Near-wall velocities of particles suspended in shear flow and a streamwise electric field

Particles with a diameter of ∼0.5 µm in a dilute (volume fractions φ_∞ < 4 × 10⁻³) suspension assemble into highly elongated structures called “bands” under certain conditions in combined Poiseuille and electroosmotic flows in opposite directions through microchannels at particle-based Reynolds numbers Re_p < < 1. The particles are first concentrated near, then form “bands” within ∼6 µm of, the channel wall. The experiments described here examine the near-wall dynamics of individual “tracer” particles during the initial concentration, or accumulation, of particles, and the steady-state stage when the particles have formed relatively stable bands at different near-wall shear rates and electric field magnitudes. Surprisingly, the near-wall upstream particle velocities are found to be consistently greater in magnitude than the expected values based on the particles being convected by the superposition of both flows and subject to electrophoresis, which is in the same direction as the Poiseuille flow. However, the particle velocities scale linearly with the change in electric field magnitude, suggesting that the particle dynamics are dominated by linear electrokinetic phenomena. If this discrepancy with theory is only due to changes in particle electrophoresis, electrophoresis is significantly reduced to values as small as 20%–50% of the Smoluchowski relation, or well below previous model predictions, even for high particle potentials.     

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.     

Electrohydrodynamic Velocity and Pumping Measurements in Water and Alcohols

Bubble and particle velocities in water and alcohols, under the influence of an electric field, were investigated in this work. Air bubbles were injected into the liquids through an electrified metal capillary insulated by glass with its tip left exposed. The end of the capillary from which the bubbles were released was conical in shape. Due to an electric field formed between the noninsulated capillary tip and a ground electrode immersed in the solvent, small bubbles were formed and used as tracers for the electrohydrodynamic (EHD) flow field. The pressure inside the capillary was measured for all liquids used in this study. For water, ethanol, and n-propanol, it was found that, at relatively low applied voltage, the pressure increases with voltage, reaches a maximum (pressure breakpoint), and then sharply decreases. This behavior is a result of the competition between the electric force appearing at the interface and the force due to the EHD flow near the capillary tip. The electric force tends to increase the pressure inside the capillary, while the EHD flow tends to decrease this pressure. For isopropanol and butanol, the pressure breakpoint was not observed in the range of voltage applied in the experiments. The EHD flow velocity was measured by using microbubbles and particles as flow tracers. An adaptive phase-Doppler velocimeter was employed to measure the velocity of bubbles, while the velocity of particles was measured by trajectory visualization of fluorescent particles. A discrepancy was observed between the two methods because of the location at which the measurements were made. It was found that average velocities of both bubbles and particles increase linearly with applied voltage. Experiments were also conducted to investigate pumping of water, which is a result of the EHD velocity near the capillary tip. The pumping flow rate was linearly related to the applied voltage and agreed well with EHD velocity measurements obtained from particle trajectories. Copyright 2000 Academic Press.     

Movement of colloidal particles in two-dimensional electric fields

We characterize the movement of carbon black particles in inhomogeneous, two-dimensional dc electric fields. Motivated by display applications, the particles are suspended in a nonpolar solvent doped with a charge control agent. The two-dimensional fields are generated between strip electrodes on a glass slide spaced 120 microm apart with field strengths up to 10(4) V/m. Such fields are insufficient to drive either electrohydrodynamic instabilities or natural convection due to ohmic heating, but they move the particles between the electrodes in about 30 s. In the center region between the strip electrodes, the particles move by electrophoresis; that is, the particle velocity is proportional to the electric field. However, when imposing a constant-potential or constant-current boundary condition at the electrodes to derive the electrical field, the electrophoretic mobility calculated from the measured particle velocities is outside the range of mobilities predicted from the theory of O'Brien and White. Near the electrodes the particles either speed up or slow down, depending on the polarity of the electrode, and these changes in velocity cannot be explained simply by electrophoresis in a spatially varying electric field. We suggest that this anomalous motion arises from electrohydrodynamic flows originating from the interaction between the space charge of the polarized layers above the electrodes and the electric field. Approximate calculations indicate such flows could be sufficiently strong to explain the anomalous trajectories near the edges of the electrodes.     

Electrophoretic measurement of water charge density and ion hydration

Water exchange between bulk water and water-ion complexes will be at equilibrium when the charge density of the complex surface equals the charge density of bulk water, producing a constant radius water-ion complex. This complex will migrate in an electric field at a velocity proportional to the complex radius. CE velocity is the sum of the complex charge-dependent velocity and the buffer electro-osmotic flow. Simultaneous use of both a base (1.07 mM imidazole) and an acid (1.5 mM MOPS) buffer negates EOF at pH 7.4. Electric fields below 300 V/cm (potassium, calcium) and 400 V/cm (magnesium) yield migration velocities with no dehydration of the water-ion complexes. The number of waters per complex increase with the ion charge density: K⁺ 1.90, Ca⁺⁺ 5.90, Mg⁺⁺ 6.59 waters/ion. The charge densities of the complexes are similar: K⁺ 1.24, Ca⁺⁺ 1.43, Mg⁺⁺ 1.21 e/nm², for an average bulk water charge density of 1.29 ± 0.11 (SD) e/nm². The addition of 0.1% Triton increases the number of waters for Mg⁺⁺ to 25.33 and lowers the charge density to 0.497 e/nm². High electric field dehydration shows that calcium will be fully dehydrated at 638.3 V/cm and magnesium fully dehydrated at 925.5 V/cm, which occur at 6.15 and 5.78 nm from the membrane. Dehydrated magnesium will then bind to calcium channels leading to decreased smooth muscle activation.     

Observations of the near-wall accumulation of suspended particles due to shear and electroosmotic flow in opposite directions

On the basis of previous studies, the particles in a dilute (volume fractions φ_∞ < 4 × 10^–3) suspension in combined Poiseuille and electroosmotic “counterflow” at flow Reynolds numbers Re ≤ 1 accumulate, then assemble into structures called “bands,” within ∼6 μm of the channel wall. The experimental studies presented here use a small fraction of tracer particles labeled with a different fluorophore from the majority “bulk” particles to visualize the dynamics of individual particles in a φ_∞ = 1.7 × 10^–3 suspension. The results at two different near-wall shear rates and three electric field magnitudes E show that the near-wall particles are concentrated about 150-fold when the bands start to form, and are then concentrated about 200-fold to a maximum near-wall volume fraction of ∼0.34. The growth in the near-wall particles during this accumulation stage appears to be exponential. This near-wall particle accumulation is presumably driven by a wall-normal “lift” force. The observations of how the particles accumulate near the wall are compared with recent analyses that predict that suspended particles subject to shear flow and a dc electric field at small particle Reynolds numbers experience such a lift force. A simple model that assumes that the particles are subject to this lift force and Stokes drag suggests that the force driving particles toward the wall, of O(10^–17 N), is consistent with the time scales for particle accumulation observed in the experiments.     

A new insight to the role of bubble properties on inertial effect in particle–bubble interaction

In this study the impact of bubble surface characterization (mobility or immobility), its diameter and velocity is investigated on inertial forces in particle–bubble collision efficiency (E_C). Three models including Sutherland (E_C-SU), Schulze (E_C-SC), and generalized Sutherland Equation (E_C-GSE) were taken into account with regard to their differences from the inertial point of view in the particle size range of 1–100?µm. Bubble diameters of 0.08, 0.12, and 0.15?cm and bubble velocities of 10, 20 and 30?cm/s were selected to study the flotation of chalcopyrite. Weber and Paddock collision model (E_C-W&P) was taken for evaluation of the effect of bubble surface mobility on E_C. It was found that when the bubble diameter is 0.12?cm, reducing bubble velocity from 30 to 20?cm/s, the inertia force can be ignored for wider range of particle size. Corresponding particle size in cross-sectional point between GSE and Schulze collision models was introduced for better evaluation of the positive and negative particle inertial effects. The best agreement between them was taken for bubble diameter of 0.12?cm and velocity of 20?cm/s. It was concluded that the influence of bubble velocity is more effective than bubble diameter regarding its role on particle inertial forces in particle–bubble interaction.     

A continuous DC-insulator dielectrophoretic sorter of microparticles

A lab-on-a-chip device is described for continuous sorting of fluorescent polystyrene microparticles utilizing direct current insulating dielectrophoresis (DC-iDEP) at lower voltages than previously reported. Particles were sorted by combining electrokinetics and dielectrophoresis in a 250 μm wide PDMS microchannel containing a rectangular insulating obstacle and four outlet channels. The DC-iDEP particle flow behaviors were investigated with 3.18, 6.20 and 10 μm fluorescent polystyrene particles which experience negative DEP forces depending on particle size, DC electric field magnitude and medium conductivity. Due to negative DEP effects, particles are deflected into different outlet streams as they pass the region of high electric field density around the obstacle. Particles suspended in dextrose added phosphate buffer saline (PBS) at conductivities ranging from 0.50 to 8.50 mS/cm at pH 7.0 were compared at 6.85 and 17.1 V/cm. Simulations of electrokinetic and dielectrophoretic forces were conducted with COMSOL Multiphysics^® to predict particle pathlines. Experimental and simulation results show the effect of medium and voltage operating conditions on particle sorting. Further, smaller particles experience smaller iDEP forces and are more susceptible to competing nonlinear electrostatic effects, whereas larger particles experience greater iDEP forces and prefer channels 1 and 2. This work demonstrates that 6.20 and 10 μm particles can be independently sorted into specific outlet streams by tuning medium conductivity even at low operating voltages. This work is an essential step forward in employing DC-iDEP for multiparticle sorting in a continuous flow, multiple outlet lab-on-a-chip device.     

Nonlinear electrokinetics and "superfast" electrophoresis

Nonlinear and nonequilibrium electrophoresis of spherical particles of radius a is shown to be possible when the solid surface allows field or current penetration. At low particle Peclet numbers, transient capacitative charging occurs until the surface polarization completely screens the external field. For a DC applied field [see text], the resulting electrokinetic velocity reaches Dukhin's maximum value of [formula: see text], where [see text] and mu are the liquid permittivity and viscosity. At high Peclet numbers, electroosmotic convection of the electroneutral bulk stops the transient charging before complete field-line exclusion. For an ion-selective and conducting spherical granule, the polarization is then determined by the steady-state Ohmic current driven by the penetrated external field. The high-Peclet electrokinetic velocity is lower, diffusivity-dependent and scales as [see text].     

Electrophoresis of a colloidal sphere in a spherical cavity with arbitrary zeta potential distributions

An analytical study is presented for the quasi-steady electrophoretic motion of a dielectric sphere situated at the center of a spherical cavity when the surface potentials are arbitrarily nonuniform. The applied electric field is constant, and the electric double layers adjacent to the solid surfaces are assumed to be much thinner than the particle radius and the gap width between the surfaces. The presence of the cavity wall causes three basic effects on the particle velocity: (1) the local electric field on the particle surface is enhanced or reduced by the wall; (2) the wall increases the viscous retardation of the moving particle; and (3) a circulating electroosmotic flow of the suspending fluid exists because of the interaction between the electric field and the charged wall. The Laplace and Stokes equations are solved analytically for the electric potential and velocity fields, respectively, in the fluid phase, and explicit formulas for the electrophoretic and angular velocities of the particle are obtained. To apply these formulas, one has to calculate only the monopole, dipole, and quadrupole moments of the zeta-potential distributions at the particle and cavity surfaces. It is found that the contribution from the electroosmotic flow developing from the interaction of the imposed electric field with the thin double layer adjacent to the cavity wall and the contribution from the wall-corrected electrophoretic driving force to the particle velocities can be superimposed as a result of the linearity of the problem.     

Theory of large agglomerates in magnetic colloids

Very large agglomerates in magnetic colloids have been observed experimentally in settling velocity experiments by Peterson and Krueger [J. Colloid Interface Sci. 62, 24 (1977)]. We investigate the size, shape, and settling velocities of the agglomerates as a function of applied magnetic field. The bases for our theory are: (a) the minimization of the energy, magnetic plus surface tension, and (b) the marginal stability of the trailing particle in the gravitationally settling agglomerate. The latter is a balance between the magnetic force holding the particle on the agglomerate and the hydrodynamic drag force pulling it away from the agglomerate. For 200-G waterbase ferrofluid, the settling velocities range from 4 x 10⁻⁴ to 4 x 10⁻³ cm/sec for applied fields from 2 to 230 Oe. The number of particles/agglomerate and the minor axis/major axis ratio vary from 10⁸ to 10¹² and 10⁻¹ to 10⁻⁴, respectively. The theory reproduces the qualitative features of the settling velocity as a function of magnetic field.     

Experimental study on the optimization of general conditions for a free‐flow electrophoresis device with a thermoelectric cooler†

With a given free‐flow electrophoresis device, reasonable conditions (electric field strength, carrier buffer conductivity, and flow rate) are crucial for an optimized separation. However, there has been no experimental study on how to choose reasonable general conditions for a free‐flow electrophoresis device with a thermoelectric cooler in view of Joule heat generation. Herein, comparative experiments were carried out to propose the selection procedure of general conditions in this study. The experimental results demonstrated that appropriate conditions were (i) <67 V/cm electric field strength; (ii) lower than 1.3 mS/cm carrier buffer conductivity (Tris‐HCl: 20 mM Tris was titrated by HCl to pH 8.0); and (iii) higher than 3.6 mL/min carrier buffer flow rate. Furthermore, under inappropriate conditions (e.g. 400 V voltage and 40 mM Tris‐HCl carrier buffer), the free‐flow electrophoresis separation would be destroyed by bubbles caused by more Joule heating. Additionally, a series of applications under the appropriate conditions were performed with samples of model dyes, proteins (bovine serum albumin, myoglobin, and cytochrome c), and cells (Escherichia coli, Streptococcus thermophilus, and Saccharomyces cerevisiae). The separation results showed that under the appropriate conditions, separation efficiency was obviously better than that in the previous experiments with randomly or empirically selected conditions.     

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.     

Temperature gradient focusing in a PDMS/glass hybrid microfluidic chip

This paper reports the application of temperature gradient focusing (TGF) in a PDMS/glass hybrid microfluidic chip. With TGF, by the combination of a temperature gradient along a microchannel, an applied electric field, and a buffer with a temperature-dependent ionic strength, analytes are focused by balancing their electrophoretic velocities against the bulk velocity of the buffer containing the analytes. In this work, Oregon Green 488 carboxylic acid was concentrated approximately 30 times as high as the initial concentration in 45 s at moderate electric strength of 70 V/cm and a temperature gradient of 55 degrees C across the PDMS/glass hybrid microfluidic chip with a 1 cm long capillary.     

Size-dependent electrophoretic motion of polystyrene particles at polyethylene glycol–dextran interfaces

Currently, there is very limited information on the electrophoretic behavior of particles at a liquid–liquid interface formed by two conducting liquid solutions. Here, electrophoretic velocities of polystyrene particles at a polyethylene glycol (PEG)–dextran (DEX) interface were investigated in this paper. Experimental results show that the particle at the interface moves in the opposite direction to the applied electric field, with a velocity much lower than that in the PEG-rich phase and a litter larger than that in the DEX-rich phase. Similarly to the movement in Newtonian fluids, the velocity increases linearly with the increase in the applied electric field. Different to particle electrophoresis in Newtonian fluids, the velocities of the particles at the PEG–DEX interface increase linearly with the decrease in particle's diameters, implying a possible size-based particle differentiation at an interface.     

Characterization of electrokinetic mobility of microparticles in order to improve dielectrophoretic concentration

Insulator-based dielectrophoresis (iDEP), an efficient technique with great potential for miniaturization, has been successfully applied for the manipulation of a wide variety of bioparticles. When iDEP is applied employing direct current (DC) electric fields, other electrokinetic transport mechanisms are present: electrophoresis and electroosmotic flow. In order to concentrate particles, iDEP has to overcome electrokinetics. This study presents the characterization of electrokinetic flow under the operating conditions employed with iDEP; in order to identify the optimal conditions for particle concentration employing DC-iDEP, microparticle image velocimetry (μPIV) was employed to measure the velocity of 1-μm-diameter inert polystyrene particles suspended inside a microchannel made from glass. Experiments were carried out by varying the properties of the suspending medium (conductivity from 25 to 100 μS/cm and pH from 6 to 9) and the strength of the applied electric field (50–300 V/cm); the velocities values obtained ranged from 100 to 700 μm/s. These showed that higher conductivity and lower pH values for the suspending medium produced the lowest electrokinetic flow, improving iDEP concentration of particles, which decreases voltage requirements. These ideal conditions for iDEP trapping (pH = 6 and σ _m = 100 μS/cm) were tested experimentally and with the aid of mathematical modeling. The μPIV measurements allowed obtaining values for the electrokinetic mobilities of the particles and the zeta potential of the glass surface; these values were used with a mathematical model built with COMSOL Multiphysics software in order to predict the dielectrophoretic and electrokinetic forces exerted on the particles; the modeling results confirmed the μPIV findings. Experiments with iDEP were carried out employing the same microparticles and a glass microchannel that contained an array of cylindrical insulating structures. By applying DC electric fields across the insulating structures array, it was seen that the dielectrophoretic trapping was improved when the electrokinetic force was the lowest; as predicted by μPIV measurements and the mathematical model. The results of this study provide guidelines for the selection of optimal operating conditions for improving insulator-based dielectrophoretic separations and have the potential to be extended to bioparticle applications. Figure Comparison of experimental measurements and mathematical modeling of electrokinetic and dielectrophoretic effects on microparticles

Molecular dynamics simulations of electroosmosis in perfluorosulfonic acid polymer

An atomistic MD simulation method has been developed to study the electroosmotic drag in the hydrated perfluorosulfonic acid polymer. The transport characteristics of the hydroniums and water molecules are evaluated from their velocity distribution functions with an electric field applied. It is shown that the microstructure of the hydrated perfluorosulfonic acid polymer is not perturbed significantly by the electric field up to 2 V/microm, and the velocity distribution functions obey the peak shifted Maxwell velocity distribution functions. The evaluated peak shifting velocities are only about 1% of the average thermal motion. The hydronium flow and water flow are evaluated from the average transport velocities or the peak shifting velocities. The electroosmotic drag coefficients from the MD simulations are in good correspondence with the experimental values. It is also shown that the electroosmotic drag coefficient has no or weak temperature dependence.     

Influence of velocity and surface temperature of alumina particles on the properties of plasma sprayed coatings

In this paper are described the main characteristics of the plasma spraying process of alumina deposits, i.e., the temperature and flow field of the plasma jets obtained with the classical spraying torches, the injection of the particles into the plasma jet, the particle surface temperature and velocities in the plasma (measured for calibrated alumina particles), and the coating generation. The measurements on the alumina particles are compared with the predictions of a mathematical model. The experimental and computed particle velocities are in rather good agreement. However, this is not the case for the particle surface temperature. Possible reasons for the discrepancy are proposed (influence of the carrier gas, thermophoretic forces, and poor penetration of the particles into the plasma core even for an injection velocity twice that of the optimal calculated one, as shown by recent measurements). Finally the correlations between the particle velocities and surface temperature, and the properties of the alumina coating (porosity, crystal structure, mechanical properties) are studied.     

Electrorheological suspensions of laponite in oil: rheometry studies

We have studied the effect of an external direct current (DC) electric field ( approximately 1 kV/mm) on the rheological properties of colloidal suspensions consisting of aggregates of laponite particles in a silicone oil. Microscopy observations show that, under application of an electric field greater than a triggering electric field Ec approximately 0.6 kV/mm, laponite aggregates assemble into chain- and/or columnlike structures in the oil. Without an applied electric field, the steady-state shear behavior of such suspensions is Newtonian-like. Under application of an electric field larger than Ec, it changes dramatically as a result of the changes in the microstructure: a significant yield stress is measured, and under continuous shear the fluid is shear-thinning. The rheological properties, in particular the dynamic and static shear stress, were studied as a function of particle volume fraction for various strengths (including null) of the applied electric field. The flow curves at constant shear rate can be scaled with respect to both the particle fraction and electric field strength onto a master curve. This scaling is consistent with simple scaling arguments. The shape of the master curve accounts for the system's complexity; it approaches a standard power-law model at high Mason numbers. Both dynamic and static yield stresses are observed to depend on the particle fraction Phi and electric field E as PhibetaEalpha, with alpha approximately 1.85 and beta approximately 1 and 1.70 for the dynamic and static yield stresses, respectively. The yield stress was also determined as the critical stress at which there occurs a bifurcation in the rheological behavior of suspensions that are submitted to a constant shear stress; a scaling law with alpha approximately 1.84 and beta approximately 1.70 was obtained. The effectiveness of the latter technique confirms that such electrorheological (ER) fluids can be studied in the framework of thixotropic fluids. The method is very reproducible; we suggest that it could be used routinely for studying ER fluids. The measured overall yield stress behavior of the suspensions may be explained in terms of standard conduction models for electrorheological systems. Interesting prospects include using such systems for guided self-assembly of clay nanoparticles.     

Diffusiophoresis and electrophoresis of a charged sphere perpendicular to two plane walls

The problem of diffusiophoretic and electrophoretic motions of a dielectric spherical particle in an electrolyte solution situated at an arbitrary position between two infinite parallel plane walls is studied theoretically in the quasisteady limit of negligible Peclet and Reynolds numbers. The applied electrolyte concentration gradient or electric field is uniform and perpendicular to the plane walls. The electric double layer at the particle surface is assumed to be thin relative to the particle radius and to the particle-wall gap widths, but the polarization effect of the diffuse ions in the double layer is incorporated. To solve the conservative equations, the general solution is constructed from the fundamental solutions in both cylindrical and spherical coordinates. The boundary conditions are enforced first at the plane walls by the Hankel transforms and then on the particle surface by a collocation technique. Numerical results for the diffusiophoretic and electrophoretic velocities of the particle relative to those of a particle under identical conditions in an unbounded solution are presented for various cases. The collocation results agree well with the approximate analytical solutions obtained by using a method of reflections. The presence of the walls can reduce or enhance the particle velocity, depending on the properties of the particle-solution system and the relative particle-wall separation distances. The boundary effects on diffusiophoresis and electrophoresis of a particle normal to two plane walls are found to be quite significant and complicated, and generally stronger than those parallel to the confining walls.