Translational motion of a spherical particle near a planar liquid-fluid interface

The translational electrophoretic motion of a colloidal spherical particle parallel to a planar liquid-fluid interface is analyzed by using the reciprocal theorem developed by Yariv and Brenner [E. Yariv, H. Brenner, J. Fluid Mech. 484 (2003) 85]. Based on the thin electric double layers assumption, analytical solutions of the forces acting on the particle are obtained, and the influence of the liquid-fluid interface on the electrophoretic velocity of the particle is studied. It is found that the speed of the particle's electrokinetic motion will increase as the separation distance between the particle and the interface decreases. This enhancement of electrophoretic mobility becomes more significant when the viscosity of the fluid phase becomes larger.     

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

The electrophoretic motion of a spherical nanoparticle, subject to an axial electric field in a nanotube filled with an electrolyte solution, has been investigated using a continuum theory, which consists of the Nernst-Planck equations for the ionic concentrations, the Poisson equation for the electric potential in the solution, and the Stokes equation for the hydrodynamic field. In particular, the effects of nonuniform surface charge distributions around the nanoparticle on its axial electrophoretic motion are examined with changes in the bulk electrolyte concentration and the surface charge of the tube's wall. A particle with a nonuniform charge distribution is shown to induce a corresponding complex ionic concentration field, which in turn influences the electric field and the fluid motion surrounding the particle and thus its electrophoretic velocity. As a result, contrary to the relatively simple dynamics of a particle with a uniform surface charge, dominated by the irradiating electrostatic force, that with a nonuniform surface charge distribution shows various intriguing behaviors due to the additional interplay of the nonuniform electro-osmotic effects.     

Electrophoretic motion of a soft spherical particle in a nanopore

Many biocolloids, biological cells and micro-organisms are soft particles, consisted with a rigid inner core covered by an ion-permeable porous membrane layer. The electrophoretic motion of a soft spherical nanoparticle in a nanopore filled with an electrolyte solution has been investigated using a continuum mathematical model. The model includes the Poisson-Nernst-Planck (PNP) equations for the ionic mass transport and the modified Stokes and Brinkman equations for the hydrodynamic fields outside and inside the porous membrane layer, respectively. The effects of the “softness” of the nanoparticle on its electrophoretic velocity along the axis of a nanopore are examined with changes in the ratio of the radius of the rigid core to the double layer thickness, the ratio of the thickness of the porous membrane layer to the radius of the rigid core, the friction coefficient of the porous membrane layer, the fixed charge inside the porous membrane layer of the particle and the ratio of the radius of the nanopore to that of the rigid core. The presence of the soft membrane layer significantly affects the particle electrophoretic mobility.     

Electrophoretic motion of a spherical particle in a converging-diverging nanotube

A charged spherical particle is concentrically positioned in a converging-diverging nanotube filled with an electrolyte solution, resulting in an electric double layer (EDL) forming around the particle's surface. In the presence of an axially applied electric field, the particle electrophoretically migrates along the axis of the nanotube due to the electrostatic and hydrodynamic forces acting on the particle. In contrast to a cylindrical nanotube with a constant cross-sectional area in which the electric field is almost uniform, the presence of a converging-diverging section in a nanotube alters the electric field, perturbs the charge distribution, and induces a pressure gradient and a recirculating flow that affect the electrostatic and hydrodynamic forces acting on both the particle and the fluid. Depending on the magnitude of the surface charge density along the nanotube's wall, the particle's electrophoretic motion may be significantly accelerated as the particle transverses the converging-diverging section. A continuum model consisting of the Nernst-Planck, Poisson, and Navier-Stokes equations for the ionic concentrations, electric potential, and flow field is implemented to compute the particle's velocity as a function of the particle's size, the nanotube's geometry, surface charges, electric field intensity, bulk electrolyte concentration, and the particle's location. When the particle is negatively charged and the wall of the nanotube is uncharged, the particle migrates in the direction opposite to that of the applied electric field and the presence of the converging-diverging section significantly accelerates the particle's motion. This, however, is not always true when the nanotube's wall is charged with the same sign as that of the particle. Once the ratio of the surface charge density of the nanotube's wall to that of the particle exceeds a certain value, the negatively charged particle will not translocate through the tube toward the anode and does not attain the maximum velocity at the throat of the converging-diverging section. One can envision such a device to be a nanofilter that allows molecules with surface charge densities much higher than that of the wall to go through the nanofilter, while preventing molecules with surface charge densities lower than that of the wall from passing through the nanofilter. The induced recirculating flow may be used to enhance mixing and to stretch, fold, and trap molecules in nanofluidic detectors and reactors.     

Analysis of self-electrophoretic motion of a spherical particle in a nanotube: effect of nonuniform surface charge density

Autonomous motions of a spherical nanoparticle in a nanotube filled with an electrolyte solution were investigated using a continuum theory, which consisted of the Nernst-Planck equations for the ionic concentrations, the Poisson equation for the electric potential in the solution, and the Stokes equation for the hydrodynamic field. Contrary to the usual electrophoresis, in which an external electric field is imposed to direct the motion of charged particles, the autonomous motion originates from the self-generated electric field due to the ionic concentration polarization of the liquid medium surrounding an asymmetrically charged particle. In addition to the particle motion, the interaction between the electric field generated and the free charges of the polarized solution induces electroosmotic flows. These autonomous motions of the fluid as well as the particle were examined with focus on the effects of the surface-charge distribution of the particle, the size of the nanotube, and the thickness of the electric double layer, which affected the direction and the speed of the particle significantly.     

Effect of surface tension and surface elasticity of a fluid-fluid interface on the motion of a particle immersed near the interface

The motion of a particle immersed in a fluid near a fluid-fluid interface is studied on the basis of the linearized Navier-Stokes equations. The motion is influenced by surface tension, dilatational surface elasticity modulus, and surface shear modulus, as well as by gravity. The backflow at the location of the particle after a sudden impulse has some universal features that are the same as for a rigid wall with stick boundary conditions. At short times the flow depends only on the mass densities of the two fluids. The nature of the short-time flow is calculated from potential flow theory. At a somewhat later time the particle shows a pronounced rebound. The maximum value of the rebound and the time at which the maximum occurs depend on the elastic properties of the interface.     

Accelerated energy transfer between molecules near a solid particle

The Forster-Dexter theory of energy transfer between molecules is generalized to include the effects of a nearby solid state particle. It is found that the energy transfer rate between a donor and acceptor molecule may be enhanced by many orders of magnitude when the molecular transition frequencies lie in the vicinity of the resonance frequency of the particle and when the particle possesses sharp features. Due to increased damping near the particle, however, this may or may not lead to increased acceptor molecule radiation.     

3-D transient electrophoretic motion of a spherical particle in a T-shaped rectangular microchannel

This paper considers the electrophoretic motion of a spherical particle in an aqueous electrolyte solution in a T-shaped rectangular microchannel, where the size of the channel is close to that of the particle. This is a complicated transient process where the electric field, the flow field, and the particle motion are coupled together. A theoretical model was developed to investigate the influences of the applied electric potentials, the zeta potentials of the channel and the particle, and the size of the particle on the particle motion. A direct numerical simulation method using the finite element method is employed. This method employs a generalized Galerkin finite element formulation that incorporates both equations of the fluid flow and equations of the particle motion into a single variational equation where the hydrodynamic interactions are eliminated. The ALE method is used to track the surface of the particle at each time step. The numerical results show that the electric field in the T-shaped microchannel is influenced by the presence of the particle, and that the particle motion is influenced by the applied electric potentials and the zeta potentials of the channel and the particle. The path of the particle motion is dominated by the local electric field and the ratio of the zeta potential of the channel to that of the particle. The particle's velocity is also dependent on its size in a small channel.     

The surface potential of a spherical colloid particle: functional theoretical approach

By using the iterative method in functional analysis, the potential of the electrical double layer of a spherical colloid particle, which is represented by the so-called Poisson-Boltzmann (PB) equation, has been solved analytically under general potential conditions. With the help of the diagram method in mathematics, the surface potential of the particle has been defined from the second iterative solution. The influence of the parameters included in the solutions on the surface potential has been studied. The results show that the surface potential of the particle increases as the temperature of the system, the aggregation number, and the concentration of ions increase, but decreases with an increase in the dielectric constant and the valence of the ions. The corresponding space charge density also has been illustrated in this work.     

Thermophoretic force on a metallic or nonmetallic particle immersed into a rarefied Plasma

Analytical results of the thermophoretic force on a metallic or nonmetallic spherical particle immersed into a rarefied plasma with a heat flux within the plasma are presented for the extreme case of free-molecule regime and thin plasma sheath. It has been shown that the thermophoresis is predominantly caused by atoms at low plasma temperatures with negligible gas ionization, while it is mainly due to ions and electrons at high plasma temperatures with great degree of ionization. The ion flux incident to a particle is constant on the whole sphere surface, while the electron flux to the metallic sphere is dependent on the -position with slightly greater value at the fore stagnation point. Consequently, there is a small difference between the metallic and nonmetallic spheres in their -distributions of the floating potential on the surface, which causes the thermophoretic force on a nonmetallic sphere to be appreciably greater than that on a metallic sphere at high plasma temperatures. Expressions for the total thermophoretic force on a metallic sphere and its components due to, respectively, atoms, ions, and electrons have been given in a closed form. Calculated results are also presented on the effects of pressure and of electron/heavy-particle temperature ratio. These results can be understood based on the variation of atom, ion, and electron thermal conductivities with the gas pressure, the temperature, and the temperature ratio.     

Thermophoretic force acting on an evaporating particle suspended in a rarefied plasma

Analytical results of the thermophoretic force on an evaporating spherical particle immersed in a rarefied plasma with a large temperature gradient are presented for the extreme case of free-molecule regime and thin plasma sheath. It has been shown that the existence of a temperature gradient in the plasma causes a nonuniform distribution of the local heat flux density on the sphere surface with its maximum value at the fore-stagnation point of the sphere, although the total heal flux to the whole particle is independent of the temperature gradient existing in the plasma. This nonuniform-distribution of the local heat flux density causes a nonuniform distribution of the. local evaporated-mass flux and related reaction force around the surface of an evaporating particle, and thus causes an additional force on the particle. Calculated results show that the thermophoretic force on an evaporating particle may substantially exceed that on a nonevaporating one, especially for the case of a metallic particle (with infinite electric conductivity). The effect of evaporation on the thermophoretic force is more pronounced as the evaporation latent heat of the particle material is comparatively low and as high plasma temperatures are involved.     

The electrophoresis of a spherical particle

The problem of predicting the electrophoretic velocity of a spherical charged particle in an infinite dielectric liquid containing impurities is re-examined. A model, somewhat different from those commonly used, is postulated, and the associated equations are formulated and are solved subject to certain approximations. The electrophoretic velocityU is found to be linear in the applied field and to vary algebraically in the parameterχ=ka.     

Influence of Brownian motion on blood platelet flow behavior and adhesive dynamics near a planar wall

We used the platelet adhesive dynamics computational method to study the influence of Brownian motion of a platelet on its flow characteristics near a surface in the creeping flow regime. Two important characterizations were done in this regard: (1) quantification of the platelet's ability to contact the surface by virtue of the Brownian forces and torques acting on it, and (2) determination of the relative importance of Brownian motion in promoting surface encounters in the presence of shear flow. We determined the Peclet number for a platelet undergoing Brownian motion in shear flow, which could be expressed as a simple linear function of height of the platelet centroid, H from the surface Pe (platelet) = . (1.56H + 0.66) for H > 0.3 microm. Our results demonstrate that at timescales relevant to shear flow in blood Brownian motion plays an insignificant role in influencing platelet motion or creating further opportunities for platelet-surface contact. The platelet Peclet number at shear rates >100 s-1 is large enough (>200) to neglect platelet Brownian motion in computational modeling of flow in arteries and arterioles for most practical purposes even at very close distances from the surface. We also conducted adhesive dynamics simulations to determine the effects of platelet Brownian motion on GPIbalpha-vWF-A1 single-bond dissociation dynamics. Brownian motion was found to have little effect on bond lifetime and caused minimal bond stressing as bond rupture forces were calculated to be less than 0.005 pN. We conclude from our results that, for the case of platelet-shaped cells, Brownian motion is not expected to play an important role in influencing flow characteristics, platelet-surface contact frequency, and dissociative binding phenomena under flow at physiological shear rates (>50 s(-1)).     

Electrolyte-dependent pairwise particle motion near electrodes at frequencies below 1 kHz

A model incorporating a phase angle between an applied electric field and the motion of particles driven by it explains electrolyte-dependent pairwise particle motion near electrodes. The model, predicting that two particles aggregate when this phase angle is greater than 90 degrees but separate when the phase angle is less than 90 degrees , was based largely on contrasting behavior in two electrolytes (KOH and NaHCO3) used with indium tin oxide (ITO) electrodes. The present contribution expands the experimental evidence for this model to KOH, NaHCO3, NaOH, NH4OH, KCl, and H2CO3 solutions with Pt, as well as ITO electrodes. The phase angle correlation was verified in all cases. Comparisons of the model predictions to experimental data show that the sign and order of magnitude of rates of change in the separation distances between particle pairs are correctly predicted.     

On the evaporation and motion of a volatile droplet near a volatile liquid surface

A problem concerning the free evaporation or condensation growth of a droplet near an infinite planar surface of the same liquid is solved. The behavior of the droplet is considered at vapor temperature and concentration gradients preset at an infinite distance from it. The boundary conditions take into account effects that are linear with respect to the Knudsen number. Equations are derived for the rate of variations in the radius of the droplet and the velocity of its steady motion induced by nonuniform temperature and concentration of the vapor. Dependences of the rate of variations in the radius and the velocity of the steady motion of the droplet on the distance from the planar surface are presented for a droplet 1 ??m in radius suspended in air.     

Donnan potential and surface potential of a spherical soft particle in an electrolyte solution

A simple numerical method, which does not involve numerical integration of the Poisson-Boltzmann equations, is presented for obtaining the relationship between the Donnan potential and surface potential of a spherical soft particle (i.e., a polyelectrolyte-coated particle) in a symmetrical electrolyte solution. We assume that a soft particle consists of the particle core of radius a covered with an ion-penetrable surface layer of polyelectrolytes of thickness d and that ionized groups of valence Z are distributed at a uniform density of N in the polyelectrolyte layer and the relative permittivity takes the same value in the regions outside and inside the polyelectrolyte layer. The Donnan potential and surface potential are determined by the values of a, d, Z, N, and the Debye-Hückel parameter kappa of the electrolyte solution. Numerical results obtained by the present method are in excellent agreement with exact results obtained by solving the nonlinear spherical Poisson-Boltzmann equations for the both regions inside and outside the polyelectrolyte layer.     

Effect of surface wettability on liquid density, structure, and diffusion near a solid surface

Molecular dynamics and Langevin dynamics simulations are used to elucidate the behavior of liquid atoms near a solid boundary. Correlations between the surface wettability and spatial variations in liquid density and structure are identified. The self-diffusion coefficient tensor is predicted, revealing highly anisotropic and spatially varying mass transfer phenomena near the solid boundary. This behavior affects self-diffusion at a range of time scales. Near a more-wetting surface, self-diffusion is impeded by strong solid-liquid interactions that induce sharp liquid density gradients and enhanced liquid structure. Conversely, near a less-wetting surface, where solid-liquid interactions are weaker, the liquid density is low, the atoms are disordered, and diffusion is enhanced. These findings suggest that altering the wettability of a micro- or nanochannel may provide a passive means for controlling the diffusion of select targets towards a functionalized surface and controlling the reaction rate in diffusion-limited reactions.     

Surface charge density/surface potential relationship for a spherical colloidal particle in a salt-free medium

On the basis of a theory of Imai and Oosawa (Busseiron Kenkyu52, 42 (1952); 59, 99 (1953)), approximate analytic expressions for the surface charge density/surface potential relationship for a spherical colloidal particle in a salt-free (aqueous or nonaqueous) medium containing only counterions are derived. There is a certain critical value of the surface charge density (or the total surface charge) separating two distinct cases: low surface charge density case and high surface charge density case. In the latter case counterion condensation occurs in the vicinity of the particle surface. The results are in excellent agreement with numerical calculations for the case of dilute suspensions.