Nonlinear Electrokinetics Research Articles

Nonlinear Electrokinetic Methods of Particles and Cells.

Nonlinear electrokinetic phenomena offer label-free, portable, and robust approaches for particle and cell assessment, including selective enrichment, separation, sorting, and characterization. The field of electrokinetics has evolved substantially since the first separation reports by Arne Tiselius in the 1930s. The last century witnessed major advances in the understanding of the weak-field theory, which supported developments in the use of linear electrophoresis and its adoption as a routine analytical technique. More recently, an improved understanding of the strong-field theory enabled the development of nonlinear electrokinetic techniques such as electrorotation, dielectrophoresis, and nonlinear electrophoresis. This review discusses the operating principles and recent applications of these three nonlinear electrokinetic phenomena for the analysis and manipulation of particles and cells and provides an overview of some of the latest developments in the field of nonlinear electrokinetics.

Rheology of dense suspensions of ideally conductive particles in an electric field

The rheological behaviour of dense suspensions of ideally conductive particles in the presence of both electric field and shear flow is studied using large-scale numerical simulations. Under the action of an electric field, these particles are known to undergo dipolophoresis (DIP), which is the combination of two nonlinear electrokinetic phenomena: induced-charge electrophoresis (ICEP) and dielectrophoresis (DEP). For ideally conductive particles, ICEP is predominant over DEP, resulting in transient pairing dynamics. The shear viscosity and first and second normal stress differences $N_1$ and $N_2$ of such suspensions are examined over a range of volume fractions $15\,\% \leq \phi \leq 50\,\%$ as a function of Mason number $Mn$ , which measures the relative importance of viscous shear stress over electrokinetic-driven stress. For $Mn < 1$ or low shear rates, the DIP is shown to dominate the dynamics, resulting in a relatively low-viscosity state. The positive $N_1$ and negative $N_2$ are observed at $\phi < 30\,\%$ , which is similar to Brownian suspensions, while their signs are reversed at $\phi \ge 30\,\%$ . For $Mn \ge 1$ , the shear thickening starts to arise at $\phi \ge 30\,\%$ , and an almost five-fold increase in viscosity occurs at $\phi = 50\,\%$ . Both $N_1$ and $N_2$ are negative for $Mn \gg 1$ at all volume fractions considered. We illuminate the transition in rheological behaviours from DIP to shear dominance around $Mn = 1$ in connection to suspension microstructure and dynamics. Lastly, our findings reveal the potential use of nonlinear electrokinetics as a means of active rheology control for such suspensions.

Analytic theory of nonlinearly coupled electrokinetics in nanochannels

The nonlinear electrokinetic response of ionic solutions is important in nanofluidics. However, quantitatively understanding the mechanisms is still a challenging problem because of a lack of analytic approaches. Here, a general framework for calculating the nonlinear electrokinetic coefficients of strongly confined electrolytes is constructed using a perturbation scheme of the pressure and voltage differences across a nanochannel. The theory is applied to an electrically neutral nanochannel filled with electrolytes, and analytic expressions for the first- and third-order electrokinetic coefficients are obtained. We demonstrate that the combination of high hydrodynamic permeability and ion–wall friction plays an essential role in nonlinear electrokinetics. Furthermore, we analytically demonstrate that the external flow induces uniform excess charge inside the nanochannel.

Alternating-current nonlinear electrokinetics in microfluidic insulator-decorated bipolar electrochemistry

We proposed herein a unique method of insulator-decorated bipolar electrochemistry (IDBE), for realizing large-scale separation of bioparticles in microchannels driven by AC dielectrophoresis (DEP). In IDBE, a pair of planar driving electrodes is placed at the bottom of channel sidewalls, between which an array of the rectangular floating electrode (FE) strips without external Ohmic contact are evenly spaced along transversal direction, and a series of insulating dielectric blocks are periodically deposited above all the inter-electrode gaps and in full contact with the channel bottom surface. By creating local field maximum and minimum at multiple sites, IDBE extends well the actuating range of DEP force field from the immediate vicinity of electrode tips in traditional bipolar electrochemistry to current fluid bulk. Considering DEP force plays the dominant role around 1 MHz, we utilize Lagrange particle tracing algorithm to calculate motion trajectories of incoming samples for testing the feasibility of microchip in continuous separation of live and dead yeast cells. By applying suitable voltage parameters, highly efficient DEP sorting is theoretically achievable under a moderate inlet flow rate, where most of the viable yeasts are trapped by positive-DEP to sharp dielectric edges, while all the incoming nonviable yeasts are repelled by negative-DEP to the top surface of both FE and insulating block to form multiple thin beams co-flowing into the channel outlet. The microfluidic device exploiting insulators on bipolar FE effectively expands the actuating range of nonlinear electrodynamics and provides invaluable guidelines for developing flexible electrokinetic frameworks in modern microfluidic systems.

Microscale nonlinear electrokinetics for the analysis of cellular materials in clinical applications: a review.

This review article presents a discussion of some of the latest advancements in the field of microscale electrokinetics for the analysis of cells and subcellular materials in clinical applications. The introduction presents an overview on the use of electric fields, i.e., electrokinetics, in microfluidics devices and discusses the potential of electrokinetic-based methods for the analysis of liquid biopsies in clinical and point-of-care applications. This is followed by four comprehensive sections that present some of the newest findings on the analysis of circulating tumor cells, blood (red blood cells, white blood cells, and platelets), stem cells, and subcellular particles (extracellular vesicles and mitochondria). The valuable contributions discussed here (with 131 references) were mainly published during the last 3 to 4 years, providing the reader with an overview of the state-of-the-art in the use of microscale electrokinetic methods in clinical analysis. Finally, the conclusions summarize the main advancements and discuss the future prospects.

Analysis of microorganisms with nonlinear electrokinetic microsystems.

Nonlinear electrokinetics (EK), specifically electrophoresis of the second kind, dielectrophoresis (DEP) and electrorotation (EROT), have gained significant interest recently for their flexibility and labeless discriminant manner of operation. The current applications of these technologies are a clear advancement from what they were when first discovered, but also still show strong signs of future growth. The present review article presents a discussion of the current uses of microscale nonlinear EK technologies as analytical, sensing, and purification tools for microorganisms. The discussion is focused on some of the latest discoveries with various nonlinear EK microfluidic techniques, such as DEP particle trapping and EROT for particle assessments, for the analysis of microorganisms ranging from viruses to parasites. Along the way, special focus was given to key research articles from within the past two years to provide the most up-to-date knowledge on the current state-of-the-art within the field of microscale EK, and from there, an outlook on where the future of the field is headed is also included.

Charge-Based Separation of Micro- and Nanoparticles.

Deterministic Lateral Displacement (DLD) is a label-free particle sorting method that separates by size continuously and with high resolution. By combining DLD with electric fields (eDLD), we show separation of a variety of nano and micro-sized particles primarily by their zeta potential. Zeta potential is an indicator of electrokinetic charge—the charge corresponding to the electric field at the shear plane—an important property of micro- and nanoparticles in colloidal or separation science. We also demonstrate proof of principle of separation of nanoscale liposomes of different lipid compositions, with strong relevance for biomedicine. We perform careful characterization of relevant experimental conditions necessary to obtain adequate sorting of different particle types. By choosing a combination of frequency and amplitude, sorting can be made sensitive to the particle subgroup of interest. The enhanced displacement effect due to electrokinetics is found to be significant at low frequency and for particles with high zeta potential. The effect appears to scale with the square of the voltage, suggesting that it is associated with either non-linear electrokinetics or dielectrophoresis (DEP). However, since we observe large changes in separation behavior over the frequency range at which DEP forces are expected to remain constant, DEP can be ruled out.

Continuous-Flow Nanoparticle Trapping Driven by Hybrid Electrokinetics in Microfluidics.

We introduce herein an efficient microfluidic approach for continuous transport and localized collection of nanoparticles via hybrid electrokinetics, which delicately combines linear and nonlinear electrokinetics driven by a composite DC-biased AC voltage signal. The proposed technique utilizes a simple geometrical structure, in which one or a series of metal strips serving as floating electrode (FE) are attached to the substrate surface and arranged in parallel between a pair of coplanar driving electrodes (DE) in a straight microchannel. On application of a DC-biased AC electric field across the channel, nanoparticles can be transported continuously by DC bulk electroosmotic flow, and then trapped selectively onto the metal strips due to AC-field induced-charge electrokinetic (ICEK) phenomenon, which behaves as counter-rotating micro-vortices around the ideally polarizable surfaces of FE. Finite-element simulation is carried out by coupling the dual-frequency electric field, flow field and sample mass transfer in sequence, for guiding a practical design of the microfluidic nanoparticle concentrator. With the optimal device geometry, the actual performance of the technique is investigated with respect to DC bias, AC voltage amplitude, and field frequency by using both latex nanospheres (∼500nm) and BSA molecules (∼10nm). Our experimental observation indicates nanoparticles are always enriched into a narrow bright band on the surface of each FE, and a horizontal concentration gradient even emerges in the presence of multiple metal strips, which therefore permits localized analyte enrichment. The proposed trapping method is supposed to guide an elaborate design of flexible electrokinetic frameworks embedding FE for continuous-flow analyte manipulation in modern microfluidic systems.

Spinning Janus doublets driven in uniform ac electric fields

We provide an experimental proof of concept for a robust, continuously rotating microstructure-consisting of two metallodielectric (gold-polystyrene) Janus particles rigidly attached to each other-which is driven in uniform ac fields by asymmetric induced-charge electro-osmosis. The pairs (doublets) are stabilized on the substrate surface which is parallel to the plane of view and normal to the direction of the applied electric field. We find that the radius of orbit and angular velocity of the pair are predominantly dependent on the relative orientations of the interfaces between the metallic and dielectric hemispheres and that the electrohydrodynamic particle-particle interactions are small. Additionally, we verify that both the angular and linear velocities of the pair are proportional to the square of the applied field which is consistent with the theory for nonlinear electrokinetics. A simple kinematic rigid body model is used to predict the paths and doublet velocities (angular and linear) based on their relative orientations with good agreement.

Electrokinetically driven concentration of particles and cells by dielectrophoresis with DC-offset AC electric field

Insulator-based dielectrophoresis (iDEP) has been successfully used for on-chip manipulations of biological samples. Despite its effectiveness, iDEP typically requires high DC voltages to achieve sufficient electric field; this is mainly due to the coupled phenomena among linear electrokinetics: electroosmosis (EO) and electrophoresis (EP) and nonlinear electrokinetics: dielectrophoresis (DEP). This paper presents a microfluidic technique using DC-offset AC electric field for electrokinetic concentration of particles and cells by repulsive iDEP. This technique introduces AC electric field for producing iDEP which is decoupled from electroosmosis (EO) and electrophoresis (EP). The repulsive iDEP is generated in a PDMS tapered contraction channel that induces non-uniform electric field. The benefits of introducing AC electric field component are threefold: (i) it contributes to DEP force acting on particles, (ii) it suppresses EO flow and (iii) it does not cause any EP motion. As a result, the required DC field component that is mainly used to transport particles on the basis of EO and EP can be significantly reduced. Experimental results supported by numerical simulations showed that the total DC-offset AC electric field strength required to concentrate 15-μm particles is significantly reduced up to 85.9% as compared to using sole DC electric field. Parametric experimental studies showed that the higher buffer concentration, larger particle size and higher ratio of AC-to-DC electric field are favorable for particle concentration. In addition, the proposed technique was demonstrated for concentration of yeast cells.

Induced Charge Electro-osmosis over Controllably Contaminated Electrodes

Recent studies in nonlinear electrokinetics reveal the standard theory to generally overpredict measured velocities, sometimes dramatically. Contamination of the driving surface provides a natural mechanism for electrokinetic suppression. We measure induced charge electro-osmosis over gold electrodes "contaminated" with silica layers of controlled thickness for nearly a thousand distinct conditions, in a system that enables direct comparisons between theoretical predictions and experimental measurements. Both the magnitude and frequency dependence of the measured slip velocity are captured quantitatively over the entire range of experiments by accounting for the physical capacitance and surface chemistry of the dielectric layer. More generally, the quantitative characterization enabled by our apparatus will prove invaluable for the rational design and prediction of electrokinetic systems.

Nonlinear electrokinetics at large voltages

The classical theory of electrokinetic phenomena assumes a dilute solution of point-like ions in chemical equilibrium with a surface whose double-layer voltage is of order the thermal voltage, kBT/e=25 mV. In nonlinear ‘induced-charge’ electrokinetic phenomena, such as ac electro-osmosis, several volts ≈100kBT/e are applied to the double layer, and the theory breaks down and cannot explain many observed features. We argue that, under such a large voltage, counterions ‘condense’ near the surface, even for dilute bulk solutions. Based on simple models, we predict that the double-layer capacitance decreases and the electro-osmotic mobility saturates at large voltages, due to steric repulsion and increased viscosity of the condensed layer, respectively. The former suffices to explain observed high-frequency flow reversal in ac electro-osmosis; the latter leads to a salt concentration dependence of induced-charge flows comparable to experiments, although a complete theory is still lacking.

Output pressure and efficiency of electrokinetic pumping of non-Newtonian fluids

Theoretical expressions of the flow rate, output pressure and thermodynamic efficiency of electrokinetic pumping of non-Newtonian fluids through cylindrical and slit microchannels are reported. Calculations are carried out in the framework of continuum fluid mechanics. The constitutive model of Ostwald-de Waele (power law) is used to express the fluid shear stress in terms of the velocity gradient. The resulting equations of flow rate and electric current are nonlinear functions of the electric potential and pressure gradients. The fact that the microstructure of non-Newtonian fluids is altered at solid–liquid interfaces is taken into account. In the case of fluids with wall depletion, both the output pressure and efficiency are found to be several times higher than that obtained with simple electrolytes under the same experimental conditions. Apart from potential applications in electrokinetic pumps, these predictions are of interest for the design of microfluidic devices that manipulate non-Newtonian fluids such as polymer solutions and colloidal suspensions. From a more fundamental point of view, the paper discusses a relevant example of nonlinear electrokinetics.

Concentration polarization and nonequilibrium electroosmotic slip in hierarchical monolithic structures

This article illustrates the appearance and electrohydrodynamic consequences of concentration polarization (CP) in hierarchically structured monolithic fixed beds used as stationary phases in CEC and related electrical-field-assisted separation techniques. Subject of the investigation are silica-based monoliths in capillary format with a bimodal pore size distribution. Ion-permselectivity in the intraskeleton pore space together with diffusive and electrokinetic transport induces depleted and enriched CP zones at the anodic and cathodic interfaces, respectively, of the cation-selective mesoporous skeleton. The extent of electrical-field-induced CP is shown to be governed by the fluid phase ionic strength, which tunes the ion-permselectivity of the mesoporous monolith skeleton via local electrical double layer overlap, and by the applied electrical field strength, which determines local transport. The analysis of quantitative confocal laser scanning microscopy data, resolving CP on the local skeleton scale, indicates that at sufficiently high field strength a transition from intraskeleton to interskeleton boundary-layer-dominated transport of charged species occurs. This transition is correlated to the onset of macroscopically measured, nonlinear EOF velocities, whose occurrence is explained in the framework of a nonequilibrium electroosmotic slip. It is shown that the onset of nonlinear electrokinetics in the system can be tuned by properties of the BGE, particularly buffer pH, which modulates the pH-dependent surface charge density and consequently the ion-permselective skeleton's charge selectivity. Finally, the CP dynamics of monolithic and particulate fixed beds are compared, and the observed differences are related to the specific morphologies of the two hierarchical fixed bed structures.

Using nonlinear ac electrokinetics vortex flow to enhance catalytic activities of sol-gel encapsulated trypsin in microfluidic devices.

A novel microstirring strategy is applied to accelerate the digestion rate of the substrate N(alpha)-benzoyl-L-arginine-4-nitroanilide (L-BAPA) catalyzed by sol-gel encapsulated trypsin. We use an ac nonlinear electrokinetic vortex flow to stir the solution in a microfluidic reaction chamber to reduce the diffusion length between the immobilized enzyme and substrate in the solution. High-intensity nonlinear electroosmotic microvortices, with angular speeds in excess of 1 cms, are generated around a small ( approximately 1.2 mm) conductive ion exchange granule when ac electric fields (133 Vcm) are applied across a miniature chamber smaller than 10 mul. Coupling between these microvortices and the on-and-off electrophoretic motion of the granule in low frequency (0.1 Hz) ac fields produces chaotic stream lines to stir substrate molecules sufficiently. We demonstrate that, within a 5-min digestion period, the catalytic reaction rate of immobilized trypsin increases almost 30-fold with adequate reproducibility (15%) due to sufficient stirring action through the introduction of the nonlinear electrokinetic vortices. In contrast, low-frequency ac electroosmotic flow without the granule, provides limited stirring action and increases the reaction rate approximately ninefold with barely acceptable reproducibility (30%). Dye molecules are used to characterize the increases in solute diffusivity in the reaction reservoir in which sol-gel particles are placed, with and without the presence of granule, and compared with the static case. The solute diffusivity enhancement data show respective increases of approximately 30 and approximately 8 times, with and without the presence of granule. These numbers are consistent with the ratios of the enhanced reaction rate.

Nonlinear electrochemical relaxation around conductors

We analyze the simplest problem of electrochemical relaxation in more than one dimension-the response of an uncharged, ideally polarizable metallic sphere (or cylinder) in a symmetric, binary electrolyte to a uniform electric field. In order to go beyond the circuit approximation for thin double layers, our analysis is based on the Poisson-Nernst-Planck (PNP) equations of dilute solution theory. Unlike most previous studies, however, we focus on the nonlinear regime, where the applied voltage across the conductor is larger than the thermal voltage. In such strong electric fields, the classical model predicts that the double layer adsorbs enough ions to produce bulk concentration gradients and surface conduction. Our analysis begins with a general derivation of surface conservation laws in the thin double-layer limit, which provide effective boundary conditions on the quasineutral bulk. We solve the resulting nonlinear partial differential equations numerically for strong fields and also perform a time-dependent asymptotic analysis for weaker fields, where bulk diffusion and surface conduction arise as first-order corrections. We also derive various dimensionless parameters comparing surface to bulk transport processes, which generalize the Bikerman-Dukhin number. Our results have basic relevance for double-layer charging dynamics and nonlinear electrokinetics in the ubiquitous PNP approximation.

Concentration Polarization-based Nonlinear Electrokinetics in Porous Media: Induced-Charge Electroosmosis

We have investigated induced-charge electroosmotic flow in a fixed bed of ion-permselective glass beads by quantitative confocal laser scanning microscopy. Externally applied electrical fields induce concentration polarization (CP) in the porous medium due to coupled mass and charge transport normal to the charge-selective interfaces. These data reveal the generation of a nonequilibrium electrical double layer in the depleted CP zones and the adjoining anodic hemispheres of the (cation-selective) glass beads above a critical field strength. This initiates CP-based induced-charge electroosmosis along curved interfaces of the quasi-electroneutral macropore space between glass beads. Caused by mutual interference of resulting nonlinear flow with (flow-inducing) space charge regions, an electrohydrodynamic instability can appear locally and realize turbulent flow behavior at low Reynolds numbers. It is characterized by a local destruction of the CP zones and concomitant removal of diffusion-limited mass transfer. More efficient pore-scale lateral mixing also improves macroscopic transport, which is reflected in the significantly reduced axial dispersion of a passive tracer.

Nonlinear electrokinetics and "superfast" electrophoresis.

Nonlinear and nonequilibrium electrophoresis of spherical particles of radius a is shown to be possible when the solid surface allows field or current penetration. At low particle Peclet numbers, transient capacitative charging occurs until the surface polarization completely screens the external field. For a DC applied field [see text], the resulting electrokinetic velocity reaches Dukhin's maximum value of [formula: see text], where [see text] and mu are the liquid permittivity and viscosity. At high Peclet numbers, electroosmotic convection of the electroneutral bulk stops the transient charging before complete field-line exclusion. For an ion-selective and conducting spherical granule, the polarization is then determined by the steady-state Ohmic current driven by the penetrated external field. The high-Peclet electrokinetic velocity is lower, diffusivity-dependent and scales as [see text].