Detrapping particles in gel electrophoresis: a numerical study of different pulsed field sequences

Large particles tend to get trapped in dead-ends more often than small particles when electrophoresed in random cross-linked gels. It is known that pulsed electric fields can be used to free particles from these traps, leading to an increase in velocity and improved size separation. Although numerical and theoretical models have been proposed for the mobility of smaller particles in the so-called Ogston sieving limit, the effect of pulsed fields on trapping has not been previously modeled. We present a numerical study of detrapping and we compare our results with those of To and Boyde (To, K.-Y., Boyde, T. R., Electrophoresis 1993, 14, 597). We use an exact numerical method to examine detrapping in various two-dimensional systems of obstacles. We also propose and investigate new ways to optimize the pulse sequence in order to separate particles of different sizes.     

An exactly solvable Ogston model of gel electrophoresis: X. Application to high-field separation techniques

Recently, we generalized our lattice model of gel electrophoresis to study the net velocity of particles being pulled by a high-intensity electric field through an arbitrary distribution of immobile obstacles (Gauthier, M. G., Slater, G. W., J. Chem. Phys. 2002, 117, 6745-6756). In this article, we show how the high-field version of our model can be used to compare the velocity of particles with different electric charges and/or physical sizes. We then investigate specific two-dimensional distributions of obstacles that can be used to separate particles, e.g., in a microfluidic device. More precisely, we compare the velocity of differently charged or sized analytes in sieving, trapping and deflecting systems to model various electrophoretic separation techniques. In particular, we study the nonlinear effects present in ratchet systems and how they can be combined with time-asymmetric pulsed fields to provide new modes of separation.     

Movement of colloidal particles in two-dimensional electric fields

We characterize the movement of carbon black particles in inhomogeneous, two-dimensional dc electric fields. Motivated by display applications, the particles are suspended in a nonpolar solvent doped with a charge control agent. The two-dimensional fields are generated between strip electrodes on a glass slide spaced 120 microm apart with field strengths up to 10(4) V/m. Such fields are insufficient to drive either electrohydrodynamic instabilities or natural convection due to ohmic heating, but they move the particles between the electrodes in about 30 s. In the center region between the strip electrodes, the particles move by electrophoresis; that is, the particle velocity is proportional to the electric field. However, when imposing a constant-potential or constant-current boundary condition at the electrodes to derive the electrical field, the electrophoretic mobility calculated from the measured particle velocities is outside the range of mobilities predicted from the theory of O'Brien and White. Near the electrodes the particles either speed up or slow down, depending on the polarity of the electrode, and these changes in velocity cannot be explained simply by electrophoresis in a spatially varying electric field. We suggest that this anomalous motion arises from electrohydrodynamic flows originating from the interaction between the space charge of the polarized layers above the electrodes and the electric field. Approximate calculations indicate such flows could be sufficiently strong to explain the anomalous trajectories near the edges of the electrodes.     

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 3 kV/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.     

Hydrodynamics of interaction of particles (including cells) with surfaces

The study of the phenomena related to the motion of particles flowing in the proximity of the wall is pursued for purely cognitive reason as well as for some important practical purposes in various fields of technology, biology and medicine.When small spherical rigid particles move in the direction parallel to the surface their velocity is smaller than that of the fluid and depends on the ratio of the distance from the wall to the particle radius. The velocity of a particle falling down in a vertical cylinder is maximal in an eccentric position. A sphere in contact with the wall remains stationary. Translational velocity of spherical rigid particles the dimension of which are comparable to that of the tube is only slightly dependent of their lateral position. The differences in the flow parameters of deformable particles in comparison with rigid ones depend on the particle and fluid viscosity coefficient. When the particles move perpendicularly toward the wall, their velocity decreases as the particle approaches the surface. The change of particle velocity is inversely proportional to the gap.There are several theories explaining the influence of the channel diameter on the suspension viscosity (sigma phenomenon); a modern approach is based on the analysis of rheological properties of suspensions. The explanations of the Fahraeus effect (i.e. the fact that the concentration of particles flowing in a tube linking two containers are smaller than that in the containers) are based on non-uniform particle distribution in a transverse cross section and on the differences of velocities of particles and medium. The deviation of the velocity profile of a suspension of rigid particles flowing through a tube from the parabolic shape (blunting) does not depend on the flow velocity; as concerns deformable particles, however, this effect is the smaller the greater is the flow velocity.When the Reynolds number for particles is greater than 10^-3, there appears a component of particle velocity perpendicular to the streamline direction.This phenomenon is the cause of the lateral migration of particles. Neutrally buoyant rigid particles migrate to a certain concentrical region situated between the tube axis and the wall (tubular pinch region). Deformable neutrally buoyant particles migrate towards the tube axis, and deformable non-neutrally buoyant particles may move either toward the tube axis or toward the wall.In the research on the influence of the flow delimiting surface on the motion of particles in suspension a considerable progress has recently been made.However, the phenomena in this field are extremely complex. At present, two main types of approach may be distinguished. On a microscopic level direct interactions between particles and surfaces are analyzed. A macroscopic approach consists in treating particle suspension as fluid, and overall influence of the surface on its properties are studied. A comprehensive theory linking these two levels has not yet emerged.     

Reptation-breathing theory of pulsed electrophoresis: dynamic regimes, antiresonance and symmetry breakdown effects

We apply the concepts of tube and reptation to the pulsed electrophoresis of DNA, considering both biased reptation and "breathing" modes (internal modes of the chain). Using suitable preaveraging approximations, analytical expressions are derived which relate displacement in crossed field electrophoresis to molecular weight, field strength, field period, pore size of the gel, and the angle between the field. These expressions provide scaling laws for the change of mobility when one (or more) of the parameters is varied as well as "universal" velocity versus molecular weight versus pulse time curves. These results are quantitatively compared with experiments. At some point which depends on field angle, field strength and chain length, however, we predict a failure of this model due to symmetry breakdown and loss of ergodicity. Qualitatively, this should lead to considerable band spreading and/or splitting of the highest DNA bands into two bands migrating sideways from the diagonal. The case of field inversion is also investigated. It is shown that only breathing modes can explain the strong differences in mobility experienced by chains of different length when opposite fields of equal amplitude are applied: the "trapping" of chains in conformations of low mobility is associated with an antiresonance-like coupling between the external field and the internal modes.     

Superfast electrophoresis of electron-type conducting particles

The features of concentration polarization caused by electric current through a unipolar conductive particle are considered. The peculiarities of the formation of an induced space charge near a particle with electron-type conductivity are analysed. It has been shown that the theoretical values of electrophoretic velocity for these particles are essentially smaller than those calculated for particles with ion-type conductivity.A new method to observe the superfast electrophoresis is developed. The electrophoretic velocity of graphite and activated carbon particles of different size (diameter, 200–500 μm) displaced in distilled water and electrolyte solutions in strong electric fields (100–500 V cm⁻¹) was measured. It is shown that, in contrast to classical electrophoresis, the electrophoretic mobility of such particles increases with the particle size and the external field strength. The experimental and theoretical results are compared. The discrepancy between theory and experiment is analysed.     

Measurement of electroosmotic and electrophoretic velocities using pulsed and sinusoidal electric fields

In this work, we explore two methods to simultaneously measure the electroosmotic mobility in microchannels and the electrophoretic mobility of micron‐sized tracer particles. The first method is based on imposing a pulsed electric field, which allows to isolate electrophoresis and electroosmosis at the startup and shutdown of the pulse, respectively. In the second method, a sinusoidal electric field is generated and the mobilities are found by minimizing the difference between the measured velocity of tracer particles and the velocity computed from an analytical expression. Both methods produced consistent results using polydimethylsiloxane microchannels and polystyrene micro‐particles, provided that the temporal resolution of the particle tracking velocimetry technique used to compute the velocity of the tracer particles is fast enough to resolve the diffusion time‐scale based on the characteristic channel length scale. Additionally, we present results with the pulse method for viscoelastic fluids, which show a more complex transient response with significant velocity overshoots and undershoots after the start and the end of the applied electric pulse, respectively.     

Diffusiophoresis of concentrated suspensions of spherical particles with distinct ionic diffusion velocities

The diffusiophoresis of a concentrated spherical dispersion of colloidal particles subject to a small electrolyte gradient is analyzed theoretically for an arbitrary zeta potential and double layer thickness. In particular, the influence of the difference in the diffusivities of cations and anions is discussed. A unit cell model is used to simulate a spherical dispersion, and a pseudospectral method is adopted to solve the equations governing the phenomenon under consideration. We show that, as in the case of an infinitely dilute dispersion, when the diffusivities of cations and anions are different, the diffusiophoretic mobility is no longer an even function of the zeta potential or double layer thickness. In contrast to the case of identical diffusivity of cations and anions, a local electric field is induced in the present case due to an unbalanced charge distribution between higher and lower concentration regions. Depending upon the direction of this induced electric field, the diffusiophoretic mobility can be larger or smaller than that for the case of identical diffusivity. The diffusiophoretic mobility is influenced mainly by the induced electric field arising from the difference in the ionic diffusivities, the concentration gradient, and the effect of double layer polarization.     

Continuous dielectrophoretic separation of particles in a spiral microchannel

Particle separation is a fundamental operation in the areas of biology and physical chemistry. A variety of force fields have been used to separate particles in microfluidic devices, among which electric field may be the most popular one due to its general applicability and adaptability. So far, however, electrophoresis‐based separations have been limited primarily to batchwise processes. Dielectrophoresis (DEP)‐based separations require in‐channel micro‐electrodes or micro‐insulators to produce electric field gradients. This article introduces a novel particle separation technique in DC electrokinetic flow through a planar double‐spiral microchannel. The continuous separation arises from the cross‐stream dielectrophoretic motion of particles induced by the non‐uniform electric field inherent to curved channels. Specifically, particles are focused by DEP to one sidewall of the first spiral, and then dielectrophoretically deflected toward the other sidewall of the second spiral at a particle‐dependent rate, leading to focused particle streams along different flow paths. This DEP‐based particle separation technique is demonstrated in an asymmetric double‐spiral microchannel by continuously separating a mixture of 5/10 μm particles and 3/5 μm particles.     

Interactions between polymer-grafted particles and bare particles for biocompatibility applications

We use self-consistent field theory (SCFT) to study the interactions between a polymer-grafted spherical particle and a bare spherical particle and explore how these interaction energies depend on the radii of the two particles and the grafting density. We find that the magnitude of the interaction energies increases with the radii of both the grafted and bare particles and with increasing grafting density. We also find a universal scaling law for the interaction potential which exhibits a power-law dependence on both particle sizes, a linear dependence on grafting density, and a logarithmic dependence on interparticle distance with a range of interaction that scales with brush height. We compare our numerical results to those obtained using the Derjaguin approximation. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2566–2577, 2009     

Concentrating particles on drop surfaces using external electric fields

We propose to use an externally applied uniform electric field to alter the distribution of particles on the surface of a drop immersed in another immiscible liquid. Specifically, we seek to generate well-defined concentrated regions at the drop surface while leaving the rest of the surface particle free. Experiments show that when the dielectric constant of the drop is greater than that of the ambient liquid the particles for which the Clausius-Mossotti factor is positive move along the drop surface to the two poles of the drop. Particles with a negative Clausius-Mossotti factor, on the other hand, move along the drop surface to form a ring near the drop equator. The opposite takes place when the dielectric constant of the drop is smaller than that of the ambient liquid, namely particles for which the Clausius-Mossotti factor is positive form a ring near the equator while those for which such a factor is negative move to the poles. This motion is due to the dielectrophoretic force that acts upon particles because the electric field on the surface of the drop is nonuniform, despite the uniformity of the applied electric field. Experiments also show that when small particles collect at the poles of a deformed drop the electric field needed to break the drop is smaller than without particles. These phenomena could be useful to concentrate particles at a drop surface within well-defined regions (poles and equator), separate two types of particles at the surface of a drop or increase the drop deformation to accelerate drop breakup.     

Transient electrophoresis in a suspension of charged particles with arbitrary electric double layers

The startup of electrophoretic motion in a suspension of spherical colloidal particles, which may be charged with constant zeta potential or constant surface charge density, due to the sudden application of an electric field is analytically examined. The unsteady modified Stokes equation governing the fluid velocity field is solved with unit cell models. Explicit formulas for the transient electrophoretic velocity of the particle in a cell in the Laplace transforms are obtained as functions of relevant parameters. The transient electrophoretic mobility is a monotonic decreasing function of the particle-to-fluid density ratio and in general a decreasing function of the particle volume fraction, but it increases and decreases with a raise in the ratio of the particle radius to the Debye length for the particles with constant zeta potential and constant surface charge density, respectively. On the other hand, the relaxation time in the growth of the electrophoretic mobility increases substantially with an increase in the particle-to-fluid density ratio and with a decrease in the particle volume fraction but is not a sensitive function of the ratio of the particle radius to the Debye length. For specified values of the particle volume fraction and particle-to-fluid density ratio in a suspension, the relaxation times in the growth of the particle mobility in transient electrophoresis and transient sedimentation are equivalent.     

Acoustofluidics 15: streaming with sound waves interacting with solid particles

In Part 15 of the tutorial series "Acoustofluidics-exploiting ultrasonic standing waves forces and acoustic streaming in microfluidic systems for cell and particle manipulation," we examine the interaction of acoustic fields with solid particles. The main focus here is the interaction of standing waves with spherical particles leading to streaming, together with some discussion on one non-spherical case. We begin with the classical problem of a particle at the velocity antinode of a standing wave, and then treat the problem of a sphere at the velocity node, followed by the intermediate situation of a particle between nodes. Finally, we discuss the effect of deviation from sphericity which brings about interesting fluid mechanics. The entire Focus article is devoted to the analysis of the nonlinear fluid mechanics by singular perturbation methods, and the study of the streaming phenomenon that ensues from the nonlinear interaction. With the intention of being instructive material, this tutorial cannot by any means be considered 'complete and comprehensive' owing to the complexity of the class of problems being covered herein.     

Dynamic electrophoretic mobility of spherical colloidal particles in salt-free concentrated suspensions

In this contribution, the dynamic electrophoretic mobility of spherical colloidal particles in a salt-free concentrated suspension subjected to an oscillating electric field is studied theoretically using a cell model approach. Previous calculations focusing the analysis on cases of very low or very high particle surface charge are analyzed and extended to arbitrary conditions regarding particle surface charge, particle radius, volume fraction, counterion properties, and frequency of the applied electric field (sub-GHz range). Because no limit is imposed on the volume fractions of solids considered, the overlap of double layers of adjacent particles is accounted for. Our results display not only the so-called counterion condensation effect for high particle charge, previously described in the literature, but also its relative influence on the dynamic electrophoretic mobility throughout the whole frequency spectrum. Furthermore, we observe a competition between different relaxation processes related to the complex electric dipole moment induced on the particles by the field, as well as the influence of particle inertia at the high-frequency range. In addition, the influences of volume fraction, particle charge, particle radius, and ionic drag coefficient on the dynamic electrophoretic mobility as a function of frequency are extensively analyzed.     

Preparation of monodisperse ellipsoidal polystyrene particles

A method is described for the preparation of monodisperse ellipsoidal particles of polystyrene in the colloidal size range. Monodisperse polystyrene particles were dispersed in a solution of polyvinyl alcohol. This dispersion was then allowed to form, by evaporation, a thin film of polyvinyl alcohol containing spherical polystyrene particles. Strips of this film were clamped into a metal frame, heated rapidly in an oil bath to 200°C and stretched to a predetermined extent in order to convert the spherical particles into ellipsoids; the film was then cooled. A wide range of axial ratios for a variety of initial particle sizes was obtained by this method.     

Electrophoresis and electric conduction in a salt-free suspension of charged particles

The electrophoresis and electric conduction of a suspension of charged spherical particles in a salt-free solution are analyzed by using a unit cell model. The linearized Poisson-Boltzmann equation (valid for the cases of relatively low surface charge density or high volume fraction of the particles) and Laplace equation are solved for the equilibrium electric potential profile and its perturbation caused by the imposed electric field, respectively, in the fluid containing the counterions only around the particle, and the ionic continuity equation and modified Stokes equations are solved for the electrochemical potential energy and fluid flow fields, respectively. Explicit analytical formulas for the electrophoretic mobility of the particles and effective electric conductivity of the suspension are obtained, and the particle interaction effects on these transport properties are significant and interesting. The scaled zeta potential, electrophoretic mobility, and effective electric conductivity increase monotonically with an increase in the scaled surface charge density of the particles and in general decrease with an increase in the particle volume fraction, keeping each other parameter unchanged. Under the Debye-Hückel approximation, the dependence of the electrophoretic mobility normalized with the surface charge density on the ratio of the particle radius to the Debye screening length and particle volume fraction in a salt-free suspension is same as that in a salt-containing suspension, but the variation of the effective electric conductivity with the particle volume fraction in a salt-free suspension is found to be quite different from that in a suspension containing added electrolyte.     

Two-dimensional crystallization of microspheres by a coplanar AC electric field

The particle-field and particle-particle interactions induced by alternating electric fields can be conveniently used for on-chip assembly of colloidal crystals. Two coplanar electrodes with a millimeter-sized gap between them are used here to assemble two-dimensional crystals from suspensions of either latex or silica microspheres. When an AC voltage is applied, the particles accumulate and crystallize on the surface between the electrodes. Light diffraction and microscopic observations demonstrate that the hexagonal crystal is always oriented with one axis along the direction of the field. The particles disassemble when the field is turned off, and the process can be repeated many times. The diffraction patterns from all consecutively formed crystals are identical. This assembly is driven by forces that depend on the electric field gradient, and a model is proposed involving a combination of dielectrophoresis and induced dipole chaining. The organization of large two-dimensional crystals allows characterization of the electrostatic interactions in the particle ensembles. The process can be controlled via the field strength, the frequency, and the viscosity of the liquid media. It could be used to make rudimentary optical switches or to separate mixtures of particles of different sizes.     

Synthesis of large-scale,narrowly dispersed,highly cross-linked,and spherical latex particles via one-step emulsion polymerization through particle coagulation

Particle coagulation technology is a facile approach to prepare large-scale and narrowly dispersed polymer particles. However, diverse shapes such as ellipsolid, snowman, dumbbell, and trimer among others were obtained if the cross-linker was directly added into the initial reaction mixtures due to the restriction of the highly cross-linking particle fusion process. In this study, we prepared sub-200?nm, narrowly dispersed, highly cross-linked, and spherical latex particles using particle coagulation technology by controlling the relation between the cross-linking net formation and particle coagulation. Depending on the addition time or feeding rate of the cross-linker (divinylbenzene, DVB), the particles with different sizes or shapes were obtained. The later the addition start time of DVB, the narrower the particle size distribution of the latex particles. Alternatively, the increase of the continuing feeding time could also be used to decrease the width of particle size distribution of the ultimate latex. In addition, narrowly dispersed and spherical latex particles also could be directly obtained by advancing the particle coagulation time using 2, 2′-Azobis (2-methylpropionamidine) dihydrochloride as a cationic initiator. Our study presents a new method that will further widen the fields of application of particle coagulation technology.