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.     

Electrokinetic characterization of porous plugs from streaming potential coupled with electrical resistance measurements

The zeta potential of mixed nickel-iron oxide particles is evaluated by a new laboratory instrument. This latter allows the measurement of streaming potential together with the electrical resistance of porous plugs. The conductivity of electrolyte inside plug (pore conductivity) is deduced from electrical resistance measurements and is used together with streaming potential to evaluate the zeta potential by accounting for the surface conduction phenomenon. It is shown that neglecting the surface conduction phenomenon leads to a substantial underestimation of the zeta potential. The coupled measurements of streaming potential and plug electrical resistance yield zeta potential values that are in very good agreement with those obtained by electrophoresis. The densification of the porous plug with increasing pressure increments is put in evidence by the decrease in measured streaming potentials. Electrical resistance measurements make it possible to account for the increase in surface conductivity resulting from the more compacted structure of the plug. By doing so, the calculated zeta potential is found to be virtually independent of the pressure difference involved in streaming potential experiments, whereas the negligence of surface conduction phenomenon leads to a decrease in the apparent zeta potential with increasing pressure level.     

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.     

Liquid transport in rectangular microchannels by electroosmotic pumping

The characteristics of electroosmotic flow in rectangular microchannels were investigated in this paper. A 2D Poisson–Boltzmann equation and the 2D momentum equation were used to model the electric double layer field and the flow field. The numerical solutions show significant influences of the channel cross-section geometry (i.e. the aspect ratio) on the velocity field and the volumetric flow rate. Also, the numerical simulation of the electroosmotic flow reveals how the velocity field and the volumetric flow rate depend on the ionic concentration, zeta potential, channel size and the applied electrical field strength.     

Characterizing zeta potential of functional nanofibers in a microfluidic device

The measurement of surface charge on nanofibers was achieved by characterizing zeta potential of the nanofibers via a newly developed device for streaming current measurement. Low flow rates were sufficient to generate detectable streaming currents in the absence of an externally applied voltage without damaging nanofiber samples. Zeta potential was calculated by using the Helmholtz-Smoluchowski equation and the measured streaming currents. Two acrylic plates were machined and assembled to form a microfluidic channel that is 150 μm high, 2.0mm wide, and 30 mm long. Two electrodes for the measurement of streaming currents were housed in the top plate. Two nanofibers of pure polyacrylonitrile (PAN) fibers and charged (TiO(2) incorporated) PAN fibers were prepared and characterized in the device. Monobasic sodium phosphate and dibasic sodium phosphate were used to prepare four different pH buffer solutions ranging from pH 5 to pH 8 in order to characterize the zeta potentials. The pure PAN nanofibers had negatively-charged surfaces regardless of pH. However, the zeta potentials of PAN/TiO(2) nanofibers changed from positive to negative at pH 6.5. The zeta potential measurements made on the nanofibers in this new microfluidic device matched with those of the powdered raw materials using a commercial Zetasizer.     

A novel method for effective field measurements in electrical field-flow fractionation

The electric field that drives separation and retention in electrical field flow fractionation (ElFFF) and cyclical electrical field-flow fractionation (CyElFFF) is a complex function of many parameters such as carrier ionic strength and pH, voltage, channel dimensions, flowrate, and electrode material. Currently there is no accurate or in situ method to measure the field during system operation. This paper introduces a technique to measure the effective electric field during ElFFF and CyElFFF operation using transient electrical spikes. With this technique we can determine the relationship between changes in carrier conductivity and flowrate during a run and their combined effect on effective field and retention in ElFFF. This technique can also be used to measure the voltage drop due to double layer capacitance in CyElFFF and the variation in effective field with frequency of the applied field. The measured effective fields for the CyElFFF and DC ElFFF techniques are also tested with a high ionic-strength buffer solution as carrier. For a high ionic-strength buffer, DC ElFFF generates a near-zero effective field (0.2% in 100 s), whereas CyElFFF can sustain much higher effective fields (~8%) even at relatively high voltages. The ability to measure the effective field allows for experiments to provide better data and for tuning and optimization of the separation run.     

Electrokinetic control of a chemical reaction in a lab-on-a-chip micro-reactor: measurement and quantitative modelling

We have investigated the complex formation/dissociation reaction between Ni(2+) ions and the ligand pyridine-2-azo-p-dimethylaniline (PADA) in a glass micro-reactor operating under electrokinetic control. An in situ, microscope-imaging technique was used to determine the spatial and temporal evolution of the reaction within the channel network of the micro-reactor. Using appropriately controlled voltage sequences, a 'slug' of PADA was injected into a stream of Ni(2+) solution. Under the experimental reaction conditions used, Ni(2+) ions are mixed with the PADA as a consequence of the species' different electrokinetic mobilities allowing the complex formation to occur at the trailing edge of the PADA slug. Following complex formation, reversal of the flow results in the partial re-formation of free PADA by dissociation of the complex, demonstrating that voltage control can be used to drive the reaction either forwards or backwards. We discuss the methods whereby all the parameters required to predict the spatial and temporal evolution of the reaction in the micro-reactor can be either measured or estimated. Based on the estimated parameters, model calculations of the concentration profiles as a function of time show good agreement with the measured data.     

Zeta potential of ion-conductive membranes by streaming current measurements

Surface charge properties have a significant influence on membrane retention and fouling performance. As a key parameter describing the surface charge of membranes used in aqueous applications, zeta potential measurements on membranes of various types have attracted great attention. During the zeta potential characterization of a series of ion-conductive sulfonated poly(sulfone) membranes, it was found that the measured streaming current varied with the thickness of the sample, which is not predicted by the classical Smoluchowski equation. Moreover, for higher conductivity membranes with an increased concentration of sulfonate groups, the zeta potential tended toward zero. It was determined that the influence of membrane bulk conductance on the measured streaming current must be taken into account in order to correctly interpret the streaming current data for ion-conductive polymers and understand the relationship between membrane chemical composition and zeta potential. Extrapolating the measured streaming current to a membrane thickness of zero has proven to be a feasible method of eliminating the error associated with measuring the zeta potential on ion conductive polymer membranes. A linear resistance model is proposed to account for the observed streaming currents where the electrolyte channel is in parallel with the ion-conductive membranes.     

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.     

The electrical conductivity and surface conduction of consolidated rock cores

A fully computerized high-pressure and high-temperature core holder device is simultaneously used to determine the electrical conductivity, zeta potential, and surface conductivity of consolidated rock cores in aqueous and nonaqueous systems. The total electrical conductivity of rock cores was determined by coupling streaming current and potential measurements. This shows that neglecting the surface conductivity Ksigma is crucial to converting the streaming potential into zeta potentials. It is observed that plots of the core total conductivity as a function of the electrolyte conductivity KL exhibit two behaviors. At low ionic strength, the core conductivity clearly depends on the contribution of surface conductivity behind the slip plane, whereas at higher ionic strength, the magnitude of the surface conductivity becomes negligible. The electrical conductivity of rock cores was found to be in good agreement with the O'Brien theory and the Briggs method. The contribution of the stagnant layer to the surface conductivity in nonaqueous systems has been shown to be significant. This shows that the stagnant layer displays significantly different behavior in different nonaqueous systems, depending on the core porosity and the double-layer overlap. The results indicate that the application of electrokinetics in petroleum reservoirs can provide important insights into reservoir fluid flow characterization.     

Patterned superhydrophobic paper for microfluidic devices obtained by writing and printing

This work outlines inexpensive patterning methodologies to create open-air microfluidic paper-based devices. A phase-separation methodology was used to obtain biomimetic superhydrophobic paper, hierarchically composed by micro and nano topographies. Writing and printing are simple actions that can be used to pattern flat superhydrophobic paper with more wettable channels. In particular, inkjet printing permits controlling the wettability of the surface by changing the darkness of the printed regions. The difference between capillary forces provides the possibility to control and drive liquid flows through the open path lines, just by titling the piece of paper. Additionally, maintaining a continuous flow, it is possible to direct the liquid at different volumetric rates in a horizontal position along non-linear channel paths printed/written over the surface.     

Determining zeta Potential and Surface Conductance by Monitoring the Current in Electro-osmotic Flow

In this paper we have outlined a simple procedure for determining zeta potential, zeta(0), and surface conductance, lambda(s), based on current monitoring in electro-osmosis. In these experiments, the average velocity was determined by measuring the amount of time required to completely displace a solution by another solution in the capillary tube. The average velocity during electro-osmosis was found to be independent of capillary size, although it was dependent on the electrolyte concentration and applied electrical field. The measured values of the zeta potential, zeta(0), were found to be independent of capillary size and the applied field, while zeta(0) is strongly dependent on the electrolyte concentration. Calculations of the specific surface conductivity lambda(s) based on current measurements reveal a relationship between lambda(s) and capillary size, in agreement with the results reported in the literature. Copyright 2000 Academic Press.     

On the streaming potential arising from flows having axial symmetry and the determination of zeta potential therefrom

Determining the zeta potential of macroscopic surfaces helps predict the surfaces' attractiveness to charged particles or cells, or tells whether the surface is clean or contaminated, among other applications. Typically, one pumps the test solution through a narrow channel formed by the test surface and measures the streaming current or streaming potential engendered thereby. It is worth considering alternative geometries: 1. The “spincoat” design, in which the test liquid is directed as a narrow jet to the axis of a disk-shaped sample rotating on its axis, offers a large signal with a small liquid flow rate, e.g. 1 mL/min. The validity of assumptions underlying the simplest analysis of this design improves as the flow rate decreases at constant rotation rate. 2. The “rotating disk”, in which the sample is spun on its axis while immersed in solution, offers much reduced surface conductance and uniform accessibility to charged entities in solution. This design also provides a means for determining the zeta potential of open porous structures without requiring compression of the sample into a plug. 3. The “impinging jet,” in which a jet of liquid is directed to a nonrotating sample, allows an arbitrary sample shape and detection of spatial variations of zeta potential. Deceleration of the radially expanding film causes a “hydraulic jump instability” some distance from the axis; the radius of the jump defines the probed area.     

Lattice Poisson-Boltzmann simulations of electro-osmotic flows in microchannels

This paper presents the numerical results of electro-osmotic flows in micro- and nanofluidics using a lattice Poisson-Boltzmann method (LPBM) which combines a potential evolution method on discrete lattices to solve the nonlinear Poisson equation (lattice Poisson method) with a density evolution method on discrete lattices to solve the Boltzmann-BGK equation (lattice Boltzmann method). In an electrically driven osmotic flow field, the flow velocity increases with both the external electrical field strength and the surface zeta potential for flows in a homogeneous channel. However, for a given electrical field strength and zeta potential, electrically driven flows have an optimal ionic concentration and an optimum width that maximize the flow velocity. For pressure-driven flows, the electro-viscosity effect increases with the surface zeta potential, but has an ionic concentration that yields the largest electro-viscosity effect. The zeta potential arrangement has little effect on the electro-viscosity for heterogeneous channels. For flows driven by both an electrical force and a pressure gradient, various zeta potential arrangements were considered for maximize the mixing enhancement with a less energy dissipation.     

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.     

Bubbles navigating through networks of microchannels

This paper describes the behavior of bubbles suspended in a carrier liquid and moving within microfluidic networks of different connectivities. A single-phase continuum fluid, when flowing in a network of channels, partitions itself among all possible paths connecting the inlet and outlet. The flow rates along different paths are determined by the interaction between the fluid and the global structure of the network. That is, the distribution of flows depends on the fluidic resistances of all channels of the network. The movement of bubbles of gas, or droplets of liquid, suspended in a liquid can be quite different from the movement of a single-phase liquid, especially when they have sizes slightly larger than the channels, so that the bubbles (or droplets) contribute to the fluidic resistance of a channel when they are transiting it. This paper examines bubbles in this size range; in the size range examined, the bubbles are discrete and do not divide at junctions. As a consequence, a single bubble traverses only one of the possible paths through the network, and makes a sequence of binary choices ("left" or "right") at each branching intersection it encounters. We designed networks so that, at each junction, a bubble enters the channel into which the volumetric flow rate of the carrier liquid is highest. When there is only a single bubble inside a network at a time, the path taken by the bubble is, counter-intuitively, not necessarily the shortest or the fastest connecting the inlet and outlet. When a small number of bubbles move simultaneously through a network, they interact with one another by modifying fluidic resistances and flows in a time dependent manner; such groups of bubbles show very complex behaviors. When a large number of bubbles (sufficiently large that the volume of the bubbles occupies a significant fraction of the volume of the network) flow simultaneously through a network, however, the collective behavior of bubbles-the fluxes of bubbles through different paths of the network-can resemble the distribution of flows of a single-phase fluid.     

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.     

Electrical circuits from capillary flow driven evaporation deposition of carbon nanotube ink in non-porous V-grooves

Low cost pliable electronics portend the advancement of novel inexpensive microfluidic electrochemical devices. In the direct printing approach, the manner of deposition of conductive material from a liquid suspension to ensure electrical continuity is crucial. We describe here an approach in which V-groove networks that make up the path of circuitry are first scribed on non-porous inexpensive surfaces. Liquid drops of carbon nanotube ink are then placed on the surface adjacent to the V-grooves to enable wicking to produce the electrical circuit. This method essentially bypasses the need for inkjet printing. We investigate the basic efficacy of the conductive networks developed using this approach and demonstrate its use in generating electrically driven liquid flow of particles in a simple open capillary channel.     

Tangential streaming potential as a tool in modeling of ion transport through nanoporous membranes

Tangential streaming potential (TSP) measurements have been carried out so as to assess the electrokinetic properties of the active layer of organic nanofiltration (NF) membranes. Due to the porous structure of NF membranes, cares must be taken to convert the experimental data into zeta potential. Indeed, an assumption that is implicitly made in Smoluchowski's theory (or in related approaches accounting for the surface conduction phenomenon) is that both streaming and conduction currents involved in the streaming potential process flow through an identical path. Such an assumption does not hold with porous membranes since the conduction current is expected to flow wherever the electric conductivity differs from zero. Consequently, a non-negligible share of the conduction current is likely to flow through the membrane body filled with the electrolyte solution. This phenomenon has been taken into account by carrying out a series of TSP measurements at various channel heights. Experiments have been conducted with various electrolyte solutions. The inferred zeta potentials have been further converted into membrane volume charge densities which have been used to predict the membrane performances in terms of rejection rates. The conventional NF theory, i.e. based on a steric/Donnan exclusion mechanism, has been found to be unable to describe the experimental rejection rates. Using the volume charge density of the membrane as an adjustable parameter, it has been shown that the conventional theory even predicts the opposite sign for the membrane charge. On the other hand, the experimental rejection rates have been well described by including dielectric effects in the exclusion mechanism. In this case, a noticeable lowering of the effective dielectric constant of the electrolyte solution inside pores has been predicted (with respect to the bulk value).     

Effects of Oil on Aqueous Foams: Electrical Conductivity of Foamed Emulsions

Three‐phase foams containing dispersed oils (also called foamed emulsion) are usually encountered in such areas as enhanced oil recovery, food foams, and in foams containing antifoams. The presence of oil causes these complex fluids to exhibit extraordinary properties in contrast to aqueous foams. We experimentally investigated, for the first time, the conductive properties of the foamed emulsions and found that the electrical conductivity increases monotonically with the volumetric liquid fraction, presenting a linear relationship. Combined with the analysis on the foaming capacity and microstructure of this complex fluid, the conductive mechanism is revealed. In these foamed emulsions, the whole conductive network is comprised of two levels of structural hierarchy, which displays a different mechanism from those of the conventional aqueous foams. The lamella of emulsions is taken as primary electrical channel, whereas the secondary electrical channel occurs in the lamella between two bubbles. This conductive behaviour is attributed to the microstructure properties of the foamed emulsions. We believe that such findings are potentially important for a better understanding of the fundamentals of these tri‐phase dispersion systems.