Electroosmotic flow: From microfluidics to nanofluidics

Investigation of induced electroosmotic flow in small-scale capillary electrophoresis devices: Strategies for control and reversal

Electroosmotic flow (EOF) is the bulk flow of solution in a capillary or microchannel induced by an applied electric potential. For capillary and microchip electrophoresis, the EOF enables analysis of both cations and anions in one separation and can be varied to modify separation speed and resolution. The EOF arises from an electrical double layer at the capillary wall and is normally controlled through the pH and ionic strength of the background buffer or with the use of additives. Understanding and controlling the electrical double layer is therefore critical for maintaining acceptable repeatability during method development. Surprisingly, in fused silica capillaries at low pH, studies observe an EOF even though the capillary surface should be neutralized. Previous work has suggested the presence of an "induced electroosmotic flow" from radial electric fields generated across the capillary wall due to the separation voltage and grounded components external to the capillary. Using thin-wall (15 µm) fused silica separation capillaries to facilitate the study of radial fields, we show that the EOF mobility depends on both the separation voltage and the location of external grounds. This is consistent with the induced EOF model, in which radial electric fields embed positive charges at the capillary walls to create an electrical double layer. The magnitude of the effect is characterized and shown to have long-range influences that are difficult to completely null by moving grounded components away from the separation capillary. Instead, active EOF control using externally applied potentials or a passive approach using a negative separation voltage are discussed as two possible methods for controlling the induced EOF. Both methods can reverse the EOF and improve the resolution and peak efficiency in amino acid separations.

Conformation Influence of DNA on the Detection Signal through Solid-State Nanopores

The detection and identification of nanoscale molecules are crucial, but traditional technology comes with a high cost and requires skilled operators. Solid-state nanopores are new powerful tools for discerning the three-dimensional shape and size of molecules, enabling the translation of molecular structural information into electric signals. Here, DNA molecules with different shapes were designed to explore the effects of electroosmotic forces (EOF), electrophoretic forces (EPF), and volume exclusion on electric signals within solid-state nanopores. Our results revealed that the electroosmotic force was the main driving force for single-stranded DNA (ssDNA), whereas double-stranded DNA (dsDNA) was primarily dominated by electrophoretic forces in nanopores. Moreover, dsDNA caused greater amplitude signals and moved faster through the nanopore due to its larger diameter and carrying more charges. Furthermore, at the same charge level and amount of bases, circular dsDNA exhibited a tighter structure compared to brush DNA, resulting in a shorter length. Consequently, circular dsDNA caused higher current-blocking amplitudes and faster passage speeds. The characterization approach based on nanopores allows researchers to get molecular information about size and shape in real time. These findings suggest that nanopore detection has the potential to streamline nanoscale characterization and analysis, potentially reducing both the cost and complexity.

Multilayer track-etched membrane-based electroosmotic pump for drug delivery

Herein, we report an electroosmotic pump (EOP) based on a multilayer track-etched polycarbonate (PC) membrane. A remarkable increase of maximum backpressure (198.2-2400 mmH2 O) of a fundamental pump unit was obtained at 0.8 mA, when the number of PC membranes was increased from 1 to 10. Meanwhile, the corresponding flow rate was increased from 80.3 to 111.7 µL/min. Furthermore, multiple pump units were assembled in series to obtain a multistage EOP. For a three-stage EOP (EOP-3), the operating voltage and power can be decreased significantly by 52%-72% under different driving currents, with a minimum power of 26.7 µW. Thus, EOP-3 can run stably over 35 h at a pulse current of 0.1 mA without the generation of gas bubbles. The pump was further integrated into a miniature device, which was successfully used to decrease the blood glucose level of diabetic rats by subcutaneous delivery of fast-acting insulin. This work brings a facile and efficient strategy to enhance the backpressure and lower the operating voltage and power of EOPs, which may find promising applications in drug delivery.

Current status and future application of electrically controlled micro/nanorobots in biomedicine

Using micro/nanorobots (MNRs) for targeted therapy within the human body is an emerging research direction in biomedical science. These nanoscale to microscale miniature robots possess specificity and precision that are lacking in most traditional treatment modalities. Currently, research on electrically controlled micro/nanorobots is still in its early stages, with researchers primarily focusing on the fabrication and manipulation of these robots to meet complex clinical demands. This review aims to compare the fabrication, powering, and locomotion of various electrically controlled micro/nanorobots, and explore their advantages, disadvantages, and potential applications.

Trends and challenges in microfluidic methods for protein manipulation-A review

Proteins are important molecules involved in an immensely large number of biological processes. Being capable of manipulating proteins is critical for developing reliable and affordable techniques to analyze and/or detect them. Such techniques would enable the production of therapeutic agents for the treatment of diseases or other biotechnological applications (e.g., bioreactors or biocatalysis). Microfluidic technology represents a potential solution to protein manipulation challenges because of the diverse phenomena that can be exploited to achieve micro- and nanoparticle manipulation. In this review, we discuss recent contributions made in the field of protein manipulation in microfluidic systems using different physicochemical principles and techniques, some of which are miniaturized versions of already established macro-scale techniques.

Electrokinetic transport phenomena in nanofluidics and their applications

Much progress has been made in the electrokinetic phenomena inside nanochannels in the last decades. As the dimensions of the nanochannels are compatible to that of the electric double layer (EDL), the electrokinetics inside nanochannels indicate many unexpected behaviors, which show great potential in the fields of material science, biology, and chemistry. This review summarizes the recent development of nanofluidic electrokinetics in both fundamental and applied research. First, the techniques for constructing nanochannels are introduced to give a guideline for choosing the optimal fabrication technique based on the specific feature of the nanochannel. Then, the theories and experimental investigations of the EDL, electroosmotic flow, and electrophoresis of nanoparticles inside the nanochannels are discussed. Furthermore, the applications of nanofluidic electrokinetics in iontronics, sensing, and biomolecule separation fields are summarized. In Section 5, some critical challenges and the perspective on the future development of nanofluidic electrokinetics are briefly proposed.

Ion transport properties in the pH-dependent bipolar nanochannels

In recent years, researchers have made significant strides in understanding the ion transport characteristics of nanochannels, resulting in the development of various materials, modifications, and shapes of nano ion channel membranes. The aim is to create a nanochannel membrane with optimal ion transport properties and high stability by adjusting factors, such as channel size, surface charge, and wettability. However, during the nanochannel film fabrication process, controlling the geometric structures of nanochannels can be challenging. Therefore, exploring the stability of nanochannel performance under different geometric structures has become an essential aspect of nanochannel design. This article focuses on the study of cylindrical nanochannel structures, which are categorized based on the different methods for generating bipolar surface charges on the channel's inner surface, either through pH gradient effects or different material types. Through these two approaches, the study designed and analyzed the stability of ion transport characteristics in two nanochannel models under varying geometric structures. Our findings indicate that nanochannels with bipolar properties generated through pH gradients demonstrate more stable ion selection, whereas nanochannels with bipolar properties generated through different materials show stronger stability in ion rectification. This conclusion provides a theoretical foundation for future nanochannel designs.

Spiers Memorial Lecture: Towards understanding of iontronic systems: electroosmotic flow of monovalent and divalent electrolyte through charged cylindrical nanopores

In many practical applications, ions are the primary charge carrier and must move through either semipermeable membranes or through pores, which mimic ion channels in biological systems. In analogy to electronic devices, the "iontronic" ones use electric fields to induce the charge motion. However, unlike the electrons that move through a conductor, motion of ions is usually associated with simultaneous solvent flow. A study of electroosmotic flow through narrow pores is an outstanding challenge that lies at the interface of non-equilibrium statistical mechanics and fluid dynamics. In this paper, we will review recent works that use dissipative particle dynamics simulations to tackle this difficult problem. We will also present a classical density functional theory (DFT) based on the hypernetted-chain approximation (HNC), which allows us to calculate the velocity of electroosmotic flows inside nanopores containing 1 : 1 or 2 : 1 electrolyte solution. The theoretical results will be compared with simulations. In simulations, the electrostatic interactions are treated using the recently introduced pseudo-1D Ewald summation method. The zeta potentials calculated from the location of the shear plane of a pure solvent are found to agree reasonably well with the Smoluchowski equation. However, the quantitative structure of the fluid velocity profiles deviates significantly from the predictions of the Smoluchowski equation in the case of charged pores with 2 : 1 electrolyte. For low to moderate surface charge densities, the DFT allows us to accurately calculate the electrostatic potential profiles and the zeta potentials inside the nanopores. For pores with 1 : 1 electrolyte, the agreement between theory and simulation is particularly good for large ions, for which steric effects dominate over the ionic electrostatic correlations. The electroosmotic flow is found to depend very strongly on the ionic radii. In the case of pores containing 2 : 1 electrolyte, we observe a reentrant transition in which the electroosmotic flow first reverses and then returns to normal as the surface change density of the pore is increased.

Tuning and Coupling Irreversible Electroosmotic Water Flow in Ionic Diodes: Methylation of an Intrinsically Microporous Polyamine (PIM-EA-TB)

Molecularly rigid polymers with internal charges (positive charges induced by amine methylation) allow electroosmotic water flow to be tuned by adjusting the charge density (the degree of methylation). Here, a microporous polyamine (PIM-EA-TB) is methylated to give a molecularly rigid anion conductor. The electroosmotic drag coefficient (the number of water molecules transported per anion) is shown to increase with a lower degree of methylation. Net water transport (without charge flow) in a coupled anionic diode circuit is demonstrated based on combining low and high electroosmotic drag coefficient materials. The AC-electricity-driven net process offers water transport (or transport of other neutral species, e.g., drugs) with net zero ion transport and without driver electrode side reactions.

Neural network predicts ion concentration profiles under nanoconfinement

Modeling the ion concentration profile in nanochannel plays an important role in understanding the electrical double layer and electro-osmotic flow. Due to the non-negligible surface interaction and the effect of discrete solvent molecules, molecular dynamics (MD) simulation is often used as an essential tool to study the behavior of ions under nanoconfinement. Despite the accuracy of MD simulation in modeling nanoconfinement systems, it is computationally expensive. In this work, we propose neural network to predict ion concentration profiles in nanochannels with different configurations, including channel widths, ion molarity, and ion types. By modeling the ion concentration profile as a probability distribution, our neural network can serve as a much faster surrogate model for MD simulation with high accuracy. We further demonstrate the superior prediction accuracy of neural network over XGBoost. Finally, we demonstrated that neural network is flexible in predicting ion concentration profiles with different bin sizes. Overall, our deep learning model is a fast, flexible, and accurate surrogate model to predict ion concentration profiles in nanoconfinement.

Electropatterning-Contemporary developments for selective particle arrangements employing electrokinetics

The selective positioning and arrangement of distinct types of multiscale particles can be used in numerous applications in microfluidics, including integrated circuits, sensors and biochips. Electrokinetic (EK) techniques offer an extensive range of options for label-free manipulation and patterning of colloidal particles by exploiting the intrinsic electrical properties of the target of interest. EK-based techniques have been widely implemented in many recent studies, and various methodologies and microfluidic device designs have been developed to achieve patterning two- and three-dimensional (3D) patterned structures. This review provides an overview of the progress in electropatterning research during the last 5 years in the microfluidics arena. This article discusses the advances in the electropatterning of colloids, droplets, synthetic particles, cells, and gels. Each subsection analyzes the manipulation of the particles of interest via EK techniques such as electrophoresis and dielectrophoresis. The conclusions summarize recent advances and provide an outlook on the future of electropatterning in various fields of application, especially those with 3D arrangements as their end goal.

Electroosmotic flow in fused deposition modeling (FDM) 3D-printed microchannels

Electroosmotic flow (EOF) was determined in tridimensional (3D)-printed microchannels with dimensions smaller than 100 µm. Fused deposition modeling 3D printing using thermoplastic filaments of PETG (polyethylene terephthalate glycol), PLA (polylactic acid), and ABS (acrylonitrile butadiene styrene) were used to fabricate the microchannels. The current monitoring method and sodium phosphate solutions at different pH values (3-10) were used for the EOF mobility (µ_EOF ) measurements, which ranged from 2.00 × 10^-4 to 12.52 × 10^-4  cm²  V^-1  s^-1 . The highest and the smallest µ_EOF were obtained for the PLA and PETG microchannels, respectively. Adding the cationic surfactant cetyltrimethylammonium bromide to the sodium phosphate solution caused EOF direction reversion in all the studied microchannels. The obtained results can be interesting for developing 3D-printed microfluidic devices, in which EOF is relevant.

Connected Droplet Shape Analysis for Nanoflow Quantification in Thin Electroosmotic Micropumps and a Tunable Convex Lens Application

Thin electroosmotic flow (EOF) micropumps can generate flow in confined spaces such as lab-on-a-chip microsystems and implantable drug delivery devices. However, status quo methods for quantifying flow and other important parameters in EOF micropumps depend on microfluidic interconnects or fluorescent particle tracking: methods that can be complex and error-prone. Here, we present a novel connected droplet shape analysis (CDSA) technique that simplifies flow rate and zeta potential quantification in thin EOF micropumps. We also show that a pair of droplets connected by an EOF pump can function as a tunable convex lens system (TCLS). We developed a biocompatible and all polymer EOF micropump with an SU-8 substrate and poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (PEDOT:PSS) electrodes. We microdrilled a channel through the electrode/SU-8/electrode layers to realize a monolithic EOF micropump. Then, we deposited a pinned droplet on each end of the microchannel so that it connected them. By controlling the EOF between the droplets and measuring the corresponding change in their shape, we quantified the nanoliter EOF rate and zeta potential at the interface of SU-8 with two liquids (deionized water and a l-glutamate neurotransmitter solution). When the droplet pair and pump were used as a TCLS, CDSA successfully predicted how the focal length would change when the pump drove fluid from one droplet to another. In summary, CDSA is a simple low-cost technique for EOF rate and zeta potential measurement, and a pair of droplets connected by an EOF micropump can function as a TCLS without any moving parts.

Resonant Nanopumps: ac Gate Voltages in Conical Nanopores Induce Directed Electrolyte Flow

Inducing transport in electrolyte-filled nanopores with dc fields has led to influential applications ranging from nanosensors to DNA sequencing. Here we use the Poisson-Nernst-Planck and Navier-Stokes equations to show that unbiased ac fields can induce comparable directional flows in gated conical nanopores. This flow exclusively occurs at intermediate driving frequencies and hinges on the resonance of two competing timescales, representing space charge development at the ends and in the interior of the pore. We summarize the physics of resonant nanopumping in an analytical model that reproduces the results of numerical simulations. Our findings provide a generic route toward real-time controllable flow patterns, which might find applications in controlling the translocation of small molecules or nanocolloids.

Pulsation Reduction Using Dual Sidewall-Driven Micropumps

Single-cell manipulation in microfluidic channels at the micrometer scale has recently become common. However, the current mainstream method using a syringe pump and a piezoelectric actuator is not suitable for long-term experiments. Some methods incorporate a pump mechanism into a microfluidic channel, but they are not suitable for mass production owing to their complex structures. Here, we propose a sidewall-driven micropump integrated into a microfluidic device as well as a method for reducing the pulsation of flow. This sidewall-driven micropump consists of small chambers lined up on both sides along the main flow path, with a wall separating the flow path and each chamber being deformed by air pressure. The chambers are pressurized to make the peristaltic motion of the wall possible, which generates flow in the main flow path. This pump can be created in a single layer, which allows a simplified structure to be achieved, although pulsation can occur when the pump is used alone. We created two types of chips with two micropumps placed in the flow path and attempted to reduce pulsation by driving them in different phases. The proposed dually driven micropump reduced pulsation when compared with the single pump. This device enables precise particle control and is expected to contribute to less costly and easier cell manipulation experiments.

A theoretical understanding of ionic current through a nanochannel driven by a viscosity gradient

HYPOTHESIS

Different thermodynamic forces owing to the gradient of temperature, electrical potential, or concentration can drive ionic current through charged membranes. It has been recently shown that a viscosity gradient can drive an electrical current through a negatively charged nanochannel (Wiener and Stein, arXiv: 1807.09106). A model description of this phenomenon, based on the Maxwell-Stefan equation will help unravel the dominating physical mechanisms in so-called visco-migration.

THEORY

To understand the physical mechanisms underlying this phenomenon, we employed the Maxwell-Stefan equation to develop a 1D model and obtain a relation between the flux of solvents and the driving forces. Viscosity gradients are known to drive transport, but the development of an electrical current has not been theoretically described prior to this work.

FINDINGS

Our 1D model shows that the ionic current depends on the ideality of the solvent, though both ideal and non-ideal scenarios demonstrated good agreement with experimental data. We employed the model to understand the impact of solution bulk ionic strength and pH on the drift of ionic species with same reservoirs solution properties. Our modeling results unveiled the significant impact of bulk solution properties on the drift of ions which is in agreement with the experiments. Moreover, we have shown that the diffusion gradient along the nanochannel contributes significantly into driving ionic species if we even apply a small ionic concentration gradient to both reservoirs. Our modeling results may pave the way for finding novel applications for drift of ions in a diffusion gradient, which can be induced by connecting reservoirs of different viscosity fluids.

A simple yet efficient approach for electrokinetic mixing of viscoelastic fluids in a straight microchannel

Many complex fluids such as emulsions, suspensions, biofluids, etc., are routinely encountered in many micro and nanoscale systems. These fluids exhibit non-Newtonian viscoelastic behaviour instead of showing simple Newtonian one. It is often needed to mix such viscoelastic fluids in small-scale micro-systems for further processing and analysis which is often achieved by the application of an external electric field and/or using the electroosmotic flow phenomena. This study proposes a very simple yet efficient  strategy to mix such viscoelastic fluids based on extensive numerical simulations. Our proposed setup consists of a straight microchannel with small patches of constant wall zeta potential, which are present on both the top and bottom walls of the microchannel. This heterogeneous zeta potential on the microchannel wall generates local electro-elastic instability and electro-elastic turbulence once the Weissenberg number exceeds a critical value. These instabilities and turbulence, driven by the interaction between the elastic stresses and the streamline curvature present in the system, ultimately lead to a chaotic and unstable flow field, thereby facilitating the mixing of such viscoelastic fluids. In particular, based on our proposed approach, we show how one can use the rheological properties of fluids and associated fluid-mechanical phenomena for their efficient mixing even in a straight microchannel.

Soft hydraulics: from Newtonian to complex fluid flows through compliant conduits

Microfluidic devices manufactured from soft polymeric materials have emerged as a paradigm for cheap, disposable and easy-to-prototype fluidic platforms for integrating chemical and biological assays and analyses. The interplay between the flow forces and the inherently compliant conduits of such microfluidic devices requires careful consideration. While mechanical compliance was initially a side-effect of the manufacturing process and materials used, compliance has now become a paradigm, enabling new approaches to microrheological measurements, new modalities of micromixing, and improved sieving of micro- and nano-particles, to name a few applications. This topical review provides an introduction to the physics of these systems. Specifically, the goal of this review is to summarize the recent progress towards a mechanistic understanding of the interaction between non-Newtonian (complex) fluid flows and their deformable confining boundaries. In this context, key experimental results and relevant applications are also explored, hand-in-hand with the fundamental principles for their physics-based modeling. The key topics covered include shear-dependent viscosity of non-Newtonian fluids, hydrodynamic pressure gradients during flow, the elastic response (deformation and bulging) of soft conduits due to flow within, the effect of cross-sectional conduit geometry on the resulting fluid-structure interaction, and key dimensionless groups describing the coupled physics. Open problems and future directions in this nascent field of soft hydraulics, at the intersection of non-Newtonian fluid mechanics, soft matter physics, and microfluidics, are noted.

Radial basis function interpolation supplemented lattice Boltzmann method for electroosmotic flows in microchannel

Large gradients of physical variables near the channel walls are characteristic of EOF. The previous numerical simulations of EOFs with the lattice Boltzmann method (LBM) utilize uniform lattice and are not efficient, especially when the electric double layer (EDL) thickness is significantly smaller than the channel height. The efficient LBM simulation of EOF in microchannel calls for a nonuniform mesh which is dense in the EDL region and sparse in the bulk region. In this article, we formulate a radial basis function (RBF)-based interpolation supplemented LBM (ISLBM) to solve the governing equations of EOF, that is, the Poisson, Nernst-Planck, and Navier-Stokes equations, in a nonuniform mesh system. Unlike the conventional ISLBM, the RBF-ISLBM determines the prestreaming distribution functions by using the local RBF-based interpolation over circular supporting regions and is particularly suitable for nonuniform meshes. The RBF-ISLBM is validated by the EOFs in infinitely long and finitely long microchannels. The results show that the RBF-ISLBM possesses excellent robustness and accuracy. Finally, we use the RBF-ISLBM to simulate the EOFs with the hitherto highest electrokinetic parameter, κa, defined by the ratio of channel height a to EDL thickness κ^-1 , in LBM simulations of EOF.

Investigation of entrance effects on particle electrophoretic behavior near a nanopore for resistive pulse sensing

Resistive pulse sensing using solid-state nanopores provides a unique platform for detecting the structure and concentration of molecules of different types of analytes in an electrolyte solution. The capture of an entity into a nanopore is subject not only to the electrostatic force but also the effect of electroosmotic flow originating from the charged nanopore surface. In this study, we theoretically analyze spherical particle electrophoretic behavior near the entrance of a charged nanopore. By investigating the effects of pore size, particle-pore distance, and salt concentration on particle velocity, we summarize dominant mechanisms governing particle behavior for a range of conditions. In the literature, the Helmholtz-Smoluchowski equation is often adopted to evaluate particle translocation by considering the zeta potential difference between the particle and nanopore surfaces. We point out that, due to the difference of the electric field inside and outside the nanopore and the influence from the existence of the particle itself, the zeta potential of the particle, however, needs to be at least 30% higher than that of the nanopore to allow the particle to enter into the nanopore when its velocity is close to zero. Accordingly, we summarize the effective salt concentrations that enable successful particle capture and detection for different pore sizes, offering direct guidance for nanopore applications.

Review of nonlinear electrokinetic flows in insulator-based dielectrophoresis: From induced charge to Joule heating effects

Insulator-based dielectrophoresis (iDEP) has been increasingly used for particle manipulation in various microfluidic applications. It exploits insulating structures to constrict and/or curve electric field lines to generate field gradients for particle dielectrophoresis. However, the presence of these insulators, especially those with sharp edges, causes two nonlinear electrokinetic flows, which, if sufficiently strong, may disturb the otherwise linear electrokinetic motion of particles and affect the iDEP performance. One is induced charge electroosmotic (ICEO) flow because of the polarization of the insulators, and the other is electrothermal flow because of the amplified Joule heating in the fluid around the insulators. Both flows vary nonlinearly with the applied electric field (either DC or AC) and exhibit in the form of fluid vortices, which have been utilized to promote some applications while being suppressed in others. The effectiveness of iDEP benefits from a comprehensive understanding of the nonlinear electrokinetic flows, which is complicated by the involvement of the entire iDEP device into electric polarization and thermal diffusion. This article is aimed to review the works on both the fundamentals and applications of ICEO and electrothermal flows in iDEP microdevices. A personal perspective of some future research directions in the field is also given.

Insulator-based dielectrophoretic focusing and trapping of particles in non-Newtonian fluids

Insulator-based dielectrophoretic (iDEP) microdevices have been limited to work with Newtonian fluids. We report an experimental study of the fluid rheological effects on iDEP focusing and trapping of polystyrene particles in polyethylene oxide, xanthan gum, and polyacrylamide solutions through a constricted microchannel. Particle focusing and trapping in the mildly viscoelastic polyethylene oxide solution are slightly weaker than in the Newtonian buffer. They are, however, significantly improved in the strongly viscoelastic and shear thinning polyacrylamide solution. These observed particle focusing behaviors exhibit a similar trend with respect to electric field, consistent with a revised theoretical analysis for iDEP focusing in non-Newtonian fluids. No apparent focusing of particles is achieved in the xanthan gum solution, though the iDEP trapping can take place under a much larger electric field than the other fluids. This is attributed to the strong shear thinning-induced influences on both the electroosmotic flow and electrokinetic/dielectrophoretic motions.