Electrokinetic potentials at the gas-aqueous interface by spinning cylinder electrophoresis

The natural buoyancy of gas bubbles has hampered conventional electrokinetic methods of evaluating charge at the gas-liquid interface. In this study, bubbles are held by centripetal force at the centre of a horizontal, rotating cylinder filled completely with liquid. Migration of the bubble along the axis of the cylinder can be achieved by applying a gravity force or an electrophoretic force. An expression for the drag coefficient has been developed and used to calculate surface charge densities and electrokinetic potentials. In the presence of potassium chloride, anionic and non-ionic surfactants, the electrokinetic potentials were negative (～2–5 mV) at the air-aqueous interface. A cationic surfactant rendered the zeta potential positive. A knowledge of the air-aqueous interfacial rheology is desirable if the drag coefficient, and consequently the zeta potential, at all types of gas-liquid interfaces is to be evaluated.     

DC-electrokinetic motion of colloidal cylinder(s) in the vicinity of a conducting wall

The boundary effects on DC-electrokinetic behavior of colloidal cylinder(s) in the vicinity of a conducting wall is investigated through a computational model. The contribution of the hydrodynamic drag, gravity, electrokinetic (i.e., electrophoretic and dielectrophoretic), and colloidal forces (i.e., forces due to the electrical double layer and van der Waals interactions) are incorporated in the model. The contribution of electrokinetic and colloidal forces are included by introducing the resulting forces as an external force acting on the particle(s). The colloidal forces are implemented with the prescribed expressions from the literature, and the electrokinetic force is obtained by integrating the corresponding Maxwell stress tensor over the particles' surfaces. The electrokinetic slip-velocity together with the thin electrical double layer assumption is applied on the surfaces. The position and velocity of the particles and the resulting electric and flow fields are obtained and the physical insight for the behavior of the colloidal cylinders are discussed in conjunction with the experimental observations in the literature.     

Electrokinetic lift force for a charged particle moving near a charged wall — a modified theory and experiment

We present the refined theory of the electrokinetic lift force for a charged particle moving at a charged wall at the distance much larger than the double layer thickness. The theory is based on the lubrication approximation for the solution of the Stokes equation for the flow around a long cylinder moving near a solid wall. The “thin double layer” approximation is used to solve the ionic balance and electro-osmotic flow equations. The electrokinetic lift force is then obtained by integration of the viscous stress tensor as well as the Maxwell stress tensor over the particle surface. The resulting lift force for the cylinder translating, rotating at the wall as well as for the stationary cylinder in the wall shear flow, is considered. Following this, we apply the Derjaguin approximation to transform the obtained results to the sphere–wall geometry and we compare our theoretical predictions with the measurements of the electrokinetic lift force performed in the “colloidal particle collider” apparatus for the latex particles suspended in the glycerol–water solutions. Our theoretical results for the electrokinetic lift force exceeds by several orders of magnitude one obtained from the previously developed theory and are in a good agreement with experimental findings.     

Focused electrophoretic motion and selected electrokinetic dispensing of particles and cells in cross-microchannels

The electrokinetic focusing and the resultant accelerated electrophoretic motion of polystyrene particles and red blood cells were visualized in microfluidic cross-channels. The experimentally measured width of the focused stream and the measured velocity increase of particles and cells at different voltage ratios follow the proposed analytical formula within the experimental error. The attained velocity increase is insensitive to the particle size, particle property (i.e., particle or cell), and particle trajectory. By solving the electrical potential field in the cross-channel at the experimental conditions, we demonstrate that the squeezed electrical field lines in the channel intersection determine the shape of the focused stream, and the nonuniform distribution of axial electrical field strength underlies the variation of particle/cell electrophoretic velocity through the focusing region. However, the dielectrophoretic force resulting from the nonuniform electrical field in the intersection seems to push the acceleration region of particles and cells slightly in the downstream direction. We have also achieved the single particle/cell dispensing by instantly triggering an electrical pulse perpendicular to the focused particulate flow in a double-cross microchannel. The electrokinetic manipulation of particle/cell in microchannels demonstrated in this work can be used for developing integrated lab-on-a-chip devices for studies of cells.     

The Electrophoretic Mobility and Electric Conductivity of a Concentrated Suspension of Colloidal Spheres with Arbitrary Double-Layer Thickness

The electrophoresis in a monodisperse suspension of dielectric spheres with an arbitrary thickness of the electric double layers is analytically studied. The effects of particle interactions are taken into account by employing a unit cell model, and the overlap of the double layers of adjacent particles is allowed. The electrokinetic equations, which govern the ionic concentration distributions, the electric potential profile, and the fluid flow field in the electrolyte solution surrounding the charged sphere in a unit cell, are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved with the surface charge density (or zeta potential) of the particle as the small perturbation parameter. Analytical expressions for the electrophoretic mobility of the colloidal sphere in closed form correct to O(zeta) are obtained. Based on the solution of the electrokinetic equations in a cell, a closed-form formula for the electric conductivity of the suspension up to O(zeta(2)) is derived from the average electric current density. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made for both the electrophoretic mobility and the electric conductivity. Copyright 2001 Academic Press.     

The lateral electric force on an off-axis sphere in a circular cylinder

The electrophoretic velocity of a sphere within a liquid-filled circular cylinder in a direction parallel to the cylinder axis has been studied by Yariv and Brenner (Phys. Fluids 2002, 14, 3354–3357; SIAM J. Appl. Math. 2003, 64, 423–441). We use their analyses of the electric field in order to determine the electrical force on the sphere along the cylinder radius (i.e., perpendicular to its axis) when either the radius of the sphere is small compared to that of the cylinder, or when the radius of the sphere is only slightly smaller than that of the cylinder. In both cases the force acts towards the centreline of the cylinder, and hence this force tends to stabilize electrophoresis of the sphere along the cylinder axis.     

Controlled protein adsorption on a silica microparticle

In the present study, controlled protein adsorption on a rigid silica microparticle is investigated numerically using classical Langmuir and two-state models under electrokinetic flow conditions. The instantaneous particle locations are simulated along a straight microchannel using an arbitrary Lagrangian−Eulerian framework in the finite element method for the electrophoretic motion of the charged particle. Within the scope of the parametric study, the strength of the external electric field (E), particle diameter (D_p), the zeta potential of the particle (ζ_p), and the location of the microparticle away from the channel wall (H) are systematically varied. The results are also compared to the data of pressure-driven flow having a parabolic flow profile at the inlet whose maximum magnitude is set to the particle's electrophoretic velocity magnitude. The validation studies reveal that the code developed for the particle motion in the present simulations agrees well with the experimental results. It is observed that protein adsorption can be controlled using electrokinetic phenomena. The plug-like flow profile in electrokinetics is beneficial for a microparticle at every spatial location in the microchannel, whereas it is not valid for the pressure-driven flow. The electric field strength and the zeta potential of the particle accelerate the protein adsorption. The wall shear stress and shear rate are good indicators to predict the adsorption process for electrokinetic flow.     

Mesoporous hollow spheres from soap bubbling

The smaller and more stable bubbles can be generated from the large parent bubbles by rupture. In the presence of a bubble blowing agent, hollow spheres can be prepared by bubbling a silica sol. Herein, the trapped gas inside the bubble acts as a template. When the porogen, i.e., other surfactant, is introduced, a mesostructured shell forms by the co-assembly with the silica sol during sol-gel process. Morphological evolution emphasizes the prerequisite of an intermediate interior gas flow rate and high exterior gas flow rate for hollow spheres. The method is valid for many compositions from inorganic, polymer to their composites.     

Widening of the elution window in micellar electrokinetic chromatography with cationic surfactants. II. Cationic additives and modifiers of the electroosmotic flow.

In micellar electrokinetic chromatography (MEKC) with cationic surfactants the migration window is significantly narrower than with anionic surfactants. In order to overcome this disadvantage of cationic surfactants, it is investigated whether it is possible to widen the migration window by reducing the velocity of the aqueous phase while the electrophoretic mobility of the micelles is maintained. Short chain alkylammonium compounds, hexamethonium bromide and hydroxypropylmethylcellulose are tested as additives to the separation electrolyte with the potential to improve the migration window via reducing the velocity of the electroosmotic flow. It will be shown that these modifiers can be successfully used in order to widen the migration window in MEKC with cationic surfactant employing an alkyltrimethylammonium bromide as micelle forming agents. Influence of the modifiers selected on retention of neutral and acidic solutes and on efficiency of the separation system is investigated.     

Electrophoresis of a concentrated dispersion of spherical particles covered by an ion-penetrable membrane layer

The electrophoretic behavior of a concentrated dispersion of soft spherical particles is investigated theoretically, taking the effects of double-layer overlapping and double-layer polarization into account. Here, a particle comprises a rigid core and an ion-penetrable layer containing fixed charge, which mimics biocolloids and particles covered by artificial membrane layers. A cell model is adopted to simulate the system under consideration, and a pseudo-spectral method based on Chebyshev polynomials is chosen for the resolution of the governing electrokinetic equations. The influence of the key parameters, including the thickness of the double layer, the concentration of particles, the surface potential of the rigid core of a particle, and the thickness, the amount of fixed charge, and the friction coefficient of the membrane layer of a particle on the electrophoretic behavior of the system under consideration is discussed. We show that while the result for the case of a dispersion containing rigid particles can be recovered as the limiting case of a dispersion containing soft particles, qualitative behaviors that are not present in the former are observed in the latter.     

Startup of electrophoresis in a suspension of colloidal spheres

The transient electrophoretic response of a homogeneous suspension of spherical particles to the step application of an electric field is analyzed. The electric double layer encompassing each particle is assumed to be thin but finite, and the effect of dynamic electroosmosis within it is incorporated. The momentum equation for the fluid outside the double layers is solved through the use of a unit cell model. Closed‐form formulas for the time‐evolving electrophoretic and settling velocities of the particles in the Laplace transform are obtained in terms of the electrokinetic radius, relative mass density, and volume fraction of the particles. The time scale for the development of electrophoresis and sedimentation is significantly smaller for a suspension with a higher particle volume fraction or a smaller particle‐to‐fluid density ratio, and the electrophoretic mobility at any instant increases with an increase in the electrokinetic particle radius. The transient electrophoretic mobility is a decreasing function of the particle volume fraction if the particle‐to‐fluid density ratio is relatively small, but it may increase with an increase in the particle volume fraction if this density ratio is relatively large. The particle interaction effect in a suspension on the transient electrophoresis is much weaker than that on the transient sedimentation of the particles.     

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.     

Boundary effects on the electrophoretic motion of cylindrical particles: concentrically and eccentrically-positioned particles in a capillary

The bounded electrophoretic motion of a cylindrical particle in a circular cylindrical microchannel is explored for two cases: (1) the particle is located on the centerline of a channel (concentrically), with a symmetric wall boundary condition since gap width is constant throughout; and (2) the particle is at an eccentric location in the channel, with an asymmetric boundary condition set by the walls. The objective is to determine the effect of different boundary conditions, geometries, and physical properties on the velocity and orientation of the cylinder with respect to the boundary. A theoretical model for the motion of the cylinder is presented and the problem is solved numerically. The steady-state simulations show that the velocity of the cylinder is reduced at small gap widths for the concentric case, but the velocity is increased at small gap widths for the eccentric case. When the cylinder is angled with respect to the horizontal in the symmetric case or is near the boundary in the asymmetric case, vertical and rotational components of velocity are predicted. In such cases, transient simulations are appropriate for most accurately representing particle motion. Two such simulations are included herein and show both horizontal and vertical translation plus rotation of the particle as a function of time.     

Particle Interactions in Diffusiophoresis and Electrophoresis of Colloidal Spheres with Thin but Polarized Double Layers

The diffusiophoretic and electrophoretic motions of two colloidal spheres in the solution of a symmetrically charged electrolyte are analyzed using a method of reflections. The particles are oriented arbitrarily with respect to the electrolyte gradient or the electric field, and they are allowed to differ in radius and in zeta potential. The thickness of the electric double layers surrounding the particles is assumed to be small relative to the radius of each particle and to the gap width between the particles, but the effect of polarization of the mobile ions in the diffuse layer is taken into account. A slip velocity of fluid and normal fluxes of solute ions at the outer edge of the thin double layer are used as the boundary conditions for the fluid phase outside the double layers. The method of reflections is based on an analysis of the electrochemical potential and fluid velocity disturbances produced by a single dielectric sphere placed in an arbitrarily varying electrolyte gradient or electric field. The solution for two-sphere interactions is obtained in expansion form correct to O(r(12)(-7)), where r(12) is the distance between the particle centers. Our analytical results are found to be in good agreement with the available numerical solutions obtained using a boundary collocation method. On the basis of a model of statistical mechanics, the results of two-sphere interactions are used to analytically determine the first-order effect of the volume fraction of particles of each type on the mean diffusiophoretic and eletrophoretic velocities in a bounded suspension. For a suspension of identical spheres, the mean diffusiophoretic velocity can be decreased or increased as the volume fraction of the particles is increased, while the mean electrophoretic velocity is reduced with the increase in the particle concentration. Generally speaking, the particle interaction effects can be quite significant in typical situations. Copyright 2000 Academic Press.     

Single particle analysis using fluidic, optical and electrophoretic force balance in a microfluidic system

A unique microfluidic system is developed which enables the interrogation of a single particle by using multiple force balances from a combination of optical force, hydrodynamic drag force, and electrophoretic force. Two types of polystyrene (PS) particles with almost identical size and refractive index (plain polystyrene (PS) particle - mean diameter: 2.06 μm, refractive index: 1.59; carboxylated polystyrene (PS-COOH) particles - mean diameter: 2.07 μm, refractive index: 1.60), which could not be distinguished by optical chromatography, reveal different electrokinetic behaviors resulting from the difference in their surface charge densities. The PS-COOH particles, despite their higher surface charge density when compared to the PS particles, experience a lower electrophoretic force, regardless of ionic strength. This phenomenon can be understood when the more prominent polarization of the counter ion cloud surrounding the PS-COOH particles is considered. The surface roughness of the carboxylated particles also plays an important role in the observed electrokinetic behavior.     

Adsorption of heavy metal ions from aqueous solution by polyrhodanine-encapsulated magnetic nanoparticles

The influence of salt concentration on the terminal velocities of gravity-driven single bubbles sliding along an inclined glass wall has been investigated, in an effort to establish whether surface forces acting between the wall and the bubble influence the latter's mobility. A simple sliding bubble apparatus was employed to measure the terminal velocities of air bubbles with radii ranging from 0.3 to 1.5 mm sliding along the interior wall of an inclined Pyrex glass cylinder with inclination angles between 0.6 and 40.1°. Experiments were performed in pure water, 10 mM and 100 mM KCl solutions. We compared our experimental results with a theory by Hodges et al. which considers hydrodynamic forces only, and with a theory developed by two of us which considers surface forces to play a significant role. Our experimental results demonstrate that the terminal velocity of the bubble not only varies with the angle of inclination and the bubble size but also with the salt concentration, particularly at low inclination angles of ～1-5°, indicating that double-layer forces between the bubble and the wall influence the sliding behavior. This is the first demonstration that terminal velocities of sliding bubbles are affected by disjoining pressure.     

Analysis of rotation-driven electrokinetic flow in microscale gap regions of rotating disk systems

In the present study, a novel theoretical model is developed for the analysis of rotating thermal-fluid flow characteristics in the presence of electrokinetic effects in the microscale gap region between two parallel disks under specified electrostatic, rotational, and thermal boundary conditions. The major flow configuration considered is a rotor-stator disk system. Axisymmetric Navier-Stokes equations with consideration of electric body force stemming from streaming potential are employed in the momentum balance. Variations of the fluid viscosity and permittivity with the local fluid temperature are considered. Between two disks, the axial distribution of the electric potential is determined by the Poisson equation with the concentration distributions of positive and negative ions obtained from Nernst-Planck equations for convection-diffusion of the ions in the flow field. Effects of disk rotation and electrostatic and thermal conditions on the electrokinetic flow and thermal characteristics are investigated. The electrohydrodynamic mechanisms are addressed with an interpretation of the coupling nature of the electric and flow fields. Finally, solutions with electric potential determined by employing nonlinear or linearized Poisson-Boltzmann equation and/or invoking assumptions of constant properties are compared with the predictions of the present model for justification of various levels of approximation in solution of the electrothermal flow behaviors in rotating microfluidic systems.     

Influence of varying electroosmotic flow on the effective diffusion in electric field gradient separations

Recently the use electric field gradient focusing (EFGF) to enhance focusing of proteins has been proposed and explored to provide significant improvement in separation resolution. The objective of EFGF is to focus proteins of specific electrophoretic mobilities at distinct stationary locations in a column or channel. This can be accomplished in a capillary by allowing the electric potential to vary in the streamwise direction. Because the electric field is varying, so also is the electrokinetic force exerted on the proteins and the electroosmotic velocity of the buffer solution. Due to the varying electric field, the Taylor diffusion characteristics will also vary along the column, causing a degradation of peak widths of some proteins, dependent on their equilibrium positions and local velocity distributions. The focus of this paper is an analysis that allows characterization of the local Taylor diffusion and resulting protein band peak width as a function of the local magnitude of the EOF relative to the average fluid velocity for both cylindrical and rectangular channels. In general the analysis shows that as the ratio of the local electroosmotic velocity to the average velocity deviates from unity, the effective diffusion increases significantly. The effectiveness of EFGF devices over a range of protein diffusivities, capillary diameters, flow velocities, and electric field gradient is discussed.     

Electroviscous Forces on a Charged Cylinder Moving Near a Charged Wall

The refined theory of the electroviscous lift forces is presented for the case when the separation distance between the particle and the wall is larger than the double-layer thickness. The theory is based on the lubrication approximation for motion of a long cylinder near a solid wall in creeping flow. The approximate analytical formula for the lift force valid for Pe相似文献   

Sedimentation velocity and potential in concentrated suspensions of charged porous spheres

The body-force-driven migration in a homogeneous suspension of polyelectrolyte molecules or charged flocs in an electrolyte solution is analyzed. The model used for the particle is a porous sphere in which the density of the hydrodynamic frictional segments, and therefore also that of the fixed charges, is constant. The effects of particle interactions are taken into account by employing a unit cell model. The overlap of the electric double layers of adjacent particles is allowed and the relaxation effect in the double layer surrounding each particle is considered. The electrokinetic equations which govern the electrostatic potential profile, the ionic concentration (or electrochemical potential energy) distributions, and the fluid velocity field inside and outside the porous particle in a unit cell are linearized by assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved for a symmetrically charged electrolyte with the density of the fixed charges as the small perturbation parameter. An analytical expression for the settling velocity of the charged porous sphere is obtained from a balance among its gravitational, electrostatic, and hydrodynamic forces. A closed-form formula for the sedimentation potential in a suspension of identical charged porous spheres is also derived by using the requirement of zero net electric current. The dependence of the sedimentation velocity and potential of the suspension on the particle volume fraction and other properties of the particle-solution system is found to be quite complicated.