle diagnostic system that is able to measure particle size and charge distributions from low stagnation pressure (≥746 Pa) and high temperature (2000–4000 K) environments in near real time. This system utilizes a sampling probe interfaced to an ejector to draw aerosol from the low pressure chamber. Particle size and charge distributions are measured with a scanning mobility particle sizer. A hypersonic impactor is mounted in parallel with the scanning mobility particle sizer to collect particles for off-line microscopic analysis. This diagnostic system has been used to measure size and charge distributions of nanoparticles (Si, Ti, Si–Ti–N, etc.) synthesized with our thermal plasma reactor. We found that the mean particle size increases with operating pressure and reactant flow rates. We also found that most particles from our reactor are neutral for particles smaller than 20 nm, and that the numbers of positively and negatively charged particles are approximately equal.     

Electrophoresis and electric conduction in a salt-free suspension of charged particles

The electrophoresis and electric conduction of a suspension of charged spherical particles in a salt-free solution are analyzed by using a unit cell model. The linearized Poisson-Boltzmann equation (valid for the cases of relatively low surface charge density or high volume fraction of the particles) and Laplace equation are solved for the equilibrium electric potential profile and its perturbation caused by the imposed electric field, respectively, in the fluid containing the counterions only around the particle, and the ionic continuity equation and modified Stokes equations are solved for the electrochemical potential energy and fluid flow fields, respectively. Explicit analytical formulas for the electrophoretic mobility of the particles and effective electric conductivity of the suspension are obtained, and the particle interaction effects on these transport properties are significant and interesting. The scaled zeta potential, electrophoretic mobility, and effective electric conductivity increase monotonically with an increase in the scaled surface charge density of the particles and in general decrease with an increase in the particle volume fraction, keeping each other parameter unchanged. Under the Debye-Hückel approximation, the dependence of the electrophoretic mobility normalized with the surface charge density on the ratio of the particle radius to the Debye screening length and particle volume fraction in a salt-free suspension is same as that in a salt-containing suspension, but the variation of the effective electric conductivity with the particle volume fraction in a salt-free suspension is found to be quite different from that in a suspension containing added electrolyte.