Simultaneous estimation of zeta potential and slip coefficient in hydrophobic microchannels

Electroosmotic flows through hydrophobic microchannels experience velocity slip at the channel wall, which increases the volumetric flow rate at a given electric potential gradient. The conventional method of zeta potential estimation using the volumetric flow rate may yield quite inaccurate zeta potential unless the velocity slip is appropriately taken care of. In the present investigation we develop a method for simultaneous estimation of zeta potential and velocity slip coefficient in the electroosmotic flow through a hydrophobic microchannel using velocity measurements. The relevant inverse problem is solved through the minimization of a performance function utilizing a conjugate gradient method. The present method is found to estimate the zeta potential and slip coefficient accurately even with noisy velocity measurements.     

A method for simultaneous estimation of inhomogeneous zeta potential and slip coefficient in microchannels

In the microchannels made of hydrophobic materials, the fluid velocity is determined by the zeta potential and velocity slip, both of which may be inhomogeneous due to the adsorption of protein to the channel wall. The inhomogeneity of zeta potential and slip coefficient sometimes causes recirculating flows which in turn affect the transport and mixing of solutes through the microchannels. In the present investigation we devise a method for the simultaneous estimation of inhomogeneous zeta potential and inhomogeneous slip coefficient using velocity measurements. A conjugate gradient method supplemented by the adjoint variable method is adopted in the solution of the relevant inverse problem to reduce the computational burden. The present method is found to estimate the inhomogeneous zeta potential and the slip coefficient simultaneously even with noisy velocity measurements. This method is expected to contribute to the optimal design and robust operation of various microfluidic devices, where the flow patterns and the volumetric flow rates are critically influenced by the profiles of inhomogeneous zeta potential and inhomogeneous slip coefficient.     

Diffusioosmosis of electrolyte solutions along a charged plane wall

The steady diffusioosmotic flow of an electrolyte solution along a dielectric plane wall caused by an imposed tangential concentration gradient is analytically examined. The plane wall may have either a constant surface potential or a constant surface charge density of an arbitrary quantity. The electric double layer adjacent to the charged wall may have an arbitrary thickness, and its electrostatic potential distribution is determined by the Poisson-Boltzmann equation. The macroscopic electric field along the tangential direction induced by the imposed electrolyte concentration gradient is obtained as a function of the lateral position. A closed-form formula for the fluid velocity profile is derived as the solution of a modified Navier-Stokes equation. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential of the wall and the properties of the electrolyte solution. For a given concentration gradient of an electrolyte along a plane wall, the magnitude of fluid velocity at a position in general increases with an increase in its electrokinetic distance from the wall, but there are exceptions. The effect of the lateral distribution of the induced tangential electric field in the double layer on the diffusioosmotic flow is found to be very significant and cannot be ignored.     

Estimation of the zeta potential and the dielectric constant using velocity measurements in the electroosmotic flows

In this paper we develop a method for the determination of the zeta potential zeta and the dielectric constant epsilon by exploiting velocity measurements of the electroosmotic flow in microchannels. The inverse problem is solved through the minimization of a performance function utilizing the conjugate gradient method. The present method is found to estimate zeta and epsilon with reasonable accuracy even with noisy velocity measurements.     

Numerical study of electroosmotic slip flow of fractional Oldroyd-B fluids at high zeta potentials

In this paper, an investigation of the electroosmotic flow of fractional Oldroyd-B fluids in a narrow circular tube with high zeta potential is presented. The Navier linear slip law at the walls is considered. The potential field is applied along the walls described by the nonlinear Poisson–Boltzmann equation. It's worth noting here that the linear Debye–Hückel approximation can't be used at the condition of high zeta potential and the exact solution of potential in cylindrical coordinates can't be obtained. Therefore, the Matlab bvp4c solver method and the finite difference method are employed to numerically solve the nonlinear Poisson–Boltzmann equation and the governing equations of the velocity distribution, respectively. To verify the validity of our numerical approach, a comparison has been made with the previous work in the case of low zeta potential and the excellent agreement between the solutions is clear. Then, in view of the obtained numerical solution for the velocity distribution, the numerical solutions of the flow rate and the shear stress are derived. Furthermore, based on numerical analysis, the influence of pertinent parameters on the potential distribution and the generation of flow is presented graphically.     

Dispersion control in microfluidic chips by localized zeta potential variation using the field effect

A new technique to minimize the effects of turn-induced dispersion within U-shaped separation channels by using the field effect within a capacitor to vary the zeta potential along the channel walls in the vicinity of the microchannel is described. The effects of the separation channel geometry, the fluid velocity profile, and the use of the field effect to control the zeta potential on the band distribution in the detection area are extensively discussed. The results for a U-shaped separation channel indicate that varying the zeta potential by controlling the field effect significantly reduces the band dispersion induced by the 90 degrees turns within the channel. Finally, it is shown that the application of the proposed localized zeta potential variation method also results in a correction of the band tilting phenomenon and a reduction in the racetrack effect.     

Band spreading control in electrophoresis microchips by localized zeta-potential variation using field-effect

The paper proposes a new technique, which varies the zeta potential along the channel walls in the vicinity of the microchannel corners in such as a way as to minimize the effects of turn-induced dispersion within U-shaped separation channels. The effects of the separation channel geometry, the fluid velocity profile, and boundary control of the zeta potential on the band distribution in the detection area are all discussed within this paper. The results for the folded square U-shaped separation channel indicate that boundary control of the zeta potential by field-effect significantly reduces the band dispersion induced by the 90[degree] turns. Finally, the results confirm that application of the proposed localized zeta potential variation method results in a correction of the band tilting phenomenon and a reduction in the racetrack effect.     

Diffusioosmosis of electrolyte solutions in a fine capillary slit

The steady diffusioosmotic flows of an electrolyte solution along a charged plane wall and in a capillary channel between two identical parallel charged plates generated by an imposed tangential concentration gradient are theoretically investigated. The plane walls may have either a constant surface potential or a constant surface charge density. The electrical double layers adjacent to the charged walls may have an arbitrary thickness and their electrostatic potential distributions are determined by the Poisson-Boltzmann equation. Solving a modified Navier-Stokes equation with the constraint of no net electric current arising from the cocurrent diffusion, electric migration, and diffusioosmotic convection of the electrolyte ions, the macroscopic electric field and the fluid velocity along the tangential direction induced by the imposed electrolyte concentration gradient are obtained semianalytically as a function of the lateral position in a self-consistent way. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential (or surface charge density) of the wall, the properties of the electrolyte solution, and other relevant factors. For a given concentration gradient of an electrolyte along a plane wall, the magnitude of fluid velocity at a position in general increases with an increase in its electrokinetic distance from the wall, but there are exceptions. The effect of the lateral distribution of the induced tangential electric field and the relaxation effect in the double layer on the diffusioosmotic flow are found to be very significant.     

Electrophoresis of Spherical Particles with a Random Distribution of Zeta Potential or Surface Charge

Electrophoresis is often used to measure the "average" zeta (zeta) potential on particles. However, it has been found by previous researchers that in making predictions of colloidal forces and stability, the distribution of zeta potential on the particles is important. This paper provides a straightforward method for measuring charge nonuniformity on colloidal spheres. It is shown that if the charge or zeta potential is random on a group of spheres, each covered with N equal-area patches, then the average magnitude of the dipole moment on the spheres is 0.92sigma(zeta)/N, and the average magnitude of the quadrupole moment is 1.302sigma(zeta)/N, where sigma(zeta) is the standard deviation of zeta potential over the surface of individual spheres. This is true for any random distribution of zeta potential, and the results emphasize that "random" implies nonuniform. It is demonstrated that since typical translational mobility measurements are much less sensitive to random charge nonuniformity than rotational mobility measurements, the latter measurement is better suited for measuring the second moment (sigma(zeta)) of zeta potential. Monte Carlo simulations were done to confirm and extend the analytical results. Copyright 2000 Academic Press.     

Diffusioosmosis of electrolyte solutions in a fine capillary tube

A theoretical study is presented for the steady diffusioosmotic flow of an electrolyte solution in a fine capillary tube generated by a constant concentration gradient imposed in the axial direction. The capillary wall may have either a constant surface potential or a constant surface charge density of an arbitrary quantity. The electric double layer adjacent to the charged wall may have an arbitrary thickness, and its electrostatic potential distribution is determined by an analytical approximation to the solution of the Poisson-Boltzmann equation. Solving a modified Navier-Stokes equation with the constraint of no net electric current arising from the cocurrent diffusion, electric migration, and diffusioosmotic convection of the electrolyte ions, the macroscopic electric field and the fluid velocity along the axial direction induced by the imposed electrolyte concentration gradient are obtained semianalytically as a function of the radial position in a self-consistent way. The direction of the diffusioosmotic flow relative to the concentration gradient is determined by the combination of the zeta potential (or surface charge density) of the wall, the properties of the electrolyte solution, and other relevant factors. For a prescribed concentration gradient of an electrolyte, the magnitude of fluid velocity at a position in general increases with an increase in its distance from the capillary wall, but there are exceptions. The effect of the radial distribution of the induced tangential electric field and the relaxation effect due to ionic convection in the double layer on the diffusioosmotic flow are found to be very significant.     

Effects of surface heterogeneity on flow circulation in electroosmotic flow in microchannels

The characteristics of electroosmotic flow in a cylindrical microchannel with non-uniform zeta potential distribution are investigated in this paper. Two-dimensional full Navier–Stokes equation is used to model the flow field and the pressure field. The numerical results show the distorted electroosmotic velocity profiles and various kinds of flow circulation resulting from the axial variation of the zeta potential. The influences of heterogeneous patterns of zeta potential on the velocity profile, the induced pressure distribution and the volumetric flow rate are discussed in this paper. This work shows that using either heterogeneous patterns of zeta potential or a combination of a heterogeneous zeta potential distribution and an applied pressure difference over the channel can generate local flow circulations and hence provide effective means to improve the mixing between different solutions in microchannels.     

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.     

One-shot screen-printed thylakoid membrane-based biosensor for the detection of photosynthetic inhibitors in discrete samples

A method is developed to determine the optimal profile of zeta potential around U turns such that the turn-induced spreading of a solute band is minimized. After proposing a velocity profile that eliminates the racetrack effect, a conjugate gradient method is adopted to find the zeta potential profile to induce the required velocity. The optimal profiles of zeta potential seem to be insensitive to the relevant parameters of electroosmotic flows. It is shown that a reduction of variance two orders of magnitude below that of a comparable turn with uniform zeta potential is easily attained by adopting the optimal profile of zeta potential, which can be realized using a UV excimer laser or external voltage control.     

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.     

In situ particle zeta potential evaluation in electroosmotic flows from time-resolved microPIV measurements

A time-resolved microPIV method is presented to measure in an EOF the particles zeta potential in situ during the transient start-up of a microdevice. The method resolves the electrophoretic velocity of fluoro-spheres used as tracer particles in microPIV. This approach exploits the short transient regime of the EOF generated after a potential drop is imposed across a microchannel and before reaching quasisteady state. During the starting of the transient regime, the electrophoretic effect is dominant in the center of the channel and the EOF is negligible. By measuring the velocity of the tracer particles with a microPIV system during that starting period, their electrophoretic velocity is obtained. The technique also resolves the temporal evolution of the EOF with three regions identified. The first region occurs before the electroosmotic effect reaches the center of the channel, the second region extends until the EOF reaches steady state, and thereafter is the third region. The two time constants separating these regions are also obtained and compared to the theory. The zeta potential of 860 nm diameter polystyrene particles is calculated for different solutions including borate buffer, sodium chloride, and deionized water. Results show that the magnitudes of the electrophoretic and electroosmotic velocities are in the range of |300| to |700| μm/s for these measurements. The zeta potential values are compared to the well-established closed cell technique showing improved accuracy. The method also resolves the characteristic response time of the EOF, showing small but important deviations from current analytical predictions. Additionally, the measurements can be performed in situ in microfluidic devices under actual working EOF conditions and without the need for calibrations.     

Boundary effects on electrophoresis of a colloidal cylinder with a nonuniform zeta potential distribution

The electrophoretic motion of a long dielectric circular cylinder with a general angular distribution of its surface potential under a transversely imposed electric field in the vicinity of a large plane wall parallel to its axis is analyzed. The thickness of the electric double layers adjacent to the solid surfaces is assumed to be much smaller than the particle radius and the gap width between the surfaces, but the applied electric field can be either perpendicular or parallel to the plane wall. The presence of the confining 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 viscous retardation of the moving particle; (3) an electroosmotic flow of the suspending fluid may exist due to the interaction between the charged wall and the tangentially imposed electric field. Through the use of cylindrical bipolar coordinates, the Laplace and Stokes equations are solved analytically for the two-dimensional electric potential and velocity fields, respectively, in the fluid phase, and explicit formulas for the quasisteady electrophoretic and angular velocities of the cylindrical particle are obtained. To apply these formulas, one has only to calculate the multipole moments of the zeta potential distribution at the particle surface. It is found that the existence of a plane wall near a nonuniformly charged particle can cause its translation or rotation which does not occur in an unbounded fluid with the same applied electric field.     

Streaming potential in open and packed fused-silica capillaries

The surface properties of novel stationary phases in packed and open tubular columns for capillary electrochromatography (CEC) were examined by measuring the streaming potential in a home made apparatus. The surfaces investigated include materials such as porous styrenic sorbents and octadecyl-silica as well as fused-silica tubing, in both raw and surface modified forms. Functionalization of the surface was carried out, for instance, by reductive amination or organosilane grafting on to capillary inner wall. The dependence of the streaming potential on pH was examined with aqueous solutions in the pH range from 2.5 to 9.0. Electrokinetic properties of 50 microm I.D. fused-silica capillaries have been determined by both streaming potential and electrosmotic flow measurements. Both methods gave similar pH profiles of the zeta-potential and the isoelectric points. This confirms the viability of our approach to evaluate the specific charged groups of the packing which is one of the important factors influencing electrosmotic flow (EOF) velocity and protein adsorption during a chromatographic run. In addition to bare silica capillaries, styrenic monolithic columns with different surface functionalities, which have been extensively used in our laboratory for CEC separation of peptides and proteins, were employed for comparison of two methods. Plots of zeta potential as a function of percent ACN show a complex behavior, indicating that zeta potential cannot be predicted simply from binary mixture solvent properties. It is demonstrated that the evaluation of the zeta potential by the streaming potential method is nondestructive, relatively fast, without untoward effects introduced by Joule heating and yet another means for the characterization of the surfaces under conditions employed in CEC.     

Analysis of electroosmotic flow with step change in zeta potential

The term electroosmotic flow refers to the bulk flow of an aqueous solution induced by the application of the electric field to the zeta potential. The characteristics of EOF in a microchannel depend upon the nature of the zeta potential, i.e., whether it is uniform or nonuniform. In this study, the full Navier-Stokes equation and the Nernst-Planck equation are used to model the change in EOF characteristics that occur when a step change in zeta potential is applied. It is found that the thickness of the electrical double layer gradually increases downstream from the location at which the zeta potential is increased. The results indicate that a step change in zeta potential causes a significant variation in the velocity profile and in the pressure distribution.     

Generation of directional EOF by interactive oscillatory zeta potential

A steady directional EOF due to a nonlinear interaction between oscillatory axial electrical fields and oscillatory wall potentials (zeta potentials) is presented. This is a new mechanism to produce such a mean flow. It is found that the flow velocity depends not on the external driving frequency but on the phase angle difference between the electric fields and the zeta potentials. The formulation can also be reduced to the static EOF straightforwardly. For the purpose of theoretical demonstration, we use the Debye-Huckel approximation for the zeta potential. Results of planar and cylindrical capillaries are given.     

Visualizing the transient electroosmotic flow and measuring the zeta potential of microchannels with a micro-PIV technique

We have demonstrated a transient micro particle image velocimetry (micro-PIV) technique to measure the temporal development of electroosmotic flow in microchannels. Synchronization of different trigger signals for the laser, the CCD camera, and the high-voltage switch makes this measurement possible with a conventional micro-PIV setup. Using the transient micro-PIV technique, we have further proposed a method on the basis of inertial decoupling between the particle electrophoretic motion and the fluid electroosmotic flow to determine the electrophoretic component in the particle velocity and the zeta potential of the channel wall. It is shown that using the measured zeta potentials, the theoretical predictions agree well with the transient response of the electroosmotic velocities measured in this work.