Nonlinear Electrophoresis Research Articles

A perspective on guided electrophoretic transport of particles in liquid crystals

Nonlinear electrophoresis in complex fluids like nematic liquid crystals provides new pathways toward achieving precisely controlled motion and assembly of microscopic objects. The nematic host introduces a paradigm shift in the mechanism of electrophoretic transport by generating unbalanced electro-osmotic flows around the colloidal particle due to symmetry breaking of the medium caused by the induced topological defects. Rationally designed particles, which induce various types of defects and asymmetries, provide new opportunities in this regard. In this Perspective article, we discuss how the asymmetry in the shape and interfacial properties help in piloting the particles using an AC electric field. Finally, we propose some feasible strategies to achieve navigational control using magnetic and photo-responsive particles, guided by orthogonal electric, magnetic fields, and light, respectively.

Separating the Living from the Dead: An Electrophoretic Approach.

Cell viability studies are essential in numerous applications, including drug development, clinical analysis, bioanalytical assessments, food safety, and environmental monitoring. Microfluidic electrokinetic (EK) devices have been proven to be effective platforms to discriminate microorganisms by their viability status. Two decades ago, live and dead Escherichia coli (E. coli) cells were trapped at distinct locations in an insulator-based EK (iEK) device with cylindrical insulating posts. At that time, the discrimination between live and dead cells was attributed to dielectrophoretic effects. This study presents the continuous separation between the live and dead E. coli cells, which was achieved primarily by combining linear and nonlinear electrophoretic effects in an iEK device. First, live and dead E. coli cells were characterized in terms of their electrophoretic migration, and then the properties of both live and dead E. coli cells were input into a mathematical model built using COMSOL Multiphysics software to identify appropriate voltages for performing an iEK separation in a T-cross iEK channel. Subsequently, live and dead cells were successfully separated experimentally in the form of an electropherogram, achieving a separation resolution of 1.87. This study demonstrated that linear and nonlinear electrophoresis phenomena are responsible for the discrimination between live and dead cells under DC electric fields in iEK devices. Continuous electrophoretic assessments, such as the one presented here, can be used to discriminate between distinct types of microorganisms including live and dead cell assessments.

Nonlinear Electrophoresis of Microparticles in Shear Thinning Fluids.

The nonlinear electric field dependence of particle electrophoresis has been demonstrated to occur in Newtonian fluids for highly charged particles under large electric fields. It has also been predicted to arise from the rheological effects of non-Newtonian fluids even at small electric fields. We present in this work an experimental verification of nonlinear electrophoresis in shear thinning xanthan gum solutions through a straight rectangular microchannel. The addition of polymer into a Newtonian buffer solution is found to change the electric field dependence from linear to superlinear for electroosmotic, electrokinetic, and electrophoretic velocities. The nonlinear index of each of these electrokinetic phenomena increases with the increasing polymer or buffer concentration, among which electrophoresis exhibits the strongest nonlinearity. Both these observed trends are captured by a dimensionless electrokinetic shear thinning number that depends on the power-law index of fluid viscosity and the Debye length.

Electrophoretic Mobility of Nanoparticles in Water.

Classical equations for colloidal mobility anticipate linear proportionality between the nanoparticle mobility and zeta potential caused by the combined electrostatics of free charges at the nanoparticle and screening bound charges of the polar solvent. Polarization of the interfacial liquid, either spontaneous due to molecular asymmetry of the solvent (water) or induced by nonelectrostatic (e.g., charge-transfer) interactions, is responsible for a static interface charge adding to the overall electrokinetic charge of the nanoparticle. The particle mobility gains a constant offset term that is formally unrelated to the zeta potential. The static charge is multiplied by the static dielectric constant of the solvent in the expression for the electrokinetic charge and is sufficiently large in magnitude to cause electrophoretic mobility of even neutral particles. At a larger scale, nonlinear electrophoresis linked to the interface quadrupole moment can potentially contribute a sufficiently negative charge to a micrometer-size nanoparticle.

Assessment of the Nonlinear Electrophoretic Migration of Nanoparticles and Bacteriophages.

Bacteriophage therapy presents a promising avenue for combating antibiotic-resistant bacterial infections. Yet, challenges exist, particularly, the lack of a straightforward purification pipeline suitable for widespread application to many phage types, as some phages are known to undergo significant titer loss when purified via current techniques. Electrokinetic methods offer a potential solution to this hurdle, with nonlinear electrophoresis emerging as a particularly appealing approach due to its ability to discern both the size and shape of the target phage particles. Presented herein is the electrokinetic characterization of the mobility of nonlinear electrophoresis for two phages (SPN3US and ϕKZ) and three types of polystyrene nanoparticles. The latter served as controls and were selected based on their sizes and surface charge magnitude. Particle tracking velocimetry experiments were conducted to characterize the mobility of all five particles included in this study. The results indicated that the selected nanoparticles effectively replicate the migration behavior of the two phages under electric fields. Further, it was found that there is a significant difference in the nonlinear electrophoretic response of phages and that of host cells, as first characterized in a previous report, illustrating that electrokinetic-based separations are feasible. The findings from this work are the first characterization of the behavior of phages under nonlinear electrophoresis effects and illustrate the potential for the development of electrokinetic-based phage purification techniques that could aid the advancement of bacteriophage therapy.

Switching Separation Migration Order by Switching Electrokinetic Regime in Electrokinetic Microsystems.

Analyte migration order is a major aspect in all migration-based analytical separations methods. Presented here is the manipulation of the migration order of microparticles in an insulator-based electrokinetic separation. Three distinct particle mixtures were studied: a binary mixture of particles with similar electrical charge and different sizes, and two tertiary mixtures of particles of distinct sizes. Each one of the particle mixtures was separated twice, the first separation was performed under low voltage (linear electrokinetic regime) and the second separation was performed under high voltage (nonlinear electrokinetic regime). Linear electrophoresis, which discriminates particles by charge, is the dominant electrokinetic effect in the linear regime; while nonlinear electrophoresis, which discriminates particles by size and shape, is the dominant electrokinetic effect in the nonlinear regime. The separation results obtained with the three particle mixtures illustrated that particle elution order can be changed by switching from the linear electrokinetic regime to the nonlinear electrokinetic regime. Also, in all cases, better separation performances in terms of separation resolution (Rs) were obtained by employing the nonlinear electrokinetic regime allowing nonlinear electrophoresis to be the discriminatory electrokinetic mechanism. These findings could be applied to analyze complex samples containing bioparticles of interest within the micron size range. This is the first report where particle elution order is altered in an iEK system.

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.

Effect of cell shape on nonlinear electrophoresis migration

This study contributes to the renewed interest in the study of nonlinear electrophoresis of colloidal particles. In this work the influence of cell shape on electrophoretic migration under the nonlinear regimes of moderate and strong field regimes was assessed. Four types of bacterial and yeast cells (one spherical, three non-spherical) were studied and their electrophoretic mobilities for the moderate and strong electric field magnitude regimes were estimated experimentally. The parameter of sphericity was employed to assess the effect cell shape on the nonlinear electrophoresis migration velocity and corresponding mobility under the two electric field magnitude regimes studied. As particle migration under nonlinear electrophoresis depends on particle size and shape, the results in terms of mobilities of nonlinear electrophoresis were presented as function of cell hydrodynamic diameter and sphericity. The results indicated that the magnitude of the mobilities of nonlinear electrophoresis for cells increase with increasing cell size and increase with increasing deviations from spherical shape, which is indicated by lower sphericity values. The results presented here are the very first assessment of the two types of mobilities of nonlinear electrophoresis of cells as a function of size and shape.

Enabling the characterization of the nonlinear electrokinetic properties of particles using low voltage.

Insulator-based electrokinetically driven microfluidic devices stimulated with direct current (DC) voltages are an attractive solution for particle separation, concentration, or isolation. However, to design successful particle manipulation protocols, it is mandatory to know the mobilities of electroosmosis, and linear and nonlinear electrophoresis of the microchannel/liquid/particle system. Several techniques exist to characterize the mobilities of electroosmosis and linear electrophoresis. However, only one method to characterize the mobility of nonlinear electrophoresis has been thoroughly assessed, which generally requires DC voltages larger than 1000 V and measuring particle velocity in a straight microchannel. Under such conditions, Joule heating, electrolysis, and the DC power source cost become a concern. Also, measuring particle velocity at high voltages is noisy, limiting characterization quality. Here we present a protocol-tested on 2 μm polystyrene particles-for characterizing the mobility of nonlinear electrophoresis of the liquid/particle system using a DC voltage of only 30 V and visual inspection of particle dynamics in a microchannel featuring insulating obstacles. Multiphysics numerical modelling was used to guide microchannel design and to correlate particle location during an experiment with electric field intensity. The method was validated against the conventional characterization protocol, exhibiting excellent agreement while significantly reducing measurement noise and experimental complexity.

Nonlinear electrophoresis of nonspherical particles in a rectangular microchannel.

Nonlinear electrophoresis offers advantageous prospects in microfluidic manipulation of particles over linear electrophoresis. Existing theories established for this phenomenon are entirely based on spherical particle models, some of which have been experimentally verified. However, there is no knowledge on if and how the particle shape may affect the nonlinear electrophoretic behavior. This work presents an experimental study of the nonlinear electrophoretic velocities of rigid peanut- and pear-shaped particles in a rectangular microchannel, which are compared with rigid spherical particles of similar diameter and surface charge in terms of the particle slenderness. We observe a decrease in the nonlinear electrophoretic mobility, whereas an increase in the nonlinear index of electric field when the particle slenderness increases from the peanut- to pear-shaped and spherical particles. The values of the nonlinear index for the nonspherical particles are, however, still within the theoretically predicted range for spherical particles. We also observe an enhanced nonlinear electrophoretic behavior in a lower concentration buffer solution regardless of the particle shape.

Dependence of Nonlinear Electrophoresis on Particle Size and Electrical Charge

This study focuses on the dependence of nonlinear electrophoretic migration of particles on the particle size and particle electrical charge. This is the first report of the experimental assessment of the mobilities of the nonlinear electrophoretic velocity of colloidal polystyrene microparticles under two distinct electric field dependences. A total of nine distinct types of polystyrene microparticles of varying size and varying electrical charge were divided into two groups to study separately the effects of particle size and the effects of particle charge. The mobilities of the nonlinear electrophoretic velocity of each particle type were determined in both the cubic and 3/2 regimes (μEP,NL(3) and μEP,NL(3/2)). The results unveiled that both mobilities had similar relationships with particle size and charge. The magnitude of both μEP,NL(3) and μEP,NL(3/2) increased with increasing particle size and decreased with increasing magnitude of particle charge. However, the observed trends were not perfect as discussed in the Results and Discussion section but still provide valuable information. These findings will aid in the design of future size-based and charge-based separations of particles and microorganisms.

Characterization of the Nonlinear Electrophoretic Behavior of Colloidal Particles in a Microfluidic Channel

Contemporary findings in the field of insulator-based electrokinetics have demonstrated that in systems under the influence of direct current (DC) fields, dielectrophoresis (DEP) is not the main electrokinetic mechanism responsible for particle manipulation but rather the sum of electroosmosis, linear and nonlinear electrophoresis. Recent microfluidic studies have brought forth a methodology capable of experimentally estimating the nonlinear electrophoretic mobility of colloidal particles. This methodology, however, is limited to particles that fit two conditions: (i) the particle charge has the same sign as the channel wall charge and (ii) the magnitude of the particle ζ-potential is lower than that of the channel wall. The present work aims to expand upon this methodology by including particles whose ζ-potential has a magnitude larger than that of the wall, referred to as "type 2" particles, as well as to report findings on particles that appear to still be under the influence of the linear electrophoretic regime even at extremely high electric fields (∼6000 V/cm), referred to as "type 3" particles. Our findings suggest that both particle size and charge are key parameters in the determination of nonlinear electrophoretic properties. Type 2 microparticles were all found to be small (diameter ∼ 1 μm) and highly charged, with ζ-potentials above -60 mV; in contrast, type 3 microparticles were all large with ζ-potentials between -40 and -50 mV. However, it was also hypothesized that other nonconsidered parameters could be influencing the results, especially at higher electric fields (>3000 V/cm). The present work also aims to identify the current limitations in the experimental determination of μEP,NL and propose a framework for future work to address the current gaps in the evolving topic of nonlinear electrophoresis of colloidal particles.

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.

Nonlinear electrophoresis of dielectric particles in Newtonian fluids.

In classical electrokinetics, the electrophoretic velocity of a dielectric particle is a linear function of the applied electric field. Theoretical studies have predicted the onset of nonlinear electrophoresis at high electric fields because of the nonuniform surface conduction over the curved particle. However, experimental studies have been left behind and are insufficient for a fundamental understanding of the parametric effects on nonlinear electrophoresis. We present in this work a systematic experimental study of the effects of buffer concentration, particle size, and particle zeta potential on the electrophoretic velocity of polystyrene particles in a straight rectangular microchannel for electric fields of up to 3kV/cm. The measured nonlinear electrophoretic particle velocity is found to exhibit a 2(±0.5)-order dependence on the applied electric field, which appears to be within the theoretically predicted 3- and 3/2-order dependences for low and high electric fields, respectively. Moreover, the obtained nonlinear electrophoretic particle mobility increases with decreasing buffer concentration (for the same particle) and particle size (for particles with similar zeta potentials) or increasing particle zeta potential (for particles with similar sizes). These observations are all consistent with the theoretical predictions for high electric fields.

Simultaneous Determination of Linear and Nonlinear Electrophoretic Mobilities of Cells and Microparticles.

Direct-current insulator-based electrokinetics (DC-iEK) is a branch of microfluidics that has demonstrated to be an attractive and efficient technique for manipulating micro- and nano- particles, including microorganisms. A unique feature of DC-iEK devices is that nonlinear EK effects are enhanced by the presence of regions of higher field intensity between the insulating structures. Accurate computational models, describing particle and cell behavior, are crucial to optimize the design and improve the performance of DC-iEK devices. The electrokinetic equilibrium condition (EEEC) is a recently introduced fundamental concept that has radically shifted the perspective behind the analysis of particle manipulation in these microfluidic devices. The EEEC takes into consideration previously neglected nonlinear effects on particle migration and indicates that these effects are central to control particle motion in DC-iEK devices. In this study, we present a simultaneous experimental characterization of linear and nonlinear electrokinetic (EK) parameters, that is, the electrophoretic mobility (μEP(1)), the particle zeta potential (ζP), the EEEC, and the electrophoretic mobility of the second kind (μEP(3)), for four types of polystyrene microparticles and four cell strains. For this, we studied the electromigration of polystyrene microparticles ranging in size from 2 to 6.8 μm, three bacteria strains (B. cereus, E. coli, and S. enterica) and a yeast cell (S. cerevisiae), ranging in size from 1 to 6.3 μm, in a polydimethylsiloxane (PDMS) microfluidic channel with a rectangular cross-section. The results illustrated that electrokinetic particle trapping can occur by linear and nonlinear electrophoresis and electroosmosis reaching an equilibrium, without the presence of insulating posts. The experimentally measured parameters reported herein will allow optimizing the design of future DC-iEK devices for a wide range of applications (e.g., to separate multiple kinds of particles and microorganisms) and for developing computational models that better represent reality.

The dynamics of band (peak) shape development in capillary zone electrophoresis in the case of two co-migrating analytes: The displacement and the tag-along effects.

Peak shapes in electrophoresis are often distorted from the ideal Gaussian shape due to disturbing phenomena, of which the most important is electromigration dispersion. For fully dissociated analytes, there is a tight analogy between nonlinear models describing a separation process in chromatography and electrophoresis. When the velocity of the separated analyte depends on the concentration of the co-analyte, the consequence is a mutual influence of the analytes couples, which distorts both analyte zones. In this paper, we introduce a nonlinear model of electromigration for the analysis of two co-migrating fully dissociated analytes. In the initial stages of separation, they influence each other, which causes much more complicated peak shapes. The analysis has revealed that the two most important phenomena-the displacement and the tag-along effects-are common both for nonlinear chromatography and electrophoresis, though their description is partly based on rather different phenomena. The comparison between the nonlinear model of electromigration we describe and the numerical computer solution of the original continuity equations has proven an almost perfect agreement. The predicted features in peak shapes in initial stages of separation have been fully confirmed by the experiments.

Nonlinear Electrophoresis of Highly Charged Nonpolarizable Particles.

Nonlinear field dependence of electrophoresis in high fields has been investigated theoretically, yet experimental studies have failed to reach consensus on the effect. In this Letter, we present a systematic study on the nonlinear electrophoresis of highly charged submicron particles in applied electric fields of up to several kV/cm. First, the particles are characterized in the low-field regime at different salt concentrations and the surface charge density is estimated. Subsequently, we use microfluidic channels and video tracking to systematically characterize the nonlinear response over a range of field strengths. Using velocity measurements on the single particle level, we prove that nonlinear effects are present at electric fields and surface charge densities that are accessible in practical conditions. Finally, we show that nonlinear behavior leads to unexpected particle trapping in channels.

Nonlinear electrophoresis of a tightly fitting sphere in a cylindrical tube

We investigate electrophoresis of a tightly fitting sphere of radius $R-h_{0}$ on the axis of a circular tube of radius $R$, using lubrication theory and ideas due to Schnitzer & Yariv (Phys. Fluids, vol. 26, 2014, 122002). The electrical charge clouds on both the cylindrical wall and the surface of the sphere are assumed thin compared to the gap between the sphere and cylinder, so that charge clouds do not overlap and ion exclusion effects are minimal. Nevertheless, non-uniform pumping of counter-ions within the charge clouds leads to a change in the ionic concentration outside the charge clouds in the narrow gap between sphere and cylinder. The electro-osmotic slip velocities at the two surfaces are modified, leading to a decrease in the electrophoretic velocity of the sphere at low Péclet numbers and an increase in the velocity at high Péclet numbers. When the field strength $E_{0}$ is low, it is known that the electrophoretic velocity $U_{0}$ is proportional to $E_{0}(\unicode[STIX]{x1D701}_{s}-\unicode[STIX]{x1D701}_{c})$ which is zero when the zeta potential $\unicode[STIX]{x1D701}_{s}$ on the sphere surface is equal to the zeta potential $\unicode[STIX]{x1D701}_{c}$ on the cylinder. The perturbation to the above low field strength electrophoretic velocity (at high Péclet number) is predicted to be proportional to $E_{0}^{3}(\unicode[STIX]{x1D701}_{s}+\unicode[STIX]{x1D701}_{c})^{2}(\unicode[STIX]{x1D70E}_{s}+\unicode[STIX]{x1D70E}_{c})$, where $\unicode[STIX]{x1D70E}_{s}$ and $\unicode[STIX]{x1D70E}_{c}$ are the surface charge densities on the sphere and cylinder. The choice of materials with similar or identical zeta potentials (and surface charge densities) for the cylinder and sphere should therefore facilitate the observation of velocities nonlinear in the field strength $E_{0}$, since the reference linear electrophoretic velocity will be small.

Nonlinear Electrophoresis of Colloids Controlled by Anisotropic Conductivity and Permittivity of Liquid-Crystalline Electrolyte

When a standard, isotropic electrolyte is replaced with a liquid crystal, a nonlinear mechanism of electrophoresis is introduced, and one unresolved issue is how the electrophoretic velocity depends on the crucial properties of the liquid crystal: the anisotropy of its dielectric permittivity and conductivity. The authors establish these dependencies with experiments and simulations, and demonstrate how to use them for controlled $r\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}v\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}r\phantom{\rule{0}{0ex}}s\phantom{\rule{0}{0ex}}a\phantom{\rule{0}{0ex}}l$ of electrokinetics, by changing either temperature or composition. This work embraces a wide range of problems, from electrokinetic phenomena and microfluidics to soft matter physics.

Influence of rigid core permittivity and double layer polarization on the electrophoresis of a soft particle: A numerical study

The nonlinear electrophoresis of a soft particle with a polarizable uncharged rigid core coated with a polyelectrolyte layer is studied. Due to the coupled nature of the governing electrokinetic equations, a numerical approach is adopted. Our numerical solutions are in good agreement with the existing experimental and theoretical results for a particle with a non-polarizable core when the impacts of the nonlinear effects are low. The induced surface potential of the dielectric rigid core has an impact on the soft particle electrophoresis. The combined effects of the solid polarization of the core and double layer polarization have not been addressed previously in the context of soft particle electrophoresis. We have found that both these effects create retardation on the electrophoresis and are significant when the applied electric field is not weak. The double layer polarization is significant when the Debye length is in the order of the particle size. The range of the applied electric field for which the electrophoretic velocity of a soft particle with a non-polarizable core varies linearly with the applied electric field may create a nonlinear variation in electrophoretic velocity when the core is considered to be polarizable.