Electrophoretic motion of a spherical particle with a symmetric nonuniform surface charge distribution in a nanotube

Electrohydrodynamics of diffuse porous colloids

The present article deals with the electrohydrodynamic motion of diffuse porous particles governed by an applied DC electric field. The spatial distribution of monomers as well as the charge distribution across the particle are considered to follow sigmoidal distribution involving decay length. Such a parameter measures the degree of inhomogeneity of the monomer distribution across the particle. The diffuse porous particles resemble several colloidal entities which are often seen in the environment as well as in biological and pharmaceutical industries. Considering the impact of bulk pH and ion steric effects, we modelled the electrohydrodynamics of such porous particulates based on the modified Boltzmann distribution for the spatial distribution of electrolyte ions and the Poisson equation for electric potential as well as the conservation of mass and momentum principles. We adopt regular perturbation analysis with weak field assumption and the perturbed equations are solved numerically to calculate the electrophoretic mobility and neutralization fraction of the particle charge during its motion as well as fluid collection efficiency. We further deduced the closed form relation between the drag force experienced by the charged porous particle and the fluid collection efficiency. In addition to the numerical results, we further derived the closed form analytical results for all the intrinsic parameters indicated above derived within the Debye-Hückel electrostatic framework and homogeneous distribution of monomers within the particle for which the decay length vanishes. The deduced mathematical results as indicated above will be useful to analyze several electrostatic and hydrodynamic features of a wide class of porous particulate and environmental entities.

The Influence of Electric Field Intensity and Particle Length on the Electrokinetic Transport of Cylindrical Particles Passing through Nanopore

The electric transport of nanoparticles passing through nanopores leads to a change in the ion current, which is essential for the detection technology of DNA sequencing and protein determination. In order to further illustrate the electrokinetic transport mechanism of particles passing through nanopores, a fully coupled continuum model is constructed by using the arbitrary Lagrangian–Eulerian (ALE) method. The model consists of the electric field described by the Poisson equation, the concentration field described by Nernst–Planck equation, and the flow field described by the Navier–Stokes equation. Based on this model, the influence of imposed electric field and particle length on the electrokinetic transport of cylindrical particles is investigated. It is found firstly the translation velocities for the longer particles remain constant when they locate inside the nanopore. Both the ion current blockade effect and the ion current enhancement effect occur when cylindrical particles enter and exit the nanopore, respectively, for the experimental parameters employed in this research. Moreover, the particle translation velocity and current fluctuation amplitude are dominated by the electric field intensity, which can be used to adjust the particle transmission efficiency and the ion current detectability. In addition, the increase in particle length changes the particle position corresponding to the peak value of the ion current, which contributes to distinguishing particles with different lengths as well.

The effects of electrostatic correlations on the ionic current rectification in conical nanopores

Ion-ion electrostatic correlations are recognized to play a significant role in the presence of concentrated multivalent electrolytes. To account for their impact on ionic current rectification phenomenon in conical nanopores, we use the modified continuum Poisson-Nernst-Planck (PNP) equations by Bazant et al. Coupled with the Stokes equations, the effects of the EOF are also included. We thoroughly investigate the dependence of the ionic current rectification ratios as a function of the double layer thickness and the electrostatic correlation length. By considering the electrostatic correlations, the modified PNP model successfully captures the ionic current rectification reversal in nanopores filled with lanthanum chloride LaCl₃ . This finding qualitatively agrees with the experimental observations that cannot be explained by the standard PNP model, suggesting that ion-ion electrostatic correlations are responsible for this reversal behavior. The modified PNP model not only can be used to explain the experiments, but also go beyond to provide a design tool for nanopore applications involving multivalent electrolytes.

Influence of electroosmotic flow on the ionic current rectification in a pH-regulated, conical nanopore

The ionic current rectification (ICR) is studied theoretically by considering a pH-regulated, conical nanopore. In particular, the effect of electroosmotic flow (EOF), which was often neglected in previous studies, is investigated by solving a set of coupled Poisson, Nernst-Planck, and Navier-Stokes equations. The behaviors of ICR under various conditions are examined by varying solution pH, bulk ionic concentration, and applied electric potential bias. We show that the EOF effect is significant when the bulk ionic concentration is medium high, the pH is far away from the iso-electric point, and the electric potential bias is high. The percentage deviation in the current rectification ratio arising from neglecting the EOF effect can be on the order of 100%. In addition, the behavior of the current rectification ratio at a high pH taking account of EOF is different both qualitatively and quantitatively from that without taking account of EOF.

Resistive-pulse analysis of nanoparticles

The development of nanopore fabrication methods during the past decade has led to the resurgence of resistive-pulse analysis of nanoparticles. The newly developed resistive-pulse methods enable researchers to simultaneously study properties of a single nanoparticle and statistics of a large ensemble of nanoparticles. This review covers the basic theory and recent advances in applying resistive-pulse analysis and extends to more complex transport motion (e.g., stochastic thermal motion of a single nanoparticle) and unusual electrical responses (e.g., resistive-pulse response sensitive to surface charge), followed by a brief summary of numerical simulations performed in this field. We emphasize the forces within a nanopore governing translocation of low-aspect-ratio, nondeformable particles but conclude by also considering soft materials such as liposomes and microgels.

Electrokinetic behavior of a pH-regulated, zwitterionic nanocylinder in a cylindrical nanopore filled with multiple ionic species

Recent advances in fabrication techniques make nano-sized pores as promising platforms for both detection and sequencing of individual biopolymers such as DNA. To simulate the electrokinetic behavior of a particle in this case, we consider the electrophoresis of a soft nanocylinder comprising a rigid core and a pH-regulated, zwitterionic polyelectrolyte layer along the axis of a rigid cylindrical nanopore. Extending the conventional electrophoresis analysis, where the liquid phase contains only one kind each of cations and anions, we assume that it contains multiple ionic species, as is usually the case in practice. The key parameters are examined for their influences on the electrokinetic behavior of a particle. These include pH, the thickness of the polyelectrolyte layer and the density of its functional groups, and the pore size. The results gathered provide necessary information for the design of an electrokinetic apparatus.

Electrokinetic particle entry into microchannels

The fundamental understanding of particle electrokinetics in microchannels is relevant to many applications. To date, however, the majority of previous studies have been limited to particle motion within the area of microchannels. This work presents the first experimental and numerical investigation of electrokinetic particle entry into a microchannel. We find that the particle entry motion can be significantly deviated from the fluid streamline by particle dielectrophoresis at the reservoir-microchannel junction. This negative dielectrophoretic motion is induced by the inherent non-uniform electric field at the junction and is insensitive to the microchannel length. It slows down the entering particles and pushes them toward the center of the microchannel. The consequence is the demonstrated particle deflection, focusing, and trapping phenomena at the reservoir-microchannel junction. Such rich phenomena are studied by tuning the AC component of a DC-biased AC electric field. They are also utilized to implement a selective concentration and continuous separation of particles by size inside the entry reservoir.

Electrophoresis of a particle at an arbitrary surface potential and double layer thickness: importance of nonuniformly charged conditions

Recent advances in material science and technology yield not only various kinds of nano- and sub-micro-scaled particles but also particles of various charged conditions such as Janus particles. The characterization of these particles can be challenging because conventional electrophoresis theory is usually based on drastic assumptions that are unable to realistically describe the actual situation. In this study, the influence of the nonuniform charged conditions on the surface of a particle at an arbitrary level of surface potential and double layer thickness on its electrophoretic behavior is investigated for the first time in the literature taking account of the effect of double-layer polarization. Several important results are observed. For instance, for the same averaged surface potential, the mobility of a nonuniformly charged particle is generally smaller than that of a uniformly charged particle, and the difference between the two depends upon the thickness of double layer. This implies that using the conventional electrophoresis theory may result in appreciable deviation, which can be on the order of ca. 20%. In addition, the nonuniform surface charge can yield double vortex in the vicinity of a particle by breaking the symmetric of the flow field, which has potential applications in mixing and/or regulating the medium confined in a submicrometer-sized space, where conventional mixing devices are inapplicable.

Electrokinetic particle translocation through a nanopore

Nanoparticle electrophoretic translocation through a single nanopore induces a detectable change in the ionic current, which enables the nanopore-based sensing for various bio-analytical applications. In this study, a transient continuum-based model is developed for the first time to investigate the electrokinetic particle translocation through a nanopore by solving the Nernst-Planck equations for the ionic concentrations, the Poisson equation for the electric potential and the Navier-Stokes equations for the flow field using an arbitrary Lagrangian-Eulerian (ALE) method. When the applied electric field is relatively low, a current blockade is expected. In addition, the particle could be trapped at the entrance of the nanopore when the electrical double layer (EDL) adjacent to the charged particle is relatively thick. When the electric field imposed is relatively high, the particle can always pass through the nanopore by electrophoresis. However, a current enhancement is predicted if the EDL of the particle is relatively thick. The obtained numerical results qualitatively agree with the existing experimental results. It is also found that the initial orientation of the particle could significantly affect the particle translocation and the ionic current through a nanopore. Furthermore, a relatively high electric field tends to align the particle with its longest axis parallel to the local electric field. However, the particle's initial lateral offset from the centerline of the nanopore acts as a minor effect.

Electrophoretic motion of a nanorod along the axis of a nanopore under a salt gradient

The phoretic translation of a charged, elongated cylindrical nanoparticle, such as a DNA molecule and nanorod, along the axis of a nanopore driven by simultaneous axial electric field and salt concentration gradient, has been investigated using a continuum model, which consists of the Poisson-Nernst-Planck equations for the ionic concentrations and electric potential, and the Stokes equations for the hydrodynamic field. The induced particle motion includes both electrophoresis, driven by the imposed electric field, and diffusiophoresis, arising from the imposed salt concentration gradient. The particle's phoretic velocity along the axis of a nanopore is computed as functions of the imposed salt concentration gradient, the ratio of the its radius to the double-layer thickness, the nanorod's aspect ratio (length/radius), the ratio of the nanopore size to the particle size, the surface-charge density of the particle, and that of the nanopore in KCl solution. The diffusiophoresis in a nanopore mainly arises from the induced electrophoresis driven by the generated electric field, stemming from the double-layer polarization, and can be used to regulate electrophoretic translocation of a nanorod, such as a DNA molecule, through a nanopore. When both the nanorod and the nanopore wall are charged, the induced electroosmotic flow arising from the interaction of the overall electric field with the double layer adjacent to the nanopore wall has a significant effect on both electrophoresis driven by the imposed electric field and diffusiophoresis driven by the imposed salt gradient.

Electrodiffusiophoretic motion of a charged spherical particle in a nanopore

The electrodiffusiophoretic motion of a charged spherical nanoparticle in a nanopore subjected to an axial electric field and electrolyte concentration gradient has been investigated using a continuum model, composed of the Poisson-Nernst-Planck equations for the ionic mass transport and the Navier-Stokes equations for the flow field. The charged particle experiences electrophoresis in response to the imposed electric field and diffusiophoresis caused solely by the imposed concentration gradient. The diffusiophoretic motion is induced by two different mechanisms, an electrophoresis driven by the generated electric field arising from the difference of ionic diffusivities and the double layer polarization and a chemiphoresis due to the induced osmotic pressure gradient around the charged nanoparticle. The electrodiffusiophoretic motion along the axis of a nanopore is investigated as a function of the ratio of the particle size to the thickness of the electrical double layer, the imposed concentration gradient, the ratio of the surface charge density of the nanopore to that of the particle, and the type of electrolyte. Depending on the magnitude and direction of the imposed concentration gradient, one can accelerate, decelerate, and even reverse the particle's electrophoretic motion in a nanopore by the superimposed diffusiophoresis. The induced electroosmotic flow in the vicinity of the charged nanopore wall driven by both the imposed and the generated electric fields also significantly affects the electrodiffusiophoretic motion.

DC electrokinetic particle transport in an L-shaped microchannel

Electrokinetic transport of particles through an L-shaped microchannel under DC electric fields is theoretically and experimentally investigated. The emphasis is placed on the direct current (DC) dielectrophoretic (DEP) effect arising from the interactions between the induced spatially nonuniform electric field around the corner and the dielectric particles. A transient multiphysics model is developed in an arbitrary Lagrangian-Eulerian (ALE) framework, which comprises the Navier-Stokes equations for the fluid flow and the Laplace equation for the electrical potential. The predictions of the DEP-induced particle trajectory shift in the L-shaped microchannel are in quantitative agreement with the obtained experimental results. Numerical studies also show that the DEP effect can alter the angular velocity and even the direction of the particle's rotation. Further parametric studies suggest that the L-shaped microfluidic channel may be utilized to focus and separate particles by size via the induced DEP effect.

Dielectrophoretic choking phenomenon in a converging-diverging microchannel

Experiments show that particles smaller than the throat size of converging-diverging microchannels can sometimes be trapped near the throat. This critical phenomenon is associated with the negative dc dielectrophoresis arising from nonuniform electric fields in the microchannels. A finite-element model, accounting for the particle-fluid-electric field interactions, is employed to investigate the conditions for this dielectrophoretic (DEP) choking in a converging-diverging microchannel for the first time. It is shown quantitatively that the DEP choking occurs for high nonuniformity of electric fields, high ratio of particle size to throat size, and high ratio of particle's zeta potential to that of microchannel.

dc electrokinetic transport of cylindrical cells in straight microchannels

Electrokinetic transport of cylindrical cells under dc electric fields in a straight microfluidic channel is experimentally and numerically investigated with emphasis on the dielectrophoretic (DEP) effect on their orientation variations. A two-dimensional multiphysics model, composed of the Navier-Stokes equations for the fluid flow and the Laplace equation for the electric potential defined in an arbitrary Lagrangian-Eulerian framework, is employed to capture the transient electrokinetic motion of cylindrical cells. The numerical predictions of the particle transport are in quantitative agreement with the obtained experimental results, suggesting that the DEP effect should be taken into account to study the electrokinetic transport of cylindrical particles even in a straight microchannel with uniform cross-sectional area. A comprehensive parametric study indicates that cylindrical particles would experience an oscillatory motion under low electric fields. However, they are aligned with their longest axis parallel to the imposed electric field under high electric fields due to the induced DEP effect.