Nonlinear Electrokinetic Phenomena 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. Expected final online publication date for the Annual Review of Analytical Chemistry, Volume 17 is May 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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.

Separation of Cells and Microparticles in Insulator-Based Electrokinetic Systems.

Presented here is the first continuous separation of microparticles and cells of similar characteristics employing linear and nonlinear electrokinetic phenomena in an insulator-based electrokinetic (iEK) system. By utilizing devices with insulating features, which distort the electric field distribution, it is possible to combine linear and nonlinear EK phenomena, resulting in highly effective separation schemes that leverage the new advancements in nonlinear electrophoresis. This work combines mathematical modeling and experimentation to separate four distinct binary mixtures of particles and cells. A computational model with COMSOL Multiphysics was used to predict the retention times (tR,p) of the particles and cells in iEK devices. Then, the experimental separations were carried out using the conditions identified with the model, where the experimental retention time (tR,e) of the particles and cells was measured. A total of four distinct separations of binary mixtures were performed by increasing the level of difficulty. For the first separation, two types of polystyrene microparticles, selected to mimic Escherichia coli and Saccharomyces cerevisiae cells, were separated. By leveraging the knowledge gathered from the first separation, a mixture of cells of distinct domains and significant size differences, E. coli and S. cerevisiae, was successfully separated. The third separation also featured cells of different domains but closer in size: Bacillus cereus versus S. cerevisiae. The last separation included cells in the same domain and genus, B. cereus versus Bacillus subtilis. Separation results were evaluated in terms of number of plates (N) and separation resolution (Rs), where Rs values for all separations were above 1.5, illustrating complete separations. Experimental results were in agreement with modeling results in terms of retention times, with deviations in the 6-27% range, while the variation between repetitions was between 2 and 18%, demonstrating good reproducibility. This report is the first prediction of the retention time of cells in iEK systems.

Dipolophoresis in concentrated suspensions of ideally polarizable spheres

The dynamics of ideally polarizable spherical particles in concentrated suspensions under the effects of nonlinear electrokinetic phenomena is analysed using large-scale numerical simulations. Particles are assumed to carry no net charge and considered to undergo the combination of dielectrophoresis and induced-charge electrophoresis termed dipolophoresis. Chaotic motion and resulting hydrodynamic diffusion are known to be driven by the induced-charge electrophoresis, which dominates the dielectrophoresis. Up to a volume fraction $\unicode[STIX]{x1D719}\approx 35\,\%$, the particle dynamics seems to be hindered by the increase in the magnitude of excluded volume interactions with concentration. However, a non-trivial suspension behaviour is observed in concentrated regimes, where the hydrodynamic diffusivity starts to increase with the volume fraction at $\unicode[STIX]{x1D719}\approx 35\,\%$, before reaching a local maximum, and then drastically decreases on approaching random close packing. Similar non-trivial behaviours are observed in the particle velocity and number-density fluctuations around volume fractions at which the non-trivial behaviour of the hydrodynamic diffusion is observed. We explain these non-trivial behaviours as a consequence of particle contacts, which are related to the dominant mechanism of particle pairings. The particle contacts are classified into attractive and repulsive classes by the nature of contacts, and in particular, the strong repulsive contact becomes predominant at $\unicode[STIX]{x1D719}>20\,\%$. Moreover, this transition is visible in the pair distribution functions, which also reveal the change in the suspension microstructure in concentrated regimes. It appears that strong and massive repulsive contacts along the direction perpendicular to an electric field promote the non-trivial suspension behaviours observed in concentrated regimes.

Nonlinear electrokinetic effects in insulator-based dielectrophoretic systems.

Insulator-based dielectrophoresis (iDEP) has emerged as a powerful tool for multiple biomicrofluidic operations, such as cell separation and concentration. The key feature for iDEP systems is the alteration of insulating microchannel geometries to create strong electric field gradients. Under AC electric fields, this strong electric field gradient can affect fluid flow by (at least) two nonlinear electrokinetic phenomena; (a) electrothermal flow due to Joule heating and (b) induced charge electroosmosis (ICEO) near the microchannel constrictions of small (but finite) permittivity and conductivity. This paper presents an experimental and theoretical study on the interplay of electrothermal and ICEO flows near microchannel constrictions with various geometries and fluid ionic strengths, which are crucial design factors for iDEP systems. Temperature rise and fluid velocities in 2D Gaussian-shaped constrictions were studied experimentally with supporting analytical estimations and numerical simulations. Additionally, we show qualitatively distinct recirculating flow patterns in 2D and 3D microchannel constrictions used for iDEP systems. Approximate analytical expressions for electrothermal and ICEO velocity scales are provided as a function of constriction geometry, bulk electrolyte concentration, and the applied electric field. Insights from this study will be useful in designing microfluidic systems for electrokinetic particle manipulation.

Direct simulation of phase delay effects on induced-charge electro-osmosis under large ac electric fields.

The standard theory of induced-charge electro-osmosis (ICEO) often overpredicts experimental values of ICEO velocities. Using a nonsteady direct multiphysics simulation technique based on the coupled Poisson-Nernst-Planck and Stokes equations for an electrolyte around a conductive cylinder subject to an ac electric field, we find that a phase delay effect concerning an ion response provides a fundamental mechanism for electrokinetic suppression. A surprising aspect of our findings is that the phase delay effect occurs even at much lower frequencies (e.g., 50 Hz) than the generally believed charging frequency of an electric double layer (typically, 1 kHz) and it can decrease the electrokinetic velocities in one to several orders. In addition, we find that the phase delay effect may also cause a change in the electrokinetic flow directions (i.e., flow reversal) depending on the geometrical conditions. We believe that our findings move toward a more complete understanding of complex experimental nonlinear electrokinetic phenomena.

Nonlinear electrokinetic phenomena around nearly insulated sharp tips in microflows

This contribution seeks to provide for the first time a combined comprehensive theoretical prediction and quantitative experimental (microparticle imaging velocimetry – μ -PIV) measurements of the nonlinear electrokinetic flow around sharp tips in order to substantiate former theoretical and qualitative experimental flow visualization results [S.K. Thamida, H.C Chang, Phys. Fluids 14 (2002) 12; P. Takhistov, K. Duginova, H.C. Chang, J. Colloid Interface Sci. 263 (2003) 133; G. Yossifon, I. Frankel, T. Miloh, Phys. Fluids 18 (2006) 117108]. The study focuses on two microchannel designs: an L-shaped channel and two isolated tips in a straight channel, important in engineering for mixing and particle-trapping purposes. The new experimental results were explained in terms of an induced-charge electrokinetic mechanism alone, without the concentration polarization mechanism as suggested by earlier studies. The vortex generation phenomenon around corners was explained in terms of the varying ratio between the equilibrium and the induced-charge zeta-potentials, showing fair qualitative agreement between numerical and experimental results. Hence, a transition from an irrotational to nonlinear-dominated flow with a vortex pattern occurs beyond a certain electric-field threshold. In particular, for the L-shaped channel case, it is demonstrated that beyond a second field threshold an upstream vortex appears in addition to the downstream one.

Induced-charge electro-osmosis

We describe the general phenomenon of `induced-charge electro-osmosis' (ICEO) -- the nonlinear electro-osmotic slip that occurs when an applied field acts on the ionic charge it {\sl induces} around a polarizable surface. Motivated by a simple physical picture, we calculate ICEO flows around conducting cylinders in steady (DC), oscillatory (AC), and suddenly-applied electric fields. This picture, and these systems, represent perhaps the clearest example of nonlinear electrokinetic phenomena. We complement and verify this physically-motivated approach using a matched asymptotic expansion to the electrokinetic equations in the thin double-layer and low potential limits. ICEO slip velocities vary like $u_s \propto E_0^2 L$, where $E_0$ is the field strength and $L$ is a geometric length scale, and are set up on a time scale $\tau_c = \lambda_D L/D$, where $\lambda_D$ is the screening length and $D$ is the ionic diffusion constant. We propose and analyze ICEO microfluidic pumps and mixers that operate without moving parts under low applied potentials. Similar flows around metallic colloids with fixed total charge have been described in the Russian literature (largely unnoticed in the West). ICEO flows around conductors with fixed potential, on the other hand, have no colloidal analog and offer further possibilities for microfluidic applications.

Complex electrosurface investigations of dispersed microphases

The structure of the electrical double layer (EDL) of colloidal systems is discussed. The methods of determination of the most important parameters of the EDL, i.e. the value of the surface-potential ψ 0, the Stern-potential ψ δ and the electrokinetic-potential ζ, the surface charge density σ 0, the electrokinetic charge σ ζ, as well as the specific surface conductance κ σ and Rel parameter are described. The application of the theory of non-linear electrosurface phenomena developed by Dukhin, Derjaguin and Shilov for calculation of the EDL parameters is discussed. The above data of the EDL characteristics for polystyrene and melamin-formaldehyde latices, suspensions of AgI, Sb 2S 3, Fe 2O 3, ZrO 2, hydromica, palygorskyte, yeast cells as well as kerosene-in-water, ET grade lubricating oil technical emulsions in different electrolyte solutions are discussed. It has been shown that in the most of cases (with the exception of AgI solution) ψ 0 or ψ δ>ζ and σ 0≫σ ζ. It indicates the presence of a considerable free charge between the surface and slipping plane due to the formation of hydrodynamically immobile water layers on the surface in which the ions retain high mobility. The necessity of complex (integrated) electrosurface measurements for the description of the electrical double layer structure is stressed. A new kind of non-linear electrokinetic phenomena, namely the superfast electrophoresis is described. The phenomenon was predicted theoretically by Dukhin and Mishchuk and investigated experimentally in detail in the author's laboratory. It has been shown that the electrophoretic mobility of large (hundreds μm) ion-type conducting particles like ion-exchanger grains/fibres or electron-type conducting particles like Al/Mg alloy, graphite and activated carbon in strong electric fields (100–1000 V/cm) exceeds the electrophoretic mobility values typical for non-conducting particles by 1–2 orders of magnitude. The mobility of such particles depends on the conductivity ratio between the particles and medium and strongly increases with the electric field gradient and the particle size. This is in contrast to classical electrophoresis. The superfast electrophoresis is due to the interaction of a strong electric field with the space charge near the surface of unipolar conducting particles. This space charge is induced by the strong external field because of the concentration polarisation.