Effect of a charged boundary on electrophoresis: a sphere at an arbitrary position in a spherical cavity

The effect of the presence of a charged boundary on the electrophoretic behavior of a particle is investigated by considering a sphere at an arbitrary position in a spherical cavity under conditions of low surface potential and weak applied electric field. Previous analyses are modified by using a more realistic electrostatic force formula and several interesting results, which are not reported in the literature, are observed. We show that the qualitative behavior of a particle depends largely on its position, its size relative to that of a cavity, and the thickness of the electric double layer. In general, the presence of a cavity has the effect of increasing the conventional hydrodynamic drag on a particle through a nonslip condition on the former. Also, a decrease in the thickness of the double layer surrounding a sphere has the effect of increasing the electrostatic force acting on its surface so that its mobility increases. However, this may not be the case when an uncharged particle in placed in a positively charged cavity, where the electroosmotic flow plays a role; for example, the mobility can exhibit a local maximum and the direction of electrophoresis can change.     

Creeping motion of an assemblage of composite spheres relative to a fluid

The sedimentation of a homogeneous distribution of spherical composite particles and the fluid flow through a bed of these particles are investigated theoretically. Each composite particle is composed of a spherical solid core and a surrounding porous shell. In the fluid-permeable porous shell, idealized hydrodynamic frictional segments are assumed to distribute uniformly. The effect of interactions among the particles is taken into explicit account by employing a fundamental cell-model representation which is known to provide good predictions for the motion of a swarm of nonporous spheres within a fluid. In the limit of a small Reynolds number, the Stokes and Brinkman equations are solved for the flow field in a unit cell, and the drag force exerted by the fluid on the particle is obtained in a closed form. For a distribution of composite spheres, the normalized mobility of the particles decreases or the particle interactions increase monotonically with a decrease in the permeability of their porous shells. The effect of particle interactions on the creeping motion of composite spheres relative to a fluid can be quite significant in some situations. In the limiting cases, the analytical solutions describing the drag force or mobility for a suspension of composite spheres reduce to those for suspensions of solid spheres and of porous spheres. The hydrodynamic behavior for composite spheres may be approximated by that for permeable spheres when the porous layer is sufficiently thick, depending on the permeability.     

Drag force acting on an evaporating particle immersed in a rarefied plasma flow

Analytical expressions are presented for the drag force acting on an evaporating or nonevaporating particle immersed in a plasma flow for the extreme case of free-molecule flow regime and thin plasma .sheath. It is shown that the drag force on a spherical particle is proportional to the square of the particle radius and to the relative velocity between the particle and the bulk plasma at low speed ratios. The existence of a relative velocity between the particle and the plasma results in a nonuniform heat flux distribution with its rnaximum value at the frontal stagnation point of tire sphere. This nonuniform distribution of the local heat fux density causes a nonuniforrn distribution of the local evaporated-mass flux and vapor reaction force around the surface of an evaporating particle, and thus induces an additional force on the particle. Consequently, the drag force acting on art evaporating particle is always greater than that on a nonevaporating one. This additional drag force due to particle evaporation is more significant for nonmetallic particles and for particle materials with lower latent heat of evaporation and lower vapor molecular mass. It increases with increasing plasma temperature and with decreasing gas pressure at the high plasma temperatures associated with appreciable gas ionization. The drag ratio increases with increasing electron/heavy-particle temperature ratio at high electron temperatures for a two-temperature plasma.     

The drag of the row of parallel chains of spherical particles in the Stokes flow

The drag of thin-layered porous deposit consisting of dendrites of identical spherical particles with respect to the flow of viscous incompressible liquid is calculated. The deposit is approximated by a model system, a row of parallel chains of particles oriented perpendicular to a flow direction. The expression is derived for the dimensionless drag force acting on the unit chain length as a function of the ratio of a particle radius to a half-distance between chain axes, a/h. It is shown that, at a/h < 0.5, the hydrodynamic equivalent of the chains is the smooth cylinder whose radius is 1.16 times smaller than the particle radius that agrees with the experiment. It is also shown that, at a/h = 1, the drag force of a particle contacting with four adjacent particles in the layer with square packing is equal to F = 44F _St, where F _St is the Stokes drag force of a spherical particle. The pressure drop in this single layer is by 3.5% higher than in the layer of spherical particles with cubic packing. At a/h = 2/√3, drag force F of the particle contacting with six particles in a single layer with hexagonal packing is equal to 340F _St.     

Drag of a Solid Particle Trapped in a Thin Film or at an Interface: Influence of Surface Viscosity and Elasticity

We propose a theoretical model for the motion of a spherical particle entrapped in a thin liquid film or in a monolayer of insoluble surfactant at the air/water interface. Both surface shear and dilational viscosity, surface diffusion, and elasticity of the film are taken into consideration. The drag force acting on the particle is analytically calculated and asymptotic expressions of the problem are provided. The relevance of the model is discussed by comparing the calculated "viscoelastic" drag, gamma(vel), to the one predicted by Saffman's theory, gamma(S), for cylindrical inclusions in membranes. Numerical analyses are performed to evaluate the contributions of the surface viscosity and the diffusion coefficient of the layer on the hydrodynamical resistance experienced by the particle. Copyright 2000 Academic Press.     

Dielectric force and relative motion between two spherical particles in electrophoresis

When two particles close to each other are in electrophoretic motion, each particle is under the influence of the nonuniform electric field generated by the other particle. Two particles may attract or repel each other due to the dielectric force, depending on their positions in the nonuniform electric field. In this work, the dielectric interaction and the subsequent relative motion of the two arbitrarily oriented spherical particles are analyzed. The dielectric force is obtained by integrating the Maxwell stress. The result is valid for arbitrary orientations of the particles under the thin electrical-double-layer assumption. The magnitude of the dielectric force is compared to the so-called inertia-induced force, which shows that the dielectric force is normally much greater than the inertia-induced force. The relative velocity of particles is determined by the force balance between the dielectric force and the Stokes drag. The regions of attraction and repulsion are defined. It is shown that a pair of particles eventually aligns parallel to the externally applied electric field, except in the case where the two particles are initially oriented perpendicular to the electric field. A closed-form analytical solution is obtained for the particle trajectory by using the approximate expression for the dielectric force valid for not-too-closely located particles.     

Direct measurement of the viscous force between two spherical particles trapped in a thin wetting film

Here we present the first direct measurement of the viscous drag force between two spherical particles of millimeter size trapped in a thin wetting film. Each particle is constrained by the liquid/air interface and the solid substrate. The viscous force is counterbalanced by another known force, the attractive capillary immersion force between identical particles protruding from the film surface. The results of the measurements provide evidence for an increased hydrodynamic force due to a non-Stokesian resistance to the particle motion. Our findings can be applied to the self-assembly of colloidal particles in a two-dimensional array for coating and to the friction between small species and a solid. Received: 19 March 1999 Accepted in revised form: 11 May 1999     

Effects of pre-oxidation temperature on coal secondary spontaneous combustion

The hydrodynamic force (drag) on spherical and irregularly shaped particles significantly increases when the particles move close to solid and permeable boundaries. The overall effect of the increased hydrodynamic drag is to hinder the particle movement in the vicinity of boundaries and this includes the Brownian movement and electrophoresis. The Monte Carlo simulation method is used to model the Brownian movement, the resulting diffusion, and the electrophoresis of spherical particles in narrow, cylindrical pores, filled with Newtonian fluids. It is observed that the effect of the pore walls is a significant reduction of the space-averaged electrophoretic velocity of the particles, which implies reduced particle flux through the pores. The hindered electrophoresis is primarily a geometric phenomenon, caused by the increased drag and depends on the size of the particles and the pore-to-particle diameter ratio. The temperature of the fluid slightly affects the hindered electrophoresis through its effect on the viscosity, which is a determinant of the Brownian force, the diffusivity and the electrophoretic velocity. The hindered electrophoresis is almost independent of the other fluid and particle properties, such as density. Based on the simulation results a non-linear correlation for the flux of particles is derived, valid in the ranges 5?<?R/α?<?120, 5 nm?<?α?<?100 nm and 273 K?<?T?<?355 K.

     

Hydrodynamic permeability of a membrane composed of porous spherical particles in the presence of uniform magnetic field

This work concerns the flow of an incompressible viscous fluid past a porous sphere in presence of transverse applied uniform magnetic field, using particle-in-cell method. The Brinkman equations are used in porous region and the Stokes equations for non-porous region. At the fluid-porous interface, the stress jump boundary condition for tangential stresses along with continuity of normal stress and velocity components are used. Four known boundary conditions on the hypothetical surface are considered and compared: Happel’s, Kuwabara’s, Kvashnin’s and Cunningham’s (Mehta-Morse’s condition). The hydrodynamic drag force experienced by a porous spherical particle in a cell and hydrodynamic permeability of membrane built up by porous spherical particles are evaluated. The patterns of streamlines are also obtained and discussed. The effect of stress jump coefficient, Hartmann number, dimensionless specific permeability of the porous particle and particle volume fraction on the hydrodynamic permeability and streamlines are discussed. Some previous results for hydrodynamic drag force and dimensionless hydrodynamic permeability have been verified.     

Photocontrolled release and uptake of a porphyrin guest by dithienylethene-tethered beta-cyclodextrin host dimers

Two photoswitchable dithienylethene-tethered beta-cyclodextrin dimers were synthesized to function as host molecules with an externally controllable binding affinity. The cyclodextrin cavities of these dimers are linked through their secondary sides by a photochromic dithienylethene unit that is connected to the secondary rim either directly (4) or through propyl spacers (9). Irradiation with light switches these dimers between a relatively flexible (open) and a rigid (closed) form. The binding properties of the dimers depend on the configuration of the dithienylethene spacer, as is shown by microcalorimetry performed with tetrakis-sulfonatophenyl porphyrin (TSPP) as a guest molecule. The differences in binding properties are most pronounced for the more rigid dimer 4, which binds TSPP 35 times more strongly in the open form (4 a) than in the closed form (4 b). The values found for the enthalpy of binding (deltaH degrees ) indicate that this difference in binding is due to the loss of cooperativity between the two beta-cyclodextrin cavities in the closed form. Molecular modeling shows that 4 b is not able to bind TSPP effectively in both cyclodextrin cavities. The open and closed forms of the more flexible dimer 9 show no substantial difference in their binding of TSPP. Thermodynamic values indicative of strong binding of TSPP by two beta-cyclodextrin cavities were measured for both forms of the dimer, and molecular modeling confirms that both are flexible enough to tightly bind TSPP. The binding differences between the forms of dimer 4 allow the photocontrolled release and uptake of TSPP, which renders control of the ratio of complexed to free TSPP in solution possible.     

Electrokinetic motion of a charged colloidal sphere in a spherical cavity with magnetic fields

The magnetohydrodynamic (MHD) effects on the translation and rotation of a charged colloidal sphere situated at the center of a spherical cavity filled with an arbitrary electrolyte solution when a constant magnetic field is imposed are analyzed at the quasisteady state. The electric double layers adjacent to the solid surfaces may have an arbitrary thickness relative to the particle and cavity radii. Through the use of a perturbation method to the leading order, the Stokes equations modified with the electric∕Lorentz force term are dealt by using a generalized reciprocal theorem. Using the equilibrium double-layer potential distribution in the fluid phase from solving the linearized Poisson-Boltzmann equation, we obtain explicit formulas for the translational and angular velocities of the colloidal sphere produced by the MHD effects valid for all values of the particle-to-cavity size ratio. For the limiting case of an infinitely large cavity with an uncharged wall, our result reduces to the relevant solution for an unbounded spherical particle available in the literature. The boundary effect on the MHD motion of the spherical particle is a qualitatively and quantitatively sensible function of the parameters a∕b and κa, where a and b are the radii of the particle and cavity, respectively, and κ is the reciprocal of the Debye screening length. In general, the proximity of the cavity wall reduces the MHD migration but intensifies the MHD rotation of the particle.     

Electroviscous Forces on a Charged Cylinder Moving Near a Charged Wall

The refined theory of the electroviscous lift forces is presented for the case when the separation distance between the particle and the wall is larger than the double-layer thickness. The theory is based on the lubrication approximation for motion of a long cylinder near a solid wall in creeping flow. The approximate analytical formula for the lift force valid for Pe相似文献   

Force-driven migration of particles in ordered porous media

Brownian dynamics simulation has been employed to study the behavior of force-driven particle migration in different ordered porous media comprised of periodically interconnected spherical cavities, representing inverted colloidal crystals. The effects of the imposed field strength and direction on the particle mobility and direction are investigated. The simulation results find that in a weak or intermediate field, the mobility normalized by the value in free solvent behaves in a similar way as the normalized diffusivity when the porosity is varied. Under a strong field, the normalized mobility can increase or decrease with the field strength, depending on the field direction relative to the cavity arrangement. If the imposed field is not aligned with any unobstructed pathway, the mobility tensor may become anisotropic and prolonged particle entrapment may also take place.     

Structure of the mesoporous silica SBA-2, determined by a percolation analysis of adsorption

We have carried out a percolation analysis of the adsorption of ethane and nitrogen in SBA-2, a structured mesoporous silica consisting of a hexagonal close-packed (hcp) array of spherical cavities connected by cylindrical channels. Our analysis explains the different uptakes of nitrogen and ethane in terms of the greater accessibility of the network to the smaller nitrogen molecule. The analysis also allows us to quantify the connectivity of the SBA-2 pore network. The effective coordination number of the cavities, defined as the average number of channels per cavity that are large enough to allow nitrogen to pass, is 4.9, much less than the theoretical maximum value of 12. Taking into account only the smaller set of channels large enough to admit ethane, the effective coordination number is 1.8, just above the percolation threshold of the network.     

Scaled particle theory for hard sphere pairs. I. Mathematical structure

We develop an extension of the original Reiss-Frisch-Lebowitz scaled particle theory that can serve as a predictive method for the hard sphere pair correlation function g(r). The reversible cavity creation work is analyzed both for a single spherical cavity of arbitrary size, as well as for a pair of identical such spherical cavities with variable center-to-center separation. These quantities lead directly to a prediction of g(r). Smooth connection conditions have been identified between the small-cavity situation where the work can be exactly and completely expressed in terms of g(r), and the large-cavity regime where macroscopic properties become relevant. Closure conditions emerge which produce a nonlinear integral equation that must be satisfied by the pair correlation function. This integral equation has a structure which straightforwardly generates a solution that is a power series in density. The results of this series replicate the exact second and third virial coefficients for the hard sphere system via the contact value of the pair correlation function. The predicted fourth virial coefficient is approximately 0.6% lower than the known exact value. Detailed numerical analysis of the nonlinear integral equation has been deferred to the subsequent paper.     

Polycationic‐Shelled Capsular and Tubular Nanostructures and Their Anionic–Guest Binding Properties

For the development of novel nanospace with unique electrostatic character, we prepared new capsular and tubular nanostructures by the quantitative assembly of metal ions and bent bisacridinium ligands. The capsule and tube have closed spherical and open cylindrical cavities, respectively, with diameters of around 1 nm surrounded by cationic polyaromatic panels. Thanks to the facile synthetic protocol (three steps), another polycationic capsule with an elliptical nanocavity was also prepared by using an elongated ligand. In spite of the absence of pendant hydrophilic groups, the spherical polyaromatic capsule shows sufficient water solubility due to the polycationic shell. Moreover, the highly cationic cavity (12+) can selectively encapsulate anionic organic compounds in water.     

Mobility matrix of a spherical particle translating and rotating in a viscous fluid confined in a spherical cell, and the rate of escape from the cell

The mobility matrix of a spherical particle moving in a spherical cavity, filled with a viscous incompressible fluid, and with no-slip boundary condition at the wall of the cavity, is evaluated from the Oseen tensor for the cavity by the method used by Lorentz for a particle near a planar wall. For the case that the particle is a rigid sphere with no-slip boundary condition the comparison with exact calculations shows that the approximation is quite accurate, provided the radius of the particle is small relative to that of the cavity, and provided the particle is not too close to the wall. The translational mobility is used to derive the diffusion tensor of a Brownian particle via an Einstein relation. The approximate result for the diffusion tensor is employed to estimate the rate of escape of a Brownian particle from a cavity with semipermeable wall.     

Electrophoresis of a charge-regulated sphere at an arbitrary position in a charged spherical cavity

The electrophoresis of a charge-regulated spherical particle at an arbitrary position in a charged spherical cavity is modeled under conditions of low surface potential (<25 mV) and weak applied electric field (<25 kV/m). The charged cavity allows us to simulate the effect of electroosmotic flow, and the charge-regulated nature of the particle permits us to model various types of surface. The problem studied previously is reanalyzed based on a more rigorous electric force formula. In particular, the influences of various types of charged conditions on the electrophoretic behavior of a particle and the roles of all the relevant forces acting on the particle are examined in detail. Several new results are found. For instance, the mobility of a particle has a local minimum as the thickness of a double layer varies, which is not seen in the cases where the surface of a particle is maintained at a constant potential and at a constant charge density.     

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.     

Software for localization and visualization of cavities in crystal structures and supramolecular assemblies

This paper describes the CAVITY software for a personal computer (AT/XT). The software is designed for seeking interstices, channels, and cavities in structures, calculating the volumes of closed cavities, constructing cross sections of cavities by the planes given by the crystallographic indices hkl or by the coordinates of points lying in the planes. The cavities and their cross sections may be visualized and stored as graphical files. The program calculates the distances between any points on the “cavity walls” and inside or outside the cavity as well as the nearest environment for any point inside the cavity. The data are input as a SHELX or ASCII file with Cartesian atomic coordinates.