Zeta potentials of polydimethylsiloxane surfaces modified by polybrene of different concentrations

Zeta potential is an important parameter for characterizing the electrokinetic properties of a solid–liquid interface. In this paper, zeta potentials of polydimethylsiloxane surfaces modified by polybrene (PB) solutions of different concentrations in Phosphate buffer solution and pure water were reported. The zeta potentials were measured by an induction current method. The measurements were validated both by a calibration curve based on the data reported in the published papers and by comparing the zeta potential determined by using the Smoluchowski equation and the measured velocity of the electrokinetic motion of particles in a microchannel.     

A method for simultaneously determining the zeta potentials of the channel surface and the tracer particles using microparticle image velocimetry technique

The zeta potentials of channel surfaces and tracer particles are of importance to the design of electrokinetic microfluidic devices, the characterization of channel materials, and the quantification of the microparticle image velocimetry (microPIV) measurement of EOFs. A method is proposed to simultaneously measure the zeta potentials of the channel surface and the tracer particles in aqueous solutions using the microPIV technique. Through the measurement of the steady velocity distributions of the tracer particles in both open- and closed-end rectangular microchannels under the same water chemistry condition, the electrophoretic velocity of the tracer particles and the EOF field of the microchannel are determined using the expressions derived in this study for the velocity distributions of charged tracer particles in the open- and closed-end rectangular microchannels. Thus, the zeta potentials of the tracer particles and the channel surfaces are simultaneously obtained using the least-square method to fit the microPIV measured velocity distribution of the tracer particles. Measurements were carried out with a microPIV system to determine the zeta potentials of the channel wall and the fluorescent tracer particles in deionized water and sodium chloride and boric acid solutions of various concentrations.     

Estimation of zeta potential by electrokinetic analysis of ionic fluid flows through a divergent microchannel

The streaming potential is generated by the electrokinetic flow effect within the electrical double layer of a charged solid surface. Surface charge properties are commonly quantified in terms of the zeta potential obtained by computation with the Helmholtz-Smoluchowski (H-S) equation following experimental measurement of streaming potential. In order to estimate a rigorous zeta potential for cone-shaped microchannel, the correct H-S equation is derived by applying the Debye-Hückel approximation and the fluid velocity of diverging flow on the specified position. The present computation provides a correction ratio relative to the H-S equation for straight cylindrical channel and enables us to interpret the effects of the channel geometry and the electrostatic interaction. The correction ratio decreases with increasing of diverging angle, which implies that smaller zeta potential is generated for larger diverging angle. The increase of Debye length also reduces the correction ratio due to the overlapping of the Debye length inside of the channel. It is evident that as the diverging angle of the channel goes to nearly zero, the correction ratio converges to the previous results for straight cylindrical channel.     

Revisit of wall‐induced lateral migration in particle electrophoresis through a straight rectangular microchannel: Effects of particle zeta potential

Previous studies have reported a lateral migration in particle electrophoresis through a straight rectangular microchannel. This phenomenon arises from the inherent wall‐induced electrical lift that can be exploited to focus and separate particles for microfluidic applications. Such a dielectrophoretic‐like force has been recently found to vary with the buffer concentration. We demonstrate in this work that the particle zeta potential also has a significant effect on the wall‐induced electrical lift. We perform an experimental study of the lateral migration of equal‐sized polystyrene particles with varying surface charges under identical electrokinetic flow conditions. Surprisingly, an enhanced focusing is observed for particles with a faster electrokinetic motion, which indicates a substantially larger electrical lift for particles with a smaller zeta potential. We speculate this phenomenon may be correlated with the particle surface conduction that is a strong function of particle and fluid properties.     

Analytical investigations on the effects of substrate kinetics on macromolecular transport and hybridization through microfluidic channels

In this paper, a generalized surface-kinetics based model is developed to analytically investigate the influences of the substrate types and the buffer compositions on the macromolecular transport and hybridization in microfluidic channels, under electrokinetic influences. For specific illustration, three typical microchannel substrates, namely silanized glass, polycarbonate and PDMS, are considered, in order to obtain analytical expressions for their zeta potentials as a function of the buffer pH and the substrate compositions. The expressions for the zeta potential are subsequently employed to derive the respective velocity distributions, under the application of electric fields of identical strengths in all cases. It is also taken into consideration that the charged macromolecules introduced into these channels are subjected to electrophoretic influences on account of the applied electric fields. Closed form expressions are derived to predict the transport behaviour of the macromolecules and their subsequent hybridization characteristics. From the analysis presented, it is shown that the modification of the channel surface with silane-treatment becomes useful for enhancing the macromolecular transport and surface hybridization, only if the buffer pH permits a large surface charge density. The analytical solutions are also compared with full-scale numerical solutions of the coupled problem of fluid dynamic and macromolecular transport in presence of the pertinent surface reactions, in order to justify the effectiveness of closed-form expressions derived in this study.     

Particle interactions in electrophoresis: I. Motion of two spheres along their line of centers

The electrophoretic motion of two charged colloidal spheres with very thin electrical double layers in a constant applied electric field along their line of centers is considered. The particles may differ in radius and in zeta potential at the surface. The electrostatic and hydrodynamic governing equations are solved in the quasi-steady situation using bipolar coordinates and the electrophoretic velocities of particles are calculated for various cases. The interaction effect between particles can be very significant when the distance between particle surfaces gets close to zero. The particle with smaller zeta potential is speeded up by the motion of the other, which is retarded at the same time by the motion of the former one, if the two spheres have unequal zeta potentials of the same electrical sign. For two particles of different signs in zeta potential, motions of both are hindered by each other. The influence of the interaction between particles in general is stronger on the smaller one than on the larger one. For the special case of two electrophoretic spheres with identical zeta potentials, there is no particle interaction for all particle sizes and separations.     

On the characterization of electrified interface

Summary Estimation of zeta potential from experimental data on electroosmotic and electrophoretic effects for Zeokarb 225 (Na⁺ form)/methanol-water system has been made and discussed. Results indicate that zeta potentials estimated from electroosmotic flux and electrophoretic mobility are not in agreement and vary with applied potential difference in a linear manner. Reasons for the variation of zeta potential with electrical field have been discussed. It has been argued that zeta potentials estimated from electroosmotic data are more reliable in comparison to the values obtained from electrophoretic data.With 2 figures and 2 tables     

An Improved Method of Determining the zeta-Potential and Surface Conductance

In the classical "slope-intercept" method of determining the zeta potential and the surface conductance, the relationship between DeltaP and E(s) is measured experimentally at a number of different channel sizes (e.g., the height of a slit channel, h). The parameter (epsilon(r)epsilon(0)DeltaP/μE(s)lambda(b)) is then plotted as a function of 1/h and linear regression is performed. The y-intercept of the regressed line is then related to the zeta-potential and its slope to the surface conductance. However, in this classical method, the electrical double layer effect or the electrokinetic effects on the liquid flow are not considered. Consequently, this technique is valid or accurate only when the following conditions are met: (1) relatively large channels are used; (2) the electrical double layer is sufficiently thin; and (3) the streaming potential is sufficiently small that the electroosmotic body force on the mobile ions in the double layer region can be ignored. In this paper a more general or improved slope-intercept method is developed to account for cases where the above three conditions are not met. Additionally a general least-squares analysis is described which accounts for uncertainty in the measured channel height as well as unequal variance in the streaming potential measurements. In this paper, both the classical and the improved slope-intercept techniques have been applied to streaming potential data measured with slit glass channels, ranging in height from 3 μm to 66 μm, for several aqueous electrolyte solutions. The comparison shows that the classical method will always overestimate both the zeta-potential and the surface conductance. Significant errors will occur when the classical method is applied to systems with small channel heights and low ionic concentrations. Furthermore, it is demonstrated that traditional regression techniques where the uncertainty is confined only to the dependent variable and each measurement is given equal weight may produce physically inconsistent results. Copyright 2000 Academic Press.     

Analysis of electrokinetic transport of a spherical particle in a microchannel

Electrokinetically driven microfluidic devices that are used for biological cell/particle manipulation (e.g., cell sorting, separation) involve electrokinetic transport of these particles in microchannels whose dimension is comparable with particles' size. This paper presents an analytical study on electrokinetic transport of a charged spherical particle in a charged parallel-plate microchannel. Under the thin electric double-layer assumption, solutions in closed-form solutions for the particle velocity and disturbed electrical and fluid velocity fields are obtained for plane-symmetric (along the channel centerline) and asymmetric (off the channel centerline) motions of a sphere in a parallel-plate microchannel. The effects of relative particle size and eccentricity (i.e., off the centerline distance) on a particle's translational and rotational velocities are analyzed.     

Problems and results of zeta-potential measurements on fibers

A survey is given on both theoretical background and methodical details of zeta-potential measurements on fibers. Electro-osmosis and streaming potential/streaming current measurements can be used in order to obtain correct zeta-potentials. Both measuring principles yield the same values for zeta-potential if the errors due to resistance measurements are avoided. This agreement as well as the independence of zeta-potential of applied voltage (in the case of electro-osmosis) and hydrostatic pressure (in the case of streaming potential/streaming current) point out that the Stern-potential at the boundary immobile/diffuse layer can be determined. Electrophoresis and measurement of other electrokinetic phenomena give values related to but not identical with the zeta-potential. Applications of electrokinetic measurements for investigating fiber problems in production, processing and finishing are reviewed. Parameters determining the zeta-potential of fibers are discussed.Dedicated to Prof. Dr. E. R. Schwarzl with congratulations for his 60th birthday.     

Diffusiophoresis in a suspension of spherical particles with arbitrary double-layer thickness

The diffusiophoresis in a homogeneous suspension of identical dielectric spheres with an arbitrary thickness of the electric double layers in a solution of a symmetrically charged electrolyte with a constant imposed concentration gradient is analytically studied. The effects of particle interactions (or particle volume fraction) 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 that govern the ionic concentration distributions, the electrostatic 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 diffusiophoretic velocity of the dielectric sphere in closed form correct to the second order of its surface charge density or zeta potential are obtained from a balance between its electrostatic and hydrodynamic forces. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made.     

Dielectrophoretic focusing of particles in a microchannel constriction using DC‐biased AC flectric fields

This paper presents a fundamental study of particle electrokinetic focusing in a single microchannel constriction. Through both experiments and simulations, we demonstrate that such dielectrophoresis‐induced particle focusing can be implemented in a much smaller magnitude of DC‐biased AC electric fields (10 kV/m in total) as compared to pure DC electric fields (up to 100 kV/m). This is attributed to the increase in the ratio of cross‐stream particle dielectrophoretic velocity to streamwise electrokinetic velocity as only the DC field component contributes to the latter. The effects of the 1 kHz frequency AC to DC electric field ratio on particle trajectories and velocity variations through the microchannel constriction are also examined, which are found to agree with the simulation results.     

Streaming potential and electroosmotic flow in heterogeneous circular microchannels with nonuniform zeta potentials: requirements of flow rate and current continuities

Real surfaces are typically heterogeneous, and microchannels with heterogeneous surfaces are commonly found due to fabrication defects, material impurities, and chemical adsorption from solution. Such surface heterogeneity causes a nonuniform surface potential along the microchannel. Other than surface heterogeneity, one could also pattern the various surface potentials along the microchannels. To understand how such variations affect electrokinetic flow, we proposed a model to describe its behavior in circular microchannels with nonuniform surface potentials. Unlike other models, we considered the continuities of flow rate and electric current simultaneously. These requirements cause a nonuniform electric field distribution and pressure gradient along the channel for both pressure-driven flow (streaming potential) and electric-field-driven flow (electroosmosis). The induced nonuniform pressure and electric field influence the electrokinetic flow in terms of the velocity profile, the flow rate, and the streaming potential.     

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.     

Transport of charged samples in fluidic channels with large zeta potentials

In this article, we present an analysis on the transport of charged samples through micro- and nanofluidic channels with large zeta potentials (|zeta| > (kBT)/e). Using the Method of Moments formulation, the diffusion-convection equation has been solved to evaluate the mean velocity and the dispersion of analyte bands in a parallel-plate device under electrokinetically- and pressure-driven flow conditions. The effect of electromigration induced by the lateral electric field within the Debye layer has been quantified in our work using a Peclet number (Pe t) based on the characteristic electrophoretic velocity of the solute molecules in the transverse direction. It has been shown that while the effects of transverse electromigration on analyte transport only depends on the product Pe t zeta* for |zeta*| = (ezeta)/kBT < 1, both these parameters independently affect the flow of charged species in large zeta potential systems. For a given value of Pe t zeta*, the mean velocity and the slug dispersivity can vary by as much as an order of magnitude in going from a small zeta potential system (|zeta*| < 1) to a channel with |zeta*| = 4.     

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.     

On the surface conductance, flow rate, and current continuities of microfluidics with nonuniform surface potentials

The characteristics of electrokinetic flow in a microchannel depend on both the nature of surface potentials, that is, whether it is uniform or nonuniform, and the electrical potential distribution along the channel. In this paper, the nonlinear Poisson-Boltzmann equation is used to model the electrical double layer and the lattice Boltzmann model coupled with the constraint of current continuity is used to simulate the microfluidic flow field in a rectangular microchannel with a step variation of surface potentials. This current continuity, including surface conduction, convection, and bulk conduction currents, has often been neglected in the literature for electroosmotic flow with nonuniform (heterogeneous) microchannels. Results show that step variation of ion distribution caused by step variation surface potential will influence significantly the electrical potential distribution along the channel and volumetric flow rate. For the system considered, we showed that the volumetric flow rate could have been overestimated by as much as 70% without consideration of the current continuity constraint.     

Diffusiophoresis in a suspension of charge-regulating colloidal spheres

An analytical study of diffusiophoresis in a homogeneous suspension of identical spherical charge-regulating particles with an arbitrary thickness of the electric double layers in a solution of a symmetrically charged electrolyte with a uniform prescribed concentration gradient is presented. The charge regulation due to association/dissociation reactions of ionogenic functional groups on the particle surface is approximated by a linearized regulation model, which specifies a linear relationship between the surface charge density and the surface potential. The effects of particle-particle electrohydrodynamic 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 that govern the electric potential profile, the ionic concentration distributions, and the fluid flow field in the electrolyte solution surrounding the particle in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved with the equilibrium surface charge density (or zeta potential) of the particle as the small perturbation parameter. Closed-form formulas for the diffusiophoretic velocity of the charge-regulating sphere correct to the second order of its surface charge density or zeta potential are derived. Our results indicate that the charge regulation effect on the diffusiophoretic mobility is quite sensitive to the boundary condition for the electric potential specified at the outer surface of the unit cell. For the limiting cases of a very dilute suspension and a very thin or very thick electric double layer, the particle velocity is independent of the charge regulation parameter.