Transient streaming potential in a finite length microchannel

Pressure-driven flow of an electrolyte solution in a microchannel with charged solid surfaces induces a streaming potential across the microchannel. Such a flow also causes rejection of ions by the microchannel, leading to different concentrations in the feed and permeate reservoirs connecting the capillary, which forms the basis of membrane based separation of electrolytes. Modeling approaches traditionally employed to assess the streaming potential development and ion rejection by capillaries often present a confusing picture of the governing electrochemical transport processes. In this paper, a transient numerical simulation of electrochemical transport process leading to the development of a streaming potential across a finite length circular cylindrical microchannel connecting two infinite reservoirs is presented. The solution based on finite element analysis shows the transient development of ionic concentrations, electric fields, and the streaming potential over the length of the microchannel. The transient analysis presented here resolves several contradictions between the two types of modeling approaches employed in assessing streaming potential development and ion rejection. The simulation results show that the streaming potential across the channel is predominantly set up at the timescale of the developing convective transport, while the equilibrium ion concentrations are developed over a considerably longer duration.     

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.     

Electrokinetic sample transport in a microchannel with spatial electrical conductivity gradients

Studies of the sample transport in a microchannel with the electrical conductivity gradient are critical to develop techniques for on-chip sample transport control. A numerical model presented in this paper, consisting of the electrical potential equation, full Navier-Stokes equation and species conservation equation, is used to simulate sample transport in a microchannel with the consideration of the conductivity gradient. There are two situations studied here, sample pumping (where sample separation is minimized by employing a high-conductivity buffer in the sample region), and sample stacking (where sample separation is expedited by using a low-conductivity buffer as the sample carrier). The effects of applied electrical potential, sample diffusion coefficient and the ratio of conductivity of the driving buffer over the sample carrying buffer are investigated by using the developed model.     

Focusing particles by induced charge electrokinetic flow in a microchannel

A novel method of sheathless particle focusing by induced charge electrokinetic flow in a microchannel is presented in this paper. By placing a pair of metal plates on the opposite walls of the channel and applying an electrical field, particle focusing is achieved due to the two pairs of vortex that constrain the flow of the particle solution. As an example, the trajectories of particles under different electrical fields with only one metal plate on one side channel wall were numerically simulated and experimentally validated. Other flow focusing effects, such as the focused width ratio (focused width/channel width) and length ratio (focused length/half‐length of metal plate) of the sample solution, were also numerically studied. The results show that the particle firstly passes through the gaps between the upstream vortices and the channel walls. Afterwards, the particle is focused to pass through the gap between the two downstream vortices that determine the focused particle position. Numerical simulations show that the focused particle stream becomes thin with the increases in the applied electrical field and the length of the metal plates. As regards to the focused length ratio of the focused stream, however, it slightly increases with the increase in the applied electrical field and almost keeps constant with the increase in the length of the metal plate. The size of the focused sample solution, therefore, can be easily adjusted by controlling the applied electrical field and the sizes of the metal plates.     

Heat transfer intensification in microchannel by induced-charge electrokinetic phenomenon: a numerical study

Journal of Thermal Analysis and Calorimetry - In this numerical investigation, the induced-charge electrokinetic phenomenon is used to intensify the convective heat transfer rate in the...     

Traveling-wave electrokinetic micropumps: velocity, electrical current, and impedance measurements

An array of microelectrodes covered in an electrolyte and energized by a traveling-wave potential produces net movement of the fluid. Arrays of platinum microelectrodes of two different characteristic sizes have been studied. For both sizes of arrays, at low voltages (<2 V pp) the electrolyte flow is in qualitative agreement with the linear theory of ac electroosmosis. At voltages above a threshold, the direction of fluid flow is reversed. The electrical impedance of the electrode-electrolyte system was measured after the experiments, and changes in the electrical properties of the electrolyte were observed. Measurements of the electrical current during pumping of the electrolyte are also reported. Transient behaviors in both electrical current and fluid velocity were observed. The Faradaic currents probably generate conductivity gradients in the liquid bulk, which in turn give rise to electrical forces. These effects are discussed in relation to the fluid flow observations.     

A new droplet breakup phenomenon in electrokinetic flow through a microchannel constriction

A completely new droplet breakup phenomenon is reported for droplets passing through a constriction in an electrokinetic flow. The breakup occurs during the droplet shape recovery process past the constriction throat by the interplay of the dielectrophoretic stress release and the interface energy for droplets with smaller permittivity than that of the ambient fluid. There are conditions for constriction ratios and droplet size that the droplet breakup occurs. The numerical predictions provided here require experimental verification, and then can give rise to a novel microfluidic device design with novel droplet manipulations.     

Transient analysis of electroosmotic flow in a slit microchannel

The transient aspects of electroosmotic flow in a slit microchannel are studied. Exact solutions for the electrical potential profile and the transient electroosmotic flow field are obtained by solving the complete Poisson-Boltzmann equation and the Navier-Stokes equation under an analytical approximation for the hyperbolic sine function. The characteristics of the transient electroosmotic flow are discussed under influences of the electric double layer and the geometric size of the microchannel.     

Quantification of electrical field-induced flow reversal in a microchannel

We characterize the electroosmotic flow in a microchannel with field effect flow control. High resolution measurements of the flow velocity, performed by micro particle image velocimetry, evidence the flow reversal induced by a local modification of the surface charge due to the presence of the gate. The shape of the microchannel cross-section is accurately extracted from these measurements. Experimental velocity profiles show a quantitative agreement with numerical results accounting for this exact shape. Analytical predictions assuming a rectangular cross-section are found to give a reasonable estimate of the velocity far enough from the walls.     

Theoretical analysis of electrokinetic flow and heat transfer in a microchannel under asymmetric boundary conditions

The main theme of the present work is to investigate the electrokinetic effects on liquid flow and heat transfer in a flat microchannel of two parallel plates under asymmetric boundary conditions including wall-sliding motion, unequal zeta potentials, and unequal heat fluxes on two walls. Based on the Debye-Huckel approximation, an electrical potential solution to the linearized Poisson-Boltzmann equation is obtained and employed in the analysis. The analytic solutions of the electrical potential, velocity distributions, streaming potential, friction coefficient, temperature distribution, and heat transfer rate are obtained, and thereby the effects of electrokinetic separation distance (K), zeta-potential level (zeta;(1)), ratio of two zeta potentials (r(zeta) identical with zeta;(2)/zeta;(1)), wall-sliding velocity (u(w)), and heat flux ratio (r(q) identical with q"(2)/q"(1)) are investigated. The present results reveal the effects of wall-sliding and zeta-potential ratio on the hydrodynamic nature of microchannel flow, and they are used to provide physical interpretations for the resultant electrokinetic effects and the underlying electro-hydrodynamic interaction mechanisms. In the final part the results of potential and velocity fields are applied in solving the energy equation. The temperature distributions and heat transfer characteristics under the asymmetrical kinematic, electric, and thermal boundary conditions considered presently are dealt with.     

Electrokinetic flow through an elliptical microchannel: effects of aspect ratio and electrical boundary conditions

The electrokinetic flow of an electrolyte solution through an elliptical microchannel is studied theoretically. The system under consideration simulates the flow of a fluid, for example, in vein. We show that, for a constant cross-sectional area, both the electroosmotic volumetric flow rate and the streaming potential increase monotonically with an increase in the aspect ratio, and both the total electric current and the electroviscous effect may exhibit a local minimum as the aspect ratio varies. Also, for a constant average potential on the channel wall, the difference between the results based on three kinds of boundary conditions, which include constant surface charge, constant surface potential, and charge-regulated surface, is inappreciable if the hydraulic diameter is larger than 1 mum.     

Differential capacitance of liquid/liquid interfaces of finite thicknesses: a finite element study

Finite element simulations were used to investigate the effect of a smooth variation of permittivity across a polarized liquid/liquid interface on the differential capacitance. The results show that a relative permittivity profile can account for the variation of ion solvation in the interfacial region, and therefore upon the diffuse double layer itself. The width and the symmetry of this profile across the interface are shown to be crucial parameters for interfacial distributions and fitting of capacitance data has been used to estimate the width of the interfacial region.     

Control of flow rate and concentration in microchannel branches by induced-charge electrokinetic flow

This paper presents a numerical study of controlling the flow rate and the concentration in a microchannel network by utilizing induced-charge electrokinetic flow (ICEKF). ICEKF over an electrically conducting surface in a microchannel will generate vortices, which can be used to adjust the flow rates and the concentrations in different microchannel branches. The flow field and concentration field were studied under different applied electric fields and with different sizes of the conducting surfaces. The results show that, by using appropriate size of the conducting surfaces in appropriate locations, the microfluidic system can generate not only streams of the same flow rate or linearly decreased flow rates in different channels, but also different, uniform concentrations within a short mixing length quickly.     

Model and verification of electrokinetic flow and transport in a micro-electrophoresis device

We investigate the electrokinetic flow and transport within a micro-electrophoresis device. A mathematical model is set up, which allows to perform two-dimensional, time-dependent finite-element simulations. The model reflects the dominant features of the system, namely electroosmosis, electrophoresis, externally-applied electrical potentials, and equilibrium chemistry. For the solution of the model equations we rely on numerical simulations of the core region, while the immediate wall region is treated analytically at leading order. This avoids extreme refinements of the numerical grid within the EDL. An asymptotic matching of both solutions and subsequent superposition, nevertheless, provides an approximation for the solution in the entire domain. The results of the simulations are verified against experimental observation and show good agreement.     

Thermal transport characteristics of AC electrokinetic flow in a micro-annulus

Journal of Thermal Analysis and Calorimetry - Alternating current electroosmotic flow and associated heat transfer under constant surface heat flux conditions are numerically examined in a...     

Sample transport and electrokinetic injection in a microchip device for chemical cytometry

Sample transport and electrokinetic injection bias are well characterized in capillary electrophoresis and simple microchips, but a thorough understanding of sample transport on devices combining electroosmosis, electrophoresis, and pressure-driven flow is lacking. In this work, we evaluate the effects of electric fields from 0 to 300 V/cm, electrophoretic mobilities from 10(-4) to 10(-6) cm(2)/Vs, and pressure-driven fluid velocities from 50 to 250 μm/s on sample injection in a microfluidic chemical cytometry device. By studying a continuous sample stream, we find that increasing electric field strength and electrophoretic mobility result in improved injection and that COMSOL simulations accurately predict sample transport. The effects of pressure-driven fluid velocity on injection are complex, and relative concentration values lie on a surface defined by pressure-driven flow rates. For high-mobility analytes, this surface is flat, and sample injection is robust despite fluctuations in flow rate. For lower mobility analytes, the surface becomes steeper, and injection depends strongly on pressure-driven flow. These results indicate generally that device design must account for analyte characteristics and specifically that this device is suited to high-mobility analytes. We demonstrate that for a suitable pair of peptides fluctuations in injection volume are correlated; electrokinetic injection bias is minimized; and electrophoretic separation is achieved.     

Ionic liquid near a charged wall: structure and capacitance of electrical double layer

We study the effects of ion size asymmetry and short-range correlations on the electrical double layer in ionic liquids: we perform molecular dynamics simulations of a model ionic liquid between two "electrodes" and calculate the differential capacitance of each as a function of the electrode potential. The capacitance curve has an asymmetric "bell-shape" character, in qualitative agreement with recent experiments and the mean- field theory (MFT) which takes into account the limitation on the maximal local density of ions. The short-range ionic correlations, not included in the MFT, lead to an overscreening effect which changes radically the structure of the double layer at small and moderate charging. With the radius of cations taken to be twice as large as anions, the position of the main capacitance maximum is shifted positively from the potential of zero charge (PZC), as predicted by MFT. An extension of the theory (EMFT), however, reproduces the simulated capacitance curve almost quantitatively. Capacitance curves for real ionic liquids will be affected by nonspherical shape of ions and sophisticated pair potentials, varying from liquid to liquid. But understanding the capacitance behavior of such model system is a basis for rationalizing those more specific features.     

Theoretical analysis of a novel electrical field assisted membrane module comprising an array of microchannel units

A novel electrical field assisted membrane module consisting of an array of microchannel units, each microchannel unit comprised of a cylindrical pore and a charged ion-selective membrane layer, is analyzed theoretically. The governing equations for the flow and the electrical fields are solved analytically under the Debye-Huckel condition and the influences of the key parameters on the flow behavior of the system under consideration are investigated through numerical simulation. We show that for a fixed microchannel radius, the volumetric flow rate through a microchannel unit has a maximal value as the radius of the cylindrical pore varies. This maximum is independent of both the strength of the applied field and the density of the fixed charges in the membrane layer, but varies with the permittivity of the membrane layer.     

A simple electrical approach to monitor dielectrophoretic focusing of particles flowing in a microchannel

This paper reports an impedance‐based system for the quantitative assessment of dielectrophoretic (DEP) focusing of single particles flowing in a microchannel. Particle lateral positions are detected in two electrical sensing zones placed before and after a DEP‐focusing region, respectively. In each sensing zone, particle lateral positions are estimated using the unbalance between the opposite pulses of a differential current signal obtained with a straightforward coplanar electrode configuration. The system is used to monitor the focusing of polystyrene beads of 7 or 10 μm diameter, under various conditions of DEP field intensities and flow rates that produce different degrees of focusing. This electrical approach represents a simple and valuable alternative to optical methods for monitoring of particle focusing systems.     

Synthesis and characterization of a hydrogel with controllable electroosmosis: a potential brain tissue surrogate for electrokinetic transport

Electroosmosis is the bulk fluid flow initiated by application of an electric field to an electrolyte solution in contact with immobile objects with a nonzero ζ-potential such as the surface of a porous medium. Electroosmosis may be used to assist analytical separations. Several gel-based systems with varying electroosmotic mobilities have been made in this context. A method was recently developed to determine the ζ-potential of organotypic hippocampal slice cultures (OHSC) as a representative model for normal brain tissue. The ζ-potential of the tissue is significant. However, determining the role of the ζ-potential in solute transport in tissue in an electric field is difficult because the tissue's ζ-potential cannot be altered. We hypothesized that mass transport properties, namely the ζ-potential and tortuosity, could be modulated by controlling the composition of a set of hydrogels. Thus, poly(acrylamide-co-acrylic acid) gels were prepared with three compositions (by monomer weight percent): acrylamide/acrylic acid 100/0, 90/10, and 75/25. The ζ-potentials of these gels at pH 7.4 are distinctly different, and in fact vary approximately linearly with the weight percent of acrylic acid. We discovered that the 25% acrylic acid gel is a respectable model for brain tissue, as its ζ-potential is comparable to the OHSC. This series of gels permits the experimental determination of the importance of electrokinetic properties in a particular experiment or protocol. Additionally, tortuosities were measured electrokinetically and by evaluating diffusion coefficients. Hydrogels with well-defined ζ-potential and tortuosity may find utility in biomaterials and analytical separations, and as a surrogate model for OHSC and living biological tissues.