On AC-Field-Induced Nonlinear Electroosmosis next to the Sharp Corner-Field-Singularity of Leaky Dielectric Blocks and Its Application in on-Chip Micro-Mixing

Micromixing within microfluidic devices: Fundamentals, design, and fabrication

As one of the hot spots in the field of microfluidic chip research, micromixers have been widely used in chemistry, biology, and medicine due to their small size, fast response time, and low reagent consumption. However, at low Reynolds numbers, the fluid motion relies mainly on the diffusive motion of molecules under laminar flow conditions. The detrimental effect of laminar flow leads to difficulties in achieving rapid and efficient mixing of fluids in microchannels. Therefore, it is necessary to enhance fluid mixing by employing some external means. In this paper, the classification and mixing principles of passive (T-type, Y-type, obstructed, serpentine, three-dimensional) and active (acoustic, electric, pressure, thermal, magnetic field) micromixers are reviewed based on the presence or absence of external forces in the micromixers, and some experiments and applications of each type of micromixer are briefly discussed. Finally, the future development trends of micromixers are summarized.

A Modified-Herringbone Micromixer for Assessing Zebrafish Sperm (MAGS)

Sperm motility analysis of aquatic model species is important yet challenging due to the small sample volume, the necessity to activate with water, and the short duration of motility. To achieve standardization of sperm activation, microfluidic mixers have shown improved reproducibility over activation by hand, but challenges remain in optimizing and simplifying the use of these microdevices for greater adoption. The device described herein incorporates a novel micromixer geometry that aligns two sperm inlet streams with modified herringbone structures that split and recombine the sample at a 1:6 dilution with water to achieve rapid and consistent initiation of motility. The polydimethylsiloxane (PDMS) chip can be operated in a positive or negative pressure configuration, allowing a simple micropipettor to draw samples into the chip and rapidly stop the flow. The device was optimized to not only activate zebrafish sperm but also enables practical use with standard computer-assisted sperm analysis (CASA) systems. The micromixer geometry could be modified for other aquatic species with differing cell sizes and adopted for an open hardware approach using 3D resin printing where users could revise, fabricate, and share designs to improve standardization and reproducibility across laboratories and repositories.

Onset of Nonlinear Electroosmotic Flow under an AC Electric Field

Nonlinearity of electroosmotic flows (EOFs) is ubiquitous and plays a crucial role in ion transport, specimen mixing, electrochemistry reaction, and electric energy storage and utilization. When and how the transition from a linear regime to a nonlinear one occurs is essential for understanding, prohibiting, or utilizing nonlinear EOF. However, due to the lack of reliable experimental instruments with high spatial and temporal resolutions, the investigation of the onset of nonlinear EOF still remains in theory. Herein, we experimentally studied the velocity fluctuations of EOFs driven by an alternating current (AC) electric field via ultrasensitive fluorescent blinking tricks. The linear and nonlinear AC EOFs are successfully identified from both the time trace and energy spectra of velocity fluctuations. The transitional electric field (E_A,C) is determined by both the convection velocity (U) and AC frequency (f_f) as E_A,C ∼ f_f^0.48-0.027U. We hope the current investigation could be essential in the development of both theory and applications of nonlinear EOFs.

Mixing and Flow Transition in an Optimized Electrokinetic Turbulent Micromixer

Micromixer is a key element in a lab on a chip for broad applications in the analysis and measurement of chemistry and engineering. Previous investigations reported that electrokinetic (EK) turbulence could be realized in a "Y" type micromixer with a cross-sectional dimension of 100 μm order. Although the ultrafast turbulent mixing can be generated at a bulk flow Reynolds number on the order of unity, the micromixer has not been optimized. In this investigation, we systematically investigated the influence of electric field intensity, AC frequency, electric conductivity ratio, and channel width at the entrance on the mixing effect and transition electric Rayleigh number in the "Y" type electrokinetic turbulent micromixer. It is found that the optimal mixing is realized in a 350 μm wide micromixer, under 100 kHz and 1.14 × 10⁵ V/m AC electric field, with an electric conductivity ratio of 1:3000. Under these conditions, a degree of mixedness of 0.93 can be achieved at 84 μm from the entrance and 100 ms. A further investigation of the critical electric field and the critical electric Rayleigh number indicates that the most unstable condition of EK flow instability is inconsistent with that of the optimal mixing in EK turbulence. To predict the evolution of EK flow under high Ra_σ and guide the design of EK turbulent micromixers, it is necessary to apply a computational turbulence model instead of linear instability analysis.

Amplification factor in DC insulator-based electrokinetic devices: a theoretical, numerical, and experimental approach to operation voltage reduction for particle trapping

Insulator-based microfluidic devices are attractive for handling biological samples due to their simple fabrication, low-cost, and efficiency in particle manipulation. However, their widespread application is limited by the high operation voltages required to achieve particle trapping. We present a theoretical, numerical, and experimental study that demonstrates these voltages can be significantly reduced (to sub-100 V) in direct-current insulator-based electrokinetic (DC-iEK) devices for micron-sized particles. To achieve this, we introduce the concept of the amplification factor-the fold-increase in electric field magnitude due to the presence of an insulator constriction-and use it to compare the performance of different microchannel designs and to direct our design optimization process. To illustrate the effect of using constrictions with smooth and sharp features on the amplification factor, geometries with circular posts and semi-triangular posts were used. These were theoretically approximated in two different systems of coordinates (bipolar and elliptic), allowing us to provide, for the first time, explicit electric field amplification scaling laws. Finite element simulations were performed to approximate the 3D insulator geometries and provide a parametric study of the effect of changing different geometrical features. These simulations were used to predict particle trapping voltages for four different single-layer microfluidic devices using two particle suspensions (2 and 6.8 μm in size). The general agreement between our models demonstrates the feasibility of using the amplification factor, in combination with nonlinear electrokinetic theory, to meet the prerequisites for the development of portable DC-iEK microfluidic systems.

Self-aligned sequential lateral field non-uniformities over channel depth for high throughput dielectrophoretic cell deflection

Dielectrophoresis (DEP) enables the separation of cells based on subtle subcellular phenotypic differences by controlling the frequency of the applied field. However, current electrode-based geometries extend over a limited depth of the sample channel, thereby reducing the throughput of the manipulated sample (sub-μL min-1 flow rates and <105 cells per mL). We present a flow through device with self-aligned sequential field non-uniformities extending laterally across the sample channel width (100 μm) that are created by metal patterned over the entire depth (50 μm) of the sample channel sidewall using a single lithography step. This enables single-cell streamlines to undergo progressive DEP deflection with minimal dependence on the cell starting position, its orientation versus the field and intercellular interactions. Phenotype-specific cell separation is validated (>μL min-1 flow and >106 cells per mL) using heterogeneous samples of healthy and glutaraldehyde-fixed red blood cells, with single-cell impedance cytometry showing that the DEP collected fractions are intact and exhibit electrical opacity differences consistent with their capacitance-based DEP crossover frequency. This geometry can address the vision of an "all electric" selective cell isolation and cytometry system for quantifying phenotypic heterogeneity of cellular systems.

Recent advancement in induced-charge electrokinetic phenomena and their micro- and nano-fluidic applications

Induced-charge electrokinetics (ICEK) remains a hot topic due to its promising applications in micro- and nano-fluidics. Over the past decade, researchers have made a great advancement in both fundamental studies and application developments. They captured (I) a flow reversal in induced-charge electroosmosis (ICEO) and attributed it to the phase delay effect of ions, (II) a chaotic ICEO and attributed it to the concentration polarization in the bulk solution, (III) a non-quadratic correlation for ICEO of non-Newtonian fluids and attributed it to the power-law viscosity, (IV) an induced-charge electrophoretic (ICEP) rotation of Janus doublets, etc. Furthermore, various ICEK-based micro- and nano-fluidic devices have been developed, namely, micropumps, particle focusers, trappers, sorters, and nanopore ion diodes. The present article provides a comprehensive review on the recent advancement of ICEK. Firstly, the fundamental studies of ICEK are introduced; then the micro- and nano-fluidic applications based on ICEK are presented; lastly, promising future directions for both fundamental and applications are discussed. This review presents the basic framework of ICEK, and can facilitate the development of ICEK-based applications.

Buoyancy-Free Janus Microcylinders as Mobile Microelectrode Arrays for Continuous Microfluidic Biomolecule Collection within a Wide Frequency Range: A Numerical Simulation Study

We numerically study herein the AC electrokinetic motion of Janus mobile microelectrode (ME) arrays in electrolyte solution in a wide field frequency, which holds great potential for biomedical applications. A fully coupled physical model, which incorporates the fluid-structure interaction under the synergy of induced-charge electroosmotic (ICEO) slipping and interfacial Maxwell stress, is developed for this purpose. A freely suspended Janus cylinder free from buoyancy, whose main body is made of polystyrene, while half of the particle surface is coated with a thin conducting film of negligible thickness, will react actively on application of an AC signal. In the low-frequency limit, induced-charge electrophoretic (ICEP) translation occurs due to symmetric breaking in ICEO slipping, which renders the insulating end to move ahead. At higher field frequencies, a brand-new electrokinetic transport phenomenon called "ego-dielectrophoresis (e-DEP)" arises due to the action of the localized uneven field on the inhomogeneous particle dipole moment. In stark contrast with the low-frequency ICEP translation, the high-frequency e-DEP force tends to drive the asymmetric dipole moment to move in the direction of the conducting end. The bidirectional transport feature of Janus microspheres in a wide AC frequency range can be vividly interpreted as an array of ME for continuous loading of secondary bioparticles from the surrounding liquid medium along its direction-controllable path by long-range electroconvection. These results pave the way for achieving flexible and high-throughput on-chip extraction of nanoscale biological contents for subsequent on-site bioassay based upon AC electrokinetics of Janus ME arrays.

Microfluidic Magnetic Mixing at Low Reynolds Numbers and in Stagnant Fluids

Microfluidic mixing becomes a necessity when thorough sample homogenization is required in small volumes of fluid, such as in lab-on-a-chip devices. For example, efficient mixing is extraordinarily challenging in capillary-filling microfluidic devices and in microchambers with stagnant fluids. To address this issue, specifically designed geometrical features can enhance the effect of diffusion and provide efficient mixing by inducing chaotic fluid flow. This scheme is known as “passive” mixing. In addition, when rapid and global mixing is essential, “active” mixing can be applied by exploiting an external source. In particular, magnetic mixing (where a magnetic field acts to stimulate mixing) shows great potential for high mixing efficiency. This method generally involves magnetic beads and external (or integrated) magnets for the creation of chaotic motion in the device. However, there is still plenty of room for exploiting the potential of magnetic beads for mixing applications. Therefore, this review article focuses on the advantages of magnetic bead mixing along with recommendations on improving mixing in low Reynolds number flows (Re ≤ 1) and in stagnant fluids.

Highly Sensitive Micropatterned Interdigitated Electrodes for Enhancing the Concentration Effect Based on Dielectrophoresis

The concentration effect of dielectrophoresis (DEP) enables detection of biomolecules with high sensitivity. In this study, microstructures were patterned between the interdigitated microelectrodes (IMEs) to increase the concentration effect of DEP. The microstructures increased the electric field gradient (∇|E2|) between the IMEs to approximately 6.61-fold higher than in the bare IMEs with a gap of 10 μm, resulting in a decreased optimal voltage to concentrate amyloid beta 42 (Aβ₄₂, from 0.8 V_pp to 0.5 V_pp) and tau-441 (from 0.9 V_pp to 0.6 V_pp) between the IMEs. Due to the concentration effect of DEP, the impedance change in the optimal condition was higher than the values in the reference condition at 2.64-fold in Aβ₄₂ detection and at 1.59-fold in tau-441 detection. This concentration effect of DEP was also verified by counting the number of gold (Au) particles which conjugated with the secondary antibody. Finally, an enhanced concentration effect in the patterned IMEs was verified by measuring the impedance change depending on the concentration of Aβ₄₂ and tau-441. Our results suggest that microstructures increase the concentration effect of DEP, leading to enhanced sensitivity of the IMEs.

Multifrequency Induced-Charge Electroosmosis

We present herein a unique concept of multifrequency induced-charge electroosmosis (MICEO) actuated directly on driving electrode arrays, for highly-efficient simultaneous transport and convective mixing of fluidic samples in microscale ducts. MICEO delicately combines transversal AC electroosmotic vortex flow, and axial traveling-wave electroosmotic pump motion under external dual-Fourier-mode AC electric fields. The synthetic flow field associated with MICEO is mathematically analyzed under thin layer limit, and the particle tracing experiment with a special powering technique validates the effectiveness of this physical phenomenon. Meanwhile, the simulation results with a full-scale 3D computation model demonstrate its robust dual-functionality in inducing fully-automated analyte transport and chaotic stirring in a straight fluidic channel embedding double-sided quarter-phase discrete electrode arrays. Our physical demonstration with multifrequency signal control on nonlinear electroosmosis provides invaluable references for innovative designs of multifunctional on-chip analytical platforms in modern microfluidic systems.

Size-Tunable Assembly of Gold Nanoparticles Using Competitive AC Electrokinetics

Alternating current (AC) electrokinetics is a facile way of patterning colloidal particles into advanced structures. We demonstrate the combined use of AC dielectrophoresis (AC-DEP) and AC electrohydrodynamics (AC-EHD) in a microwell electrode geometry for size-tunable assembly of gold nanoparticles (AuNPs) into one-dimensional microwires and two-dimensional films. The AC-DEP force scales with both particle size and field frequency, whereas the AC-EHD force depends only on the field frequency. So, a critical particle diameter ( d_c) exists, below which the EHD phenomenon becomes more important and beyond which the DEP force is dominating. We performed theoretical and experimental studies to determine " d_c" and how it gets affected by operating parameters like field frequency, voltage, particle number, electrolyte concentration, electrode size, and geometry. Our results show that the morphologies of the colloidal structures transition from films to microwires as the NP diameters vary from nanometers (< d_c) to microns (> d_c), and no assembly takes place at intermediate sizes (∼ d_c). While the film formation is governed purely by surface EHD flows, microwire synthesis is a result of EHD-assisted DEP phenomenon. Also, a minimum particle number, a low salt concentration, and an optimum frequency range is required to initiate assembly.

Asymmetrical Induced Charge Electroosmotic Flow on a Herringbone Floating Electrode and Its Application in a Micromixer

Enhancing mixing is of significant importance in microfluidic devices characterized by laminar flows and low Reynolds numbers. An asymmetrical induced charge electroosmotic (ICEO) vortex pair generated on the herringbone floating electrode can disturb the interface of two-phase fluids and deliver the fluid transversely, which could be exploited to accomplish fluid mixing between two neighbouring fluids in a microscale system. Herein we present a micromixer based on an asymmetrical ICEO flow induced above the herringbone floating electrode array surface. We investigate the average transverse ICEO slip velocity on the Ridge/Vee/herringbone floating electrode and find that the microvortex generated on the herringbone electrode surface has good potential for mixing the miscible liquids in microfluidic systems. In addition, we explore the effect of applied frequencies and bulk conductivity on the slip velocity above the herringbone floating electrode surface. The high dependence of mixing performance on the floating electrode pair numbers is analysed simultaneously. Finally, we investigate systematically voltage intensity, applied frequencies, inlet fluid velocity and liquid conductivity on the mixing performance of the proposed device. The microfluidic micromixer put forward herein offers great opportunity for fluid mixing in the field of micro total analysis systems.

Editorial for the Special Issue on Micro/Nano-Chip Electrokinetics, Volume II

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On Developing Field-Effect-Tunable Nanofluidic Ion Diodes with Bipolar, Induced-Charge Electrokinetics

We introduce herein the induced-charge electrokinetic phenomenon to nanometer fluidic systems; the design of the nanofluidic ion diode for field-effect ionic current control of the nanometer dimension is developed by enhancing internal ion concentration polarization through electrochemical transport of inhomogeneous inducing-counterions resulting from double gate terminals mounted on top of a thin dielectric layer, which covers the nanochannel connected to microfluidic reservoirs on both sides. A mathematical model based on the fully-coupled Poisson-Nernst-Plank-Navier-Stokes equations is developed to study the feasibility of this structural configuration causing effective ionic current rectification. The effect of various physiochemical and geometrical parameters, such as the native surface charge density on the nanochannel sidewalls, the number of gate electrodes (GE), the gate voltage magnitude, and the solution conductivity, permittivity, and thickness of the dielectric coating, as well as the size and position of the GE pair of opposite gate polarity, on the resulted rectification performance of the presented nanoscale ionic device is numerically analyzed by using a commercial software package, COMSOL Multiphysics (version 5.2). Three types of electrohydrodynamic flow, including electroosmosis of 1st kind, induced-charge electroosmosis, and electroosmosis of 2nd kind that were originated by the Coulomb force within three distinct charge layers coexist in the micro/nanofluidic hybrid network and are shown to simultaneously influence the output current flux in a complex manner. The rectification factor of a contrast between the 'on' and 'off' working states can even exceed one thousand-fold in the case of choosing a suitable combination of several key parameters. Our demonstration of field-effect-tunable nanofluidic ion diodes of double external gate electrodes proves invaluable for the construction of a flexible electrokinetic platform for ionic current control and may help transform the field of smart, on-chip, integrated circuits.