Nonuniform Surface Potentials Research Articles

Electroosmotic mixing in a microchannel with heterogeneous slip dependent zeta potential

We investigate the electroosmotic mixing characteristics for flow through a hydrophobic microchannel with interfacial slip dependent heterogeneous surface charge. A comprehensive theoretical framework is developed to solve the Poisson–Boltzmann equation for the induced potential within the electrical double layer, mass and momentum conservation equations for fluid flow, and species transport equation with appropriate boundary conditions. We identify two different flow regimes based on diffusive Peclet number such that in the first regime the value of mixing efficiency is almost 100% as the recirculation zones formed due to the non-uniform surface potential provide sufficient convection mixing and the flow rate enhances with the slip length. The critical value of Peclet number increases with both the slip length and Debye parameter. In the next regime the effect of interfacial slip is significant in altering the mixing performance and the mixing efficiency decreases both with the slip and Debye parameter. The patch surface potential modulates the flow rate and mixing performance and, in this context, different range of patch surface potential for the considered physicochemical parameters is identified for which both the flow rate and mixing efficiency enhances due to the interfacial slip.

Numerical study of the vortex-induced electroosmotic mixing of non-Newtonian biofluids in a nonuniformly charged wavy microchannel: Effect of finite ion size.

We propose a micromixer for obtaining better efficiency of vortex induced electroosmotic mixing of non-Newtonian bio-fluids at a relatively higher flow rate, which finds relevance in many biomedical and biological applications. To represent the rheology of non-Newtonian fluid, we consider the Carreau model in this study, while the applied electric field drives the constituent components in the micromixer. We show that the spatial variation of the applied field, triggered by the topological change of the bounding surfaces, upon interacting with the non-uniform surface potential gives rise to efficient mixing as realized by the formation of vortices in the proposed micromixer. Also, we show that the phase-lag between surface potential leads to the formation of asymmetric vortices. This behavior offers better mixing performance following the appearance of undulation on the flow pattern. Finally, we establish that the assumption of a point charge in the paradigm of electroosmotic mixing, which is not realistic as well, under-predicts the mixing efficiency at higher amplitude of the non-uniform zeta potential. The inferences of the present analysis may guide as a design tool for micromixer where rheological properties of the fluid and flow actuation parameters can be simultaneously tuned to obtain phenomenal enhancement in mixing efficiency.

Analytical Solution of Time-Periodic Electroosmotic Flow through Cylindrical Microchannel with Non-Uniform Surface Potential.

Time-periodic electroosmotic flow (EOF) with heterogeneous surface charges on channel walls can potentially be used to mix species or reagent molecules in microfluidic devices. Although significant research efforts have been placed to understand different aspects of EOF, its role in the mixing process is still poorly understood, especially for non-homogeneous surface charge cases. In this work, dynamic aspects of EOF in a cylindrical capillary are analyzed for heterogeneous surface charges. Closed form analytical solutions for time-periodic EOF are obtained by solving the Navier–Stokes equation. An analytical expression of induced pressure is also obtained from the velocity field solution. The results show that several vortices can be formed inside the microchannel with sinusoidal surface charge distribution. These vortices change their pattern and direction as the electric field change its strength and direction with time. In addition, the structure and strength of the vorticity depend on the frequency of the external electric field and the size of the channel. As the electric field frequency or channel diameter increases, vortices are shifted towards the channel surface and the perturbed flow region becomes smaller, which is not desired for effective mixing. Moreover, the number of vorticities depends on the periodicity of the surface charge.

Dielectrophoretic choking phenomenon in a converging-diverging microchannel for Janus particles.

The dielectrophoretic (DEP) choking phenomenon is revisited for Janus particles that are transported electrokinetically through a microchannel constriction by a direct-current (DC) electric field. The negative DEP force that would block a particle with a diameter significantly smaller than that of the constriction at its inlet is seen to be relaxed by the rotation of the Janus particle in a direction that minimizes the magnitude of the DEP force. This allows the particle to pass through the constriction completely. An arbitrary Lagrangian-Eulerian (ALE) numerical method is used to solve the nonlinearly coupled electric field, flow field, and moving particle, and the DEP force is calculated by the Maxwell stress tensor (MST) method. The results show how Janus particles with non-uniform surface potentials overcome the DEP force and present new conditions for the DEP choking by a parametric study. Particle transportation through microchannel constrictions is ubiquitous, and particle surface properties are more likely to be non-uniform than not in practical applications. This study provides new insights of importance for non-uniform particles transported electrokinetically in a microdevice.

Electroosmosis over non-uniformly charged surfaces: modified Smoluchowski slip velocity for second-order fluids

In the present paper we focus on deriving the modified Smoluchowski slip velocity of second-order fluids, for electroosmotic flows over plane surfaces with arbitrary non-uniform surface potential in the presence of thin electric double layers (EDLs). We employ matched asymptotic expansion to stretch the electric double layer and subsequently apply regular asymptotic expansions taking the Deborah number ($De$) as the gauge function. Modified slip velocities correct up to $O(De^{2})$ are presented. Two sample cases are considered to demonstrate the effects of viscoelasticity on slip velocity: (i) an axially periodic patterned potential and (ii) a step-change-like variation in the surface potential. The central result of our analysis is that, unlike Newtonian fluids, the electroosmotic slip velocity for second-order fluids does not, in general, align with the direction of the applied external electric field. Proceeding further forward, we show that the slip velocity in a given direction may, in fact, depend on the applied electric field strength in a mutually orthogonal direction, considering three dimensionality of the flow structure. In addition, we demonstrate that the modified slip velocity is not proportional to the zeta potential, as in the cases of Newtonian fluids; rather it depends strongly on the gradients of the interfacial potential as well. Our results are likely to have potential implications so far as the design of charge modulated microfluidic devices transporting rheologically complex fluids is concerned, such as for mixing and bio-reactive system analysis in lab-on-a-chip-based micro-total-analysis systems handling bio-fluids.

Enhancement of flow mixing in micro and nano channels

The aim is to increase the mixing potential of ion species in micro and nano channels with heterogeneous surface potential. We discuss the generation of vortical flow, due to the presence of wall heterogeneity at different locations in the channel. The flow characteristics are obtained by numerical solution of the Poisson equation, the Nernst--Planck equation, and the Navier--Stokes equation, simultaneously. A numerical method based on the pressure correction iterative algorithm is adopted to compute the flow field and mole fraction of the ions. The strong recirculation vortices which appear above the heterogeneities generate a strong pressure gradient which increases mixing performance. References F. Tian, B. Li and D. Y. Kwok, Tradeoff between mixing and transport for EOF in hetero. microchannels with nonuniform surface potentials. Langmuir 21:1126–1131, 2005. doi:10.1021/la048203e R. H. Liu, M. A. Stremler, K. V. Sharp, M. G. Olsen, J. G. Santiago, R. J. Adrian, H. Aref and D. J. Beebe, Passive mixing in a three dimensional serpentine microchannel. J. Microelectromech. S. 9:190–197, 2000. doi:10.1109/84.846699 Z. M. Wu, Z. J. Zhao, J. X. Yang, L. P. Liu and X. L. Yang, Freq.-modulation-type MI sensor with nanocrystalline ribbon core. Sensor. Actuat. A:Phys. 121:430–433, 2005. doi:10.1016/j.sna.2005.03.019 S. Bhattacharyya and A. K. Nayak, Combined Effect of Surface Roughness and Heterogeneity of Wall Potential on Electroosmosis in Microfluidic/Nanofuidic Channels. J. Fluids Eng. 132:041103, 2010. doi:10.1115/1.4001308 A. Ajdari, Electro-Osmosis on Inhomogeneously Charged Surfaces. Phy. Rev. Lett. 75:755–758, 1995. doi:10.1103/PhysRevLett.75.755 D. Erickson and D. Li Influence of surface heterogeneity on electrokinetically driven microfluidic mixing. Langmuir 18:1883–1892, 2002. doi:10.1021/la015646z L. M. Fu , J. Y. Lin and R. J. Yang, Analysis of electroosmtoic flow with step change in zeta potential. J. Colloid. Interf. Sci. 258:266–275, 2003. doi:10.1016/S0021-9797(02)00078-4 H. Watzig, S. Kaupp and M. Graf, Inner surface properties of capillaries for electrophoresis. Trac-Trend. Anal. Chem. 22:588–604, 2003. doi:10.1016/S0165-9936(03)01102-6 Z. Zheng and D. Hansford, and A. T. Conlisk, Effect of multivalent ions on EOF in micro- and nanochannels. Electrophoresis 24:3006–3017, 2003. doi:10.1002/elps.200305561 J. Wang, M. Wang and Z. Li, Lattice Poisson–Boltzmann Simulations of Electro-Osmotic Flows in Microchannels. J. Colloid. Interf. Sci. 296:729–736, 2006. doi:10.1016/j.jcis.2005.09.042 A. K. Nayak, An Analysis of Steady/Unsteady Electroosmotic flows Through Charged cylindrical nano channel. Theor. Comp. Fluid Dyn. 27:885–902, 2013. doi:10.1007/s00162-013-0295-0

A Coupled Lattice Boltzmann Method to Solve Nernst–Planck Model for Simulating Electro-osmotic Flows

In this paper, we focus on the nonlinear coupling mechanism of the Nernst---Planck model and propose a coupled lattice Boltzmann method (LBM) to solve it. In this method, a new LBM for the Nernst---Planck equation is developed, a multi-relaxation-time (MRT)-LBM for flow field and an LBM for the Poisson equation are used. And then, we discuss the choice of the model and found that the MRT-LBM is much more stable and accurate than the LBGK model. A reasonable iterative sequence and evolution number for each LBM are proposed by considering the properties of the coupled LBM. The accuracy and stability of the presented coupled LBM are also discussed through simulating electro-osmotic flows (EOF) in micro-channels. Furthermore, to test the applicability of it, the EOF with non-uniform surface potential in micro-channels based on the Nernst---Planck model is simulated. And we investigate the effects of non-uniform surface potential on the pattern of the EOF at different external applied electric fields. Finally, a comparison of the difference between the Nernst---Planck model and the Poisson---Boltzmann model is presented.

Broadening of metal-oxide-semiconductor admittance characteristics: Measurement, sources, and its effects on interface state density analyses

The admittance characteristics of a well understood oxide system of Gd0.25Ga0.15O0.60/Ga2O3 on In0.53Ga0.47As are studied at low temperature where the majority of the defect states are frozen. The capacitance-voltage (C-V) characteristics are broadened beyond those expected for an ideal sample. The broadening is ascribed to the presence of a non-uniform surface potential. We report a simple method for measuring the surface potential distribution width using the ac signal amplitude dependence of the C-V profile. A distribution of surface potentials can explain the observed behavior, but only if it includes the admittance of the semiconductor. This is in contrast to the usual approximation that the effect of a distribution of surface potentials on the admittance of the semiconductor is ignored. It is found that the charge state of defect states in the oxide and variation in the doping density of the substrate contribute to the broadening. The implications for inclusion of the semiconductor admittance for the interpretation of ideal characteristics and for the analysisof characteristics with interface states are explored. Both the conductance method and the quasi-equilibrium C-V methods are affected to some extent. An alternative method that can more accurately extract information from the admittance characteristics of the MOS samples is proposed.

Effect of nonuniform surface potential on electroosmotic flow at large applied electric field strength

Electroosmotic flow in nanochannels with non-uniform wall potential is investigated. While several researchers have presented results for the case of periodic potential and sudden change in potential, most of the previous work in this area is based on the Debye-Hückel approximation and the validity of Boltzmann distribution for ionic species. In this paper, the nonlinear distributions of potential, velocity and mole fractions are calculated numerically based on the Poisson-Nernst-Planck model including convective effects. The distribution of potential and species concentration are shown to be different from the Boltzmann distribution at large applied electric field strength. The convective effect is also investigated and found to be negligible.

The influence of surface microchemistry in protective film formation on multi-phase magnesium alloys

The high strength:weight ratio of magnesium alloys makes them an ideal metal for automotive and aerospace applications where weight reduction is of significant concern. Unfortunately, magnesium alloys are highly susceptible to corrosion particularly in salt-spray conditions. This has limited their use in the automotive and aerospace industries, where exposure to harsh service conditions is unavoidable. The simplest way to avoid corrosion is to coat the magnesium-based substrate by a process such as electroless plating, which is a low-cost, non line of sight process. Magnesium is classified as a difficult to plate metal due to its high reactivity. This means that in the presence of air magnesium very quickly forms a passive oxide layer that must be removed prior to plating. Furthermore, high aluminium content alloys are especially difficult to plate due to the formation of intermetallic species at the grain boundaries, resulting in a non-uniform surface potential across the substrate and thereby further complicating the plating process. The objective of this study is to understand how the magnesium alloy microstructure influences the surface chemistry of the alloy during both pretreatment and immersion copper coating of the substrate. A combination of scanning electron microscopy, energy dispersive spectroscopy and scanning Auger microscopy has been used to study the surface chemistry at the various stages of the coating process. Our results indicate that the surface chemistry of the alloy is different on the aluminum rich β phase of the material compared to the magnesium matrix which leads to preferential deposition of the metal on the aluminum rich phase of the alloy.

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.

Tradeoff between Mixing and Transport for Electroosmotic Flow in Heterogeneous Microchannels with Nonuniform Surface Potentials

Electroosmotic flow (EOF) is a phenomenon associated with the movement of an aqueous solution induced by the application of an electric field in microchannels. The characteristics of EOF depend on the nature of the surface potential, i.e., whether it is uniform or nonuniform. In this paper, a lattice Boltzmann model (LBM) combined with the Poisson-Boltzmann equation is used to simulate flow field in a rectangular microchannel with nonuniform (step change) surface potentials. The simulation results indicate that local circulations can occur near a heterogeneous region with nonuniform surface potentials, in agreement with those by other authors. Largest circulations, which imply a highest mixing efficiency due to convection and short-range diffusion, were found when the average surface potential is zero, regardless of whether the distribution of the heterogeneous patches is symmetric or asymmetric. In this work, we have illustrated that there is a trade-off between the mixing and liquid transport in EOF microfluidics. One should not simply focus on mixing and neglect liquid transport, as performed in the literature. Excellent mixing could lead to a poor transport of electroosmotic flow in microchannels.

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.

The calculation of grain charge in a dense dusty plasma with a nonuniform surface potential

Any study of astrophysical and laboratory dusty plasmas takes into consideration the calculation of individual dust grain charge when part of a dust cloud. At sufficiently high dust cloud densities, the effective Debye length of the cloud is of the same order as the intergrain distance, and the individual dust grains cannot be considered to be electrically isolated. As well, at moderate plasma temperatures, currents such as the secondary-electron current become significant and can be strongly radius-dependent at submicron levels. Thus, in these dusty plasma regimes the dust surface potential is not uniform throughout a cloud which has a distribution of grain sizes. We present the derivation of dust grain charge in a cloud with a size distribution immersed in a plasma, the dust cloud surface potential being nonuniform.

Charging in a dusty plasma with a size distribution: a comparison of three models

There has recently been a renewed interest in the charging of dust grains in a plasma and its effect not only on dust dynamics in astrophysical and solar system environments but also in laboratory plasma processing and semiconductor manufacturing. The calculation of individual dust grain charges in a dust cloud with a size distribution is a challenging one, especially under sufficiently dense cloud conditions and moderately high plasma temperatures when secondary electron currents become significant. Both the capacitance of the dust cloud and the significant charging currents must be taken into account. Three models for calculating individual dust grain charges are compared. The first model considers the dust cloud to consist of isolated grains immersed in plasma. The second model uses a uniform potential for the dust cloud and thus finds the charges using an appropriate capacitance for the cloud. The third model assumes a nonuniform grain surface potential and uses a solution to Poisson's equation to calculate the grain charges. The models are applied to a dense dusty plasma environment, appropriate for Saturn's F-ring. The implications for coagulation in presolar environments are also discussed.

Interactions between Two Spherical Particles with Nonuniform Surface Potentials: The Linearized Poisson–Boltzmann Theory

Using the linearized Poisson–Boltzmann theory, electrical double layer interactions are calculated between two nonuniform spherical colloidal particles with mean potential zero. Most results are for the case of surface potentials modeled by a single spherical harmonic and aligned relative to each other. As previously observed for flat surfaces, interactions decay more rapidly as a function of separation between spheres with such periodic, “single-mode” potentials than between spheres with uniform potentials. The Deryaguin approximation for single-mode spheres is tested and calculations are made of the force and torque that particles in a doublet exert on one another. Many of the concepts developed from models of flat plates with periodic aligned surface potentials are shown to be useful in this more general case. Attempts to explain recent differential electrophoresis experiments on the basis of nonuniform double layers fail in that the maximum restraining torques produced under plausible assumptions about the amplitude of nonuniformity are an order of magnitude smaller than those implied by the measurements. The main reason for this is that the torques are too small at the separations characteristic of a secondary minimum. The effect of misalignment of single-mode spheres is assessed by calculating the distribution of interaction energies over a set of relative orientations generated by quasi-random sampling. Finally, a method for generating spheres with “random” surface potentials is devised and potentials of mean force are calculated for pairs of spheres with such surface potentials. Comparison with the single-mode case is kept at a qualitative level, in the absence of detailed knowledge of how realistic such “random” surfaces are.

Solutions of the linearized Poisson–Boltzmann equation through the use of random walk simulation method

It is shown that the random walk simulation technique, through the choice of a suitable set of rules, can be adapted to the problem of solving the linearized Poisson–Boltzmann equation, for general cases involving constant surface potentials. In order to validate the technique, the results of the method are compared to the exact solutions for a number of analytically tractable problems. Excellent agreements between the two sets of results are found in all cases. Further examples of the application of the method are given by considering systems involving nonideal colloidal particles. In particular, the solutions of the linearized Poisson–Boltzmann equation for simple models of porous colloids, as well as particles with nonuniform surface potentials, have been obtained. The implication of these preliminary results for the electrostatic interactions between such nonideal colloidal particles are briefly discussed.

Influence of nonuniform surface potential on the measurement of plasma parameters by electrostatic probes

In the theory of electrostatic probes, it is usually assumed that the probe surface potential is uniform. However, nonuniformity of the surface work function produces a nonuniformity in surface potential which may modify the current collection. This effect is examined for an infinite cylinder immersed in a collisionless plasma in the limit when Debye length is much greater than probe radius, by numerically following charged‐particle orbits in a Laplace potential. It is shown that only large‐scale, macroscopic potential nonuniformities are important for the current collection, and that microscopic nonuniformities are smoothed over relatively short distance by the Laplace equation character of the potential.

Nonuniform surface potentials and their observation by surface sensitive techniques

Various models of Schottky barrier formation have been proposed in the last few years which involve metallurgical interactions at the metal–semiconductor interface. Most of these models involve nonuniform lateral variations in the surface potential. For metallic clusters and/or anion clusters, these variations involve a relatively large size scale (tens to hundreds of angstroms). For interface defect formation, the suggestion of cluster formation energy as the driving force for defect formation could also lead to a nonuniform distribution of pinning sites on a similar size scale. We have studied the effects of various spatial distributions of pinning sites (e.g., surface defects, clusters of anions and/or adsorbed metal atoms) and variations of their energy levels upon surface potentials and their depth distribution via a two-dimensional finite difference program that integrates Poisson’s equation. Our results suggest that surface sensitive spectroscopies provide a less than exact measure of pinning levels in many such cases. For example, for 1018 n-GaAs and pinning site separation of 100 Å, our calculations imply a Kelvin probe band-bending result for the surface potential of ≊0.15 V less than the ‘‘pinning’’ value (for pinning values of 0.8 and 0.6). Furthermore, such nonuniform distributions alter the effect of probe depth. The surface potential determined via e.g., UPS, with a 20 Å mean free path, would differ from the ‘‘true’’ surface averaged value by ≊0.09 eV for a uniform 0.8 V surface; while this difference is ≊0.07 for 100 Å separations, and ≊0.05 for 400 Å separations, the ratio of this λ dependent term to the total measured band bending increases as the distance between pinning sites increases. Note that a pinning level 0.8 eV below the conduction band minimum leads (under the assumptions of 100 Å between sites, probe depth ≊20 Å, and 1018 cm−3 bulk doping) to a ‘‘measured’’ surface potential within 0.6 eV of the conduction band minimum. These results should impact the interpretation of surface dependent studies of Schottky barrier formation, especially for specific models of such formation.