Strong Deformation of the Thick Electric Double Layer around a Charged Particle during Sedimentation or Electrophoresis

Sedimentation of a Charged Soft Sphere within a Charged Spherical Cavity

The sedimentation of a soft particle composed of an uncharged hard sphere core and a charged porous surface layer inside a concentric charged spherical cavity full of a symmetric electrolyte solution is analyzed in a quasi-steady state. By using a regular perturbation method with small fixed charge densities of the soft sphere and cavity wall, a set of linearized electrokinetic equations relevant to the fluid velocity field, electrical potential profile, and ionic electrochemical potential energy distributions are solved. A closed-form formula for the sedimentation velocity of the soft sphere is obtained as a function of the ratios of core-to-particle radii, particle-to-cavity radii, particle radius-to-Debye screening length, and particle radius-to-porous layer permeation length. The existence of the surface charge on the cavity wall increases the settling velocity of the charged soft sphere, principally because of the electroosmotic enhancement of fluid recirculation within the cavity induced by the sedimentation potential gradient. When the porous layer space charge and cavity wall surface charge have the same sign, the particle velocity is generally enhanced by the presence of the cavity. When these fixed charges have opposite signs, the particle velocity will be enhanced/reduced by the presence of the cavity if the wall surface charge density is sufficiently large/small relative to the porous layer space charge density in magnitude. The effect of the wall surface charge on the sedimentation of the soft sphere increases with decreases in the ratios of core-to-particle radii, particle-to-cavity radii, and particle radius-to-porous layer permeation length but is not a monotonic function of the ratio of particle radius-to-Debye length.

Hydrodynamic simulations of sedimenting dilute particle suspensions under repulsive DLVO interactions

We present guidelines to estimate the effect of electrostatic repulsion in sedimenting dilute particle suspensions. Our results are based on combined Langevin dynamics and lattice Boltzmann simulations for a range of particle radii, Debye lengths and particle concentrations. They show a simple relationship between the slope K of the concentration-dependent sedimentation velocity and the range χ of the electrostatic repulsion normalized by the average particle-particle distance. When χ → 0, the particles are too far away from each other to interact electrostatically and K = 6.55 as predicted by the theory of Batchelor. As χ increases, K likewise increases as if the particle radius increased in proportion to χ up to a maximum around χ = 0.4. Over the range χ = 0.4-1, K relaxes exponentially to a concentration-dependent constant consistent with known results for ordered particle distributions. Meanwhile the radial distribution function transitions from a disordered gas-like to a liquid-like form. Power law fits to the concentration-dependent sedimentation velocity similarly yield a simple master curve for the exponent as a function of χ, with a step-like transition from 1 to 1/3 centered around χ = 0.6.

Nanoparticles Loaded Thermoresponsive In Situ Gel for Ocular Antibiotic Delivery against Bacterial Keratitis

Antibiotics delivered through conventional dosage against ophthalmic infections show lower therapeutic efficacy due to their low residence time. Therefore, there is a great need to design and develop novel dosage forms that would increase the ocular residence time of antibiotics at the site of infection. This study describes the development of nanoparticles laden in situ gelling solution, intended to sustain antibiotic release for improved therapeutic efficiency. Oxytetracycline-loaded gelatin-polyacrylic acid nanoparticles were prepared and incorporated in poloxamer-N407 solution. The rheological properties of the system were studied concerning time and temperature. Moreover, in vivo biocompatibility of the system was ascertained using the Draize test and histological studies. Finally, the optimized formulation was evaluated for in vitro antibacterial activity against one of the most common keratitis causing bacteria, Pseudomonas aeruginosa. Additionally, the in vivo efficacy was evaluated on the rabbit’s eye conjunctivitis model. The formulation showed a sustained effect against keratitis; furthermore, the antibacterial activity was comparable with the commercial product.

Electrostatic Stabilization of Nano Liquid Metals in Doped Nonpolar Liquids

Liquid metals and alloys are attracting renewed attention owing to their potential for application in various advanced technologies. Eutectic gallium-indium (EGaIn) has been focused on in particular because of its integrated advantages of high conductivity, low melting point, and low toxicity. In this study, the colloidal behavior of nano-dispersed EGaIn in nonpolar oils is investigated. Although the nonpolar oil continuous phase is commonly considered to be free of electric charges, electrostatic repulsion appears to be crucial in the colloidal stabilization of the nano-dispersed EGaIn phases, the modulation of which is possible by doping the oil phases with different types of oil-soluble surfactants. The qualitative correlation between the observed colloidal stabilities and the "zero field" particle mobilities inferred from the field-dependent electrophoretic mobilities indicates that the electric charging of EGaIn particles in surfactant-doped nonpolar oils is a static phenomenon that is maintained in equilibrium, rather than a solely field-induced process. A systematic investigation of the charging properties of these unique biphasic particles, consisting of the liquid Ga-In bulk and the solid Ga₂ O₃ surface that formed spontaneously, reveals the complicated system-dependent nature of the charging mechanisms mediated by ionic and nonionic surfactants in nonpolar media.

The latest advances on nonlinear insulator-based electrokinetic microsystems under direct current and low-frequency alternating current fields: a review

This review article presents an overview of the evolution of the field of insulator-based dielectrophoresis (iDEP); in particular, it focuses on insulator-based electrokinetic (iEK) systems stimulated with direct current and low-frequency(< 1 kHz) AC electric fields. The article covers the surge of iDEP as a research field where many different device designs were developed, from microchannels with arrays of insulating posts to devices with curved walls and nano- and micropipettes. All of these systems allowed for the manipulation and separation of a wide array of particles, ranging from macromolecules to microorganisms, including clinical and biomedical applications. Recent experimental reports, supported by important theoretical studies in the field of physics and colloids, brought attention to the effects of electrophoresis of the second kind in these systems. These recent findings suggest that DEP is not the main force behind particle trapping, as it was believed for the last two decades. This new research suggests that particle trapping, under DC and low-frequency AC potentials, mainly results from a balance between electroosmotic and electrophoretic effects (linear and nonlinear); although DEP is present in these systems, it is not a dominant force. Considering these recent studies, it is proposed to rename this field from DC-iDEP to DC-iEK (and low-frequency AC-iDEP to low-frequency AC-iEK). Whereas much research is still needed, this is an exciting time in the field of microscale EK systems, as these new findings seem to explain the challenges with modeling particle migration and trapping in iEK devices, and provide perhaps a better understanding of the mechanisms behind particle trapping.

Determination of the zeta potential of planar solids in nonpolar liquids

ZetaSpin determines zeta potential by measuring the streaming potential generated by rotating a disk-shaped sample about its axis while submerged in the liquid. The apparatus and procedure developed for ZetaSpin in aqueous solutions was adapted for use in highly nonpolar fluids like surfactant-doped alkanes. Perhaps most unexpected is the need for up to 10 min (instead of a fraction of one second for aqueous solutions) for the electrometer to display changes in streaming potential in response to changes in rotation speed. Four tests (suggested by theory) confirm that the potential finally reported by the electrometer was indeed the streaming potential. Compared to electrophoresis, ZetaSpin does not require a value for the Debye length, avoids the complication caused by the electric-field-dependence of electrophoretic mobility and can be used with planar samples as well as colloidal particles.

Settling of a charged hydrophobic rigid colloid in aqueous media under generalized gravitational field

The hindrance created by the induced electric filed on the sedimentation of a charged colloid in an aqueous media is studied through numerical modeling. The colloid is considered to be hydrophobic, sedimenting under gravity or a centrifugal force (generalized gravity). The deformation of the charge cloud around the colloid induces an electric field, which generates electrical dipole force on the colloid. The sedimentation velocity is governed by the balance of an electric force, hydrodynamic drag, and gravitational force. Governing equations based on the first principle of electrokinetics is solved numerically through a control volume approach. The dependence of the sedimentation velocity on the electrical properties and slip length of the colloid is investigated. The sedimentation velocity of the charged colloid is slower than the corresponding uncharged particle and this deviation magnifies as the charge density as well as particle slip length is increased. An enhanced g-factor creates a size dependency of the charged colloids. The induced sedimentation field is obtained to analyze the electrokinetics. Surface hydrophobicity enhances the sedimentation velocity, which in turn manifests the induced sedimentation field. However, the sedimentation velocity of a charged hydrophobic colloid is lower than the corresponding uncharged hydrophobic particle and this deviation manifests as slip length is increased.

Electroviscous effect for a confined nanosphere in solution

A charged colloidal particle suspended in an electrolyte experiences electroviscous stresses arising from motion-driven electrohydrodynamic phenomena. Under certain conditions, the additional contribution from electroviscous drag forces to the total drag experienced by the moving particle can lead to measurable deviations of particle diffusion coefficients from values predicted by the well known Stokes-Einstein relation that describes diffusive behavior of small particles in an unbounded charge-free fluid. In this study, we investigate the role of electroviscous stresses on nanoparticle diffusion in confined geometries using both simulations and experiment. We compare our experimental measurements with the results of a numerically solved continuum model based on the Poisson-Nernst-Planck-Stokes system of equations and find good agreement between experiment and theory. Depending on the radius of the counterion species in solution and the degree of confinement, we find that the viscous drag on polystyrene nanoparticles can be augmented by approximately 10-25% compared to the values predicted by pure hydrodynamic models in the absence of free charge in the fluid. This enhancement corresponds approximately to a 5-10% increase compared to the electroviscous contribution for a charged particle in an unbounded fluid. Contrary to recent reports in the experimental literature, we find neither experimental nor theoretical evidence of an anomalously large enhancement of electroviscous forces on a confined charged nanoparticle in solution.

Electrophoresis of dielectric and immiscible-liquid-layer-encapsulated colloids in aqueous media

In this paper we consider the electrophoresis of a functionalized nanoparticle in electrolyte solution. The undertaken particle is comprised of a rigid inner core encapsulated with a layer of dielectric liquid (e.g., oil or lipid layer), which is immiscible to the bulk aqueous medium. The peripheral liquid layer of the undertaken nanoparticle contains mobile charges due to presence of solubilized surfactants. The mobile electrolyte ions can penetrate across the peripheral layer depending on the difference in the Born energy of the both phases. Such types of nanoparticles have received substantial attention due to their widespread applications in biomedical research. The electric double layer (EDL) is governed by the linearized Poisson-Boltzmann equation under a low potential limit and the electroosmotic flow field is governed by modified Stokes equation. We adopt the flat-plate formalism to obtain the closed analytical expression for the electrophoretic mobility of the undertaken particle under a thin EDL approximation. The dependence of electrophoretic mobility on the pertinent parameters is also illustrated.

Biphasic signals during nanopore translocation of DNA and nanoparticles due to strong ion cloud deformation

We report a theory for biphasic ionic current signals during DNA and nanoparticle translocation through a solid-state nanopore that produces scaling results consistent with those of finite element simulations (FEM), molecular dynamics (MD) simulations and experiments. For standard nanopores designed for potential rapid sequencing applications, the electric field is enhanced by orders of magnitude due to field focusing and can severely deform the ion-cloud around the charged DNA. Highly fore-aft asymmetric space charge distribution leads to a universal quasi-steady comet-like structure with a long tail. In contrast to previous biphasic theories, the charge density and length of the tail, which are responsible for the negative resistive pulse, are shown to depend sensitively on the dimensionless applied field, the Peclet number Pe, with a ∓1 scaling, due to a balance between tangential migration and normal diffusion. An optimum Pe is predicted where the negative pulse has the maximum amplitude.

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.

Sedimentation Velocity and Potential in Dilute Suspensions of Charge-Regulating Porous Spheres

The sedimentation of a charge-regulating porous sphere surrounded by an arbitrary electric double layer, which usually models a permeable polyelectrolyte coil or an aggregate of nanoparticles, is analyzed for the first time. The hydrodynamic frictional segments and ionogenic functional groups uniformly distribute in the porous sphere, and a regulation mechanism for the dissociation and association reactions occurring at these functional groups linearly relates the local electric potential to fixed charge density. The linearized electrokinetic equations governing the ionic concentration (or electrochemical potential energy), electric potential, and fluid velocity fields are solved for the case of a small basic fixed charge density by the regular perturbation method. Analytical formulae for the sedimentation velocity of a porous sphere and sedimentation potential of a dilute suspension of porous spheres are then obtained. The charge regulation tends to reduce the electrokinetic retardation to sedimentation velocity and the sedimentation potential (can be as much as 50 and 25%, respectively) compared to the case that the fixed charge density is a constant. Both the electrokinetic retardation to sedimentation velocity and the sedimentation potential vanish at the isoelectric point of the particles. The increase in the bulk concentration of the potential-determining ions crossing the isoelectric point changes signs of the fixed charges and thus causes a reversal in the direction of the sedimentation potential. The effects of charge regulation on the sedimentation of porous particles differ substantially from those of hard particles.

The lift force on a charged sphere that translates and rotates in an electrolyte

The distortion of the charge cloud around a uniformly charged, dielectric, rigid sphere that translates and rotates in an unbounded binary, symmetric electrolyte at zero Reynolds number is examined. The zeta potential of the particle ζ is assumed small relative to the thermal voltage scale. It is assumed that the equilibrium structure of the cloud is slightly distorted, which requires that the Péclet numbers characterizing distortion due to particle translation, Pe t = U a / D , and rotation, Pe r = Ω a 2 / D , are small compared to unity. Here, a is radius of the particle; D is the ionic diffusion coefficient; U = | U | and Ω = | Ω | , where U and Ω are the rectilinear and angular velocities of the particle, respectively. Perturbation expansions for small Pe t and Pe r are employed to calculate the nonequilibrium structure of the cloud, whence the force and torque on the particle are determined. In particular, we predict that the sphere experiences a force orthogonal to its directions of translation and rotation. This "lift" force arises from the nonlinear distortion of the cloud under the combined actions of particle translation and rotation. The lift force is given by F lift = L ( κ a ) ( ε a 3 ζ 2 / D 2 ) U × Ω [ 1 + O ( Pe t , Pe r ) ] . Here, ε is the permittivity of the electrolyte; κ - 1 is the Debye length; and L ( κ a ) is a negative function that decreases in magnitude with increasing κ a . The lift force implies that an unconstrained particle would follow a curved path; an electrokinetic analog of the inertial Magnus effect. Finally, the implication of the lift force on cross-streamline migration of an electrophoretic particle in shear flow is discussed.

Sedimentation Velocity and Potential in Dilute Suspensions of Charged Porous Shells

The sedimentation of a charged spherical porous shell with arbitrary inner and outer radii, which can model a permeable microcapsule or vesicle, in a general electrolyte solution is analytically examined. The relaxation effect in the electric double layers of arbitrary thickness around the porous shell is considered. The differential equations governing the electric potential profile, ionic electrochemical potential energy (or concentration) distributions, and fluid velocity field are linearized by taking the system to be only slightly distorted from equilibrium. These linearized equations are solved using a perturbation method with the density of the fixed charge of the porous shell as the small perturbation parameter. Closed-form formulas for the sedimentation velocity of a porous shell and sedimentation potential in a suspension of porous shells are obtained from a force balance and a zero current requirement, respectively. Both the charge-induced sedimentation velocity retardation and sedimentation potential are monotonic increasing functions of the relative shell thickness, and these increases are substantial if the shell is thin. The sedimentation velocity and potential are complex functions of the electrokinetic radius and normalized flow penetration length of the porous shell. In the limit of the porous shells with zero inner radius, our formulas for the sedimentation velocity and potential reduce to the results obtained for the intact porous spheres.

Interfaces Charged by a Nonionic Surfactant

Highly hydrophobic, water-insoluble nonionic surfactants are often considered irrelevant to the ionization of interfaces at which they adsorb, despite observations that suggest otherwise. In the present study, we provide unambiguous evidence for the participation of a water-insoluble surfactant in interfacial ionization by conducting electrophoresis experiments for surfactant-stabilized nonpolar oil droplets in aqueous continuous phase. It was found that the surfactant with amine headgroup positively charged the surface of oil suspended in aqueous continuous phase (oil/water interface), which is consistent with its basic nature. In nonpolar oil continuous phase, the same surfactant positively charged the surface of solid silica (solid/oil interface) which is often considered acidic. The latter observation is exactly opposite to what the traditional acid-base mechanism of surface charging would predict, most clearly suggesting the possibility for another charging mechanism.