Rheology-modulated alterations in electro-magneto-hydrodynamic flows in a narrow cylindrical capillary: Contrasting trends in high and low surface charge limits

We investigate electrokinetic transport of power-law fluids in a narrow cylindrical capillary in the presence of a transverse magnetic field. The governing equations including the full Poisson-Boltzmann equation and the Cauchy momentum equation with power-law constitutive behavior are solved numerically, without being restrictive to low surface potential limits. The influence of the power-law index, wall zeta potential, relative strength of electromagnetic force over viscous force (as represented by the Hartmann number), and the lateral electric field strength on the variation of the volumetric flow rate is analyzed. Our results reveal a significant augmentation in the net-throughput beyond the traditionally explored low surface-charge limits, especially for shear-thinning fluids, defying the established notions. These fundamental theoretical premises may act as essential precursors towards developing deeper insights on fluidic transport bio-nanopores under electro-magneto- hydrodynamic influences.     

Electric field control and analyte transport in Si/SiO2 fluidic nanochannels

This article presents an analysis of the electric field distribution and current transport in fluidic nanochannels fabricated by etching of a silicon chip. The channels were overcoated by a SiO2 layer. The analysis accounts for the current leaks across the SiO2 layer into the channel walls. Suitable voltage biasing of the Si substrate allows eliminating of the leaks or using them to modify the potential distribution of the fluid. Shaping the potential in the fluid can be utilized for solute focusing and separations in fluidic nanochannels.     

Electrokinetic control of fluid flow in native poly(dimethylsiloxane) capillary electrophoresis devices

Capillary zone electrophoresis (CZE) devices fabricated in poly(dimethylsiloxane) (PDMS) require continuous voltage control of all intersecting channels in the fluidic network in order to avoid catastrophic leakage at the intersections. This contrasts with the behavior of similar flow channel designs fabricated in glass substrates. When the injection plugs are shaped by voltage control and leakage from side channels is controlled by the application of pushback voltages during separation, fluorescein samples give 64 200 theoretical plates (7000 V separation voltage, E = 1340 V/cm). Native PDMS devices exhibit stable retention times (+/- 8.6% RSD) over a period of five days when filled with water. Contact angles were unchanged (+/- 1.9% RSD) over a period of 16 weeks of dry storage, in contrast to the known behavior of plasma-oxidized PDMS surfaces. Electroosmotic flow (EOF) was observed in the direction of the cathode for the buffer systems studied (phosphate, pH 3-10.5), in the presence or absence of hydrophobic ions such as tetrabutylammonium or dodecyl sulfate. Electroosmotic mobilities of 1.49 x 10(-5) and 5.84 x 10(-4) cm2/Vs were observed on average at pH 3 and 10.5, respectively, the variation strongly suggesting that silica fillers in the polymer dominate the zeta potential of the material. Hydrophobic compounds such as dodecyl sulfate and BODIPY 493/503 adsorbed strongly to the PDMS, indicating the hydrophobicity of the channel walls is clearly problematic for CZE analysis of hydrophobic analytes. A method to stack multiple channel layers in PDMS is also described.     

Transport of charged samples in fluidic channels with large zeta potentials

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

The Debye-Hückel approximation: its use in describing electroosmotic flow in micro- and nanochannels

In this work we consider the electroosmotic flow in a rectangular channel. We consider a mixture of water or other neutral solvent and a salt compound, such as sodium chloride, and other buffers for which the ionic species are entirely dissociated. Results are produced for the case where the channel height is much greater than the width of the electric double layer (EDL) (microchannel) and for the case where the channel height is of the order or slightly greater than the width of the EDL (nanochannel). At small cation, anion concentration differences the Debye-Hückel approximation is appropriate; at larger concentration differences, the Gouy-Chapman picture of the electric double emerges naturally. In the symmetric case, the velocity field and the potential are identical. We specifically focus in this paper on the limits of the Debye-Hückel approximation for a simplified version of a phosphate-buffered saline (PBS) mixture. The fluid is assumed to behave as a continuum and the volume flow rate is observed to vary linearly with channel height for electrically driven flow in contrast to pressure-driven flow which varies as height cubed. This means that very large pressure drops are required to drive flows in small channels. However, useful volume flow rates may be obtained at a very low driving voltage. In the course of the solution, we establish the relationship between the wall mole fractions of the electrolytes and the zeta potential. Multivalent electrolyte mixtures are also considered.     

pH-Regulated nanopore conductance with overlapped electric double layers

There has been a significant growth of interest in single nanopore ionic devices that could control the transport of ions and rectify ionic current. To improve the advance of relevant nanofluidic devices, a model is derived for the first time to investigate the zeta potential and ionic conductance of a cylindrical nanopore with overlapped electric double layer as functions of pH, salt concentration as well as the Stern layer capacitance. The developed model is validated by the experimental data of the nanopore conductance. Results show that in addition to the magnitudes, the relevant behaviors of zeta potential and conductance of the nanopore might be significantly influenced by the Stern layer.     

Electrophoretic motion of a sphere in a microchannel under the gravitational field

This paper considered electrophoretic motion of a sphere in an aqueous electrolyte solution in a microchannel under the gravitational field. In an externally applied electric field, the negatively charged sphere will move toward the anode. At the same time, the sphere will move toward the lower channel wall due to the density difference and the gravity. When the sphere moves very close to the lower wall, the buoyancy, the electric double layer interaction force, and the van der Waals force balance the gravity force, so the sphere moves parallel to the lower wall. A theoretical model for the electrophoretic motion of a sphere in a microchannel, with the consideration of the electrophoretic retardation effect, is presented in this paper. It was found that the sphere's motion in the microchannel is affected by its size, the density difference, the zeta potentials of the sphere and the channel wall, and the applied electric strength. The effects of these factors on the sphere's transport distance in the microchannel are discussed. It was found that the spheres with the same surface charge could be separated by their size within a certain range of ka in aqueous solutions in the microchannel.     

Electrokinetic-vortex formation near a two-part cylinder with same-sign zeta potentials in a straight microchannel

Vortex formation near a two-part cylinder with zeta potentials of different values but the same sign under an external DC electric field is numerically investigated in this paper. The cylinder, inserted in a straight microchannel filled with an aqueous solution, is composed of an upstream part and a downstream part. When a DC electric field is applied in the channel, under certain conditions, the vortex will form near the cylinder due to the different velocities of electroosmotic flow generated on the cylinder surface. The numerical results reveal that the larger the velocity difference of electroosmotic flow generated on the two-part cylinder and the smaller the channel width, the more conducive to vortex formation in the channel. In addition, if the zeta potential ratios of cylinder downstream part to upstream part and channel wall to cylinder upstream part are unchanged, the DC electric field strength and the zeta potential value do not affect the pattern of vortices formed in the channel. This study provides a way for vortex formation in microchannels and has the potential application in microfluidic devices.     

Method to determine the effective ζ potential in a microchannel with an embedded gate electrode

We present a theoretical model to determine the effective zeta potential ζ(eff) in microfluidic channels where an embedded, insulated gate electrode allows for external tuning of a portion of the channel surface charge. In addition, we derive a method to determine ζ(eff) in such channels, for any value of salt concentration, using the solution displacement technique. To do so, we simulate typical current-monitoring measurements using our model, and highlight the experimental parameters that lead to inaccurate results using this procedure with an heterogenous channel. Our method corrects for such inaccuracies by using our model with experimental data to find the correct value of ζ(eff) . Finally, we perform experiments to demonstrate our method and the use of our model with a silica-PMDS microchannel system with an embedded Ti-Au-Ti gate electrode that covers 50% of the bottom surface of the channel. We show that our theory captures the salient features of our experiments, thereby offering a useful tool to predict effective zeta potential in channels with a nonuniform zeta potential.     

An analytical approach to the effect of finite-sized end reservoirs on electroosmotic transport through narrow confinements

The presence of end reservoirs often alters the electrical potential distributions inside narrow fluidic confinements of electrokinetically actuated miniaturized devices to a significant extent. This paper examines the influence of finite size effect of the end reservoirs on the concerned potential distribution analytically, using the Schwarz-Christoffel conformal mapping. The effective electric field directly acting across the channel is accordingly represented by a calibration curve, which sums up the role of the key geometric parameters (reservoir-to-channel height and length ratios) on the potential distribution. The analytical model is further augmented to assess the flow characteristics through the channel. The results indicate that the alterations in the flow characteristics due to alterations in the effective electric field on account of the finite size effects of the end reservoirs can turn out to be significantly more prominent than the corresponding alterations due to the axial pressure gradients induced by the sudden contraction and expansion effects associated with the end reservoirs. The derived results can be further utilized to facilitate the practical design of miniaturized fluidic devices, using conveniently tractable analytical tools.     

Calculation of the dynamic impedance of the double layer on a planar electrode by the theory of electrokinetics

Applications of microelectromechanical systems in the biotechnological arena (bioMEMS) are a subject of great current interest. Accurate calculation of electric field distribution in these devices is essential to the understanding and design of processes such as dielectrophoresis and AC electroosmosis that drive MEMS-based devices. In this paper, we present the calculation of the electrical double-layer impedance (Z(el)) of an ideally polarizable plane electrode using the standard model of colloidal electrokinetics. The frequency variation of the electrical potential drop across the double layer above a planar electrode in a general electrolyte solution is discussed as a function of the electrode zeta potential zeta, the Debye length kappa(-1), the electrolyte composition and the bulk region thickness L.     

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

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

Fluidic communication between multiple vertically segregated microfluidic channels connected by nanocapillary array membranes

Hybrid microfluidic/nanofluidic devices offer unique capabilities for manipulating and analyzing minute volumes of expensive or hard-to-obtain samples. Here, multilayer poly-(methyl methacrylate) microchips, with multiple spatially isolated microfluidic channels interconnected by nanocapillary array membranes (NCAMs), are fabricated using an adhesive contact printing process. The NCAMs, positioned between the microfluidic channel layers, add functionality to the inter-microchannel fluid transfer unit operation. They do so because the transport of specific analytes through the NCAM can be controlled by adjusting the ionic strength, the polarity of the applied bias, the surface charge density, and the pore size. A simplified, floating injection technique for NCAM-coupled nanofluidic devices is described and compared with conventional biased injection. In the floating injection approach, a voltage is applied across the injection channel and the slight electric field extension at the cross-section is used to transfer analytes through the nanopores to the separation channel. Floating injection excels in plug reproducibility, separation resolution, and operation simplicity, although it decreases assay throughput relative to biased injection. Floating injection can avoid the uneven distribution of analytes in the microfluidic channel that sometimes results from biased injection because of the volume mismatch between NCAM nanopore transport capacity and the supply of fluid. Moreover, the pressure-driven flow caused by the mismatch of the EOFs in the microfluidic channels connected by an NCAM must be considered when using NCAMs with pore diameters below 50 nm.     

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.     

Theoretical study on potential distribution and electroosmotic flow velocity in microscale channel

A developed mathematical model for calculating potential distribution inside the electrical double layer is explored in this paper based on the Poisson-Boltzmann equation. By modifying the ion concentration, we numerically simulated the potential profile inside the actual electrical double layer according to the zeta potential. Then a theoretical analysis on the streamwise electroosmotic velocity in microscale channel is presented. Furthermore, the expression of the electroosmotic velocity is significantly suppressed after considering the Helmboltz-Smolucbowski equation boundary conditions. The results show that the calculated electroosmotic values basically agree with the experimental ones. Therefore, this provides the data for micro- and nano-channels’ electrophoretic transport, as well as separation of neutral and charged electrolyte.     

Model based design of a microfluidic mixer driven by induced charge electroosmosis

Mixing chemical or biological samples with reagents for chemical analysis is one of the most time consuming operations on microfluidic platforms. This is primarily due to the low rate of diffusive transport in liquid systems. Additionally, much research has focused on detection, rather than sample preparation. In response, we describe a mixer for microfluidic sample preparation based on the electrokinetic phenomenon of induced-charge-electroosmosis (ICEO). ICEO creates microvortices within a fluidic channel by application of alternating current (AC) electric fields. The microvortices are driven by electrostatic forces acting on the ionic charge induced by the field near polarizable materials. By enabling mixing to be turned on or off within a channel of fixed volume, these electronically controlled mixers prevent sample dilution-a common problem with other strategies. A three-dimensional model based on the finite volume method was developed to calculate the electric field, fluid flow, and mass transport in a multi-species liquid. After preliminary experiments, the model was used to rapidly prototype a wide range of designs. A new microfabrication process was developed for devices with vertical sidewalls having conductive metal coatings and embedded electrodes. Mixing experiments were carried out in the devices and the results were compared to the model.     

Starting electroosmotic flow in an annulus and in a rectangular channel

The initial electroosmotic flow through a small pore or microchannel with annular or rectangular cross section is studied under the Debye-Hückel approximation. Analytical series solutions and their asymptotic behavior for small and large non-dimensional electrokinetic widths are found for these two basic cases. The explicit and accurate solutions are particularly useful for examining various geometric/physical effects on the transient time scales and the flow rates for the transient states. The steady flow rate of the smaller channel may be disproportionately smaller than a reference channel if the electric double layer is thick, but will be in close proportion to the area ratio if the electric double layer is thin. A smaller channel compared to a reference channel has a shorter transient time scale, and the transient flow has characters very different from the steady state if the electric double layer is thin. The total transient flow rate of several smaller pores or channels may exceed largely that of a single large pore or channel with the same total cross section on the transient time scale of the smaller channels. The results have important implications on liquid transport in micropores or channels by pulse voltages or more general time-varying voltages.     

Chitosan-mediated in situ biomolecule assembly in completely packaged microfluidic devices

We report facile in situ biomolecule assembly at readily addressable sites in microfluidic channels after complete fabrication and packaging of the microfluidic device. Aminopolysaccharide chitosan's pH responsive and chemically reactive properties allow electric signal-guided biomolecule assembly onto conductive inorganic surfaces from the aqueous environment, preserving the activity of the biomolecules. A transparent and nonpermanently packaged device allows consistently leak-free sealing, simple in situ and ex situ examination of the assembly procedures, fluidic input/outputs for transport of aqueous solutions, and electrical ports to guide the assembly onto the patterned gold electrode sites within the channel. Both in situ fluorescence and ex situ profilometer results confirm chitosan-mediated in situ biomolecule assembly, demonstrating a simple approach to direct the assembly of biological components into a completely fabricated device. We believe that this strategy holds significant potential as a simple and generic biomolecule assembly approach for future applications in complex biomolecular or biosensing analyses as well as in sophisticated microfluidic networks as anticipated for future lab-on-a-chip devices.     

Inherently aligned microfluidic electrodes composed of liquid metal

This paper describes the fabrication and characterization of microelectrodes that are inherently aligned with microfluidic channels and in direct contact with the fluid in the channels. Injecting low melting point alloys, such as eutectic gallium indium (EGaIn), into microchannels at room temperature (or just above room temperature) offers a simple way to fabricate microelectrodes. The channels that define the shape and position of the microelectrodes are fabricated simultaneously with other microfluidic channels (i.e., those used to manipulate fluids) in a single step; consequently, all of the components are inherently aligned. In contrast, conventional techniques require multiple fabrication steps and registration (i.e., alignment of the electrodes with the microfluidic channels), which are technically challenging. The distinguishing characteristic of this work is that the electrodes are in direct contact with the fluid in the microfluidic channel, which is useful for a number of applications such as electrophoresis. Periodic posts between the microelectrodes and the microfluidic channel prevent the liquid metal from entering the microfluidic channel during injection. A thin oxide skin that forms rapidly and spontaneously on the surface of the metal stabilizes mechanically the otherwise low viscosity, high surface tension fluid within the channel. Moreover, the injected electrodes vertically span the sidewalls of the channel, which allows for the application of uniform electric field lines throughout the height of the channel and perpendicular to the direction of flow. The electrodes are mechanically stable over operating conditions commonly used in microfluidic applications; the mechanical stability depends on the magnitude of the applied bias, the nature of the bias (DC vs. AC), and the conductivity of the solutions in the microfluidic channel. Electrodes formed using alloys with melting points above room temperature ensure mechanical stability over all of the conditions explored. As a demonstration of their utility, the fluidic electrodes are used for electrohydrodynamic mixing, which requires extremely high electric fields (~10(5) V m(-1)).