Bidisperse electrorheological fluids using hydrolyzed styrene-acrylonitrile copolymer particles: synergistic effect of mixed particle size

Monodisperse micron-sized styrene-acrylonitrile copolymer (SAN) particles with three different sizes (about 5, 10, and 15 microm) were prepared by a two-step seeded polymerization and used for a study of bidisperse electrorheological (ER) suspensions. The effect of the particle size and the size-mixing fraction on ER properties was studied with varying the size of these monodisperse copolymer particles. When the two particle sizes were mixed, the suspension generally showed a decrease in the shear yield stress, reaching a minimum value. However, a bidisperse ER suspension of large particles containing a small fraction of fine particles showed an interesting synergy effect of size mixing on ER response, giving enhanced yield stresses over the other size-mixing fractions. This synergistic ER suspension also showed a great increase in the viscoelastic property. The current density of suspensions was maximum at the synergistic bidisperse suspension. This synergy effect in a particular bidisperse suspension was investigated in view of the structure model consideration and was concluded to be due to a close packing and a peculiar structural ordering at an optimum size ratio and mixing fraction.     

Effects of particle size segregation on crossflow microfiltration performance: Control mechanism for concentration polarisation and particle fractionation

Although the principal mechanisms of crossflow microfiltration (MF) are well-known, the practical applicability of the resulting microfiltration models is still limited. This can be largely attributed to the lack of understanding of effects of polydispersity in the particulate suspensions, as relevant to concentration polarisation in MF. This paper describes an investigation of concentration polarisation behaviour of bidisperse suspensions, in the regime where shear-induced diffusion is the dominant back-transport mechanism. In the transient flux regime, the particle deposition onto the membrane was monitored by means of confocal scanning laser microscopy. As in accordance with the linear dependence of the shear-induced diffusivity on a², only the small particles in the bidisperse suspensions were found to deposit onto the membrane. The back-transport flux that was calculated from the deposition rate and the actual permeate flux, was found to be independent of the composition of the suspension, whereas it was equal to the back-transport flux of a monodisperse suspension of the small particles only, with a similar total particle fraction. These results can be explained with the occurrence of particle size segregation in the feed flow, which leads to an enrichment with small particles of the suspension near the membrane. The findings are also shown to be relevant to particle fractionation processes by MF. In such fractionation processes, particle size segregation is found to have a strong effect on the separation characteristics such as particle size and fat content of the permeate. A polydisperse suspension could be fractionated using a membrane having a pore size larger than the largest particles present. The fractionation thus results not from size exclusion in the membrane, but from segregation effects in the feed channel.     

Wall-retardation effects on particles settling through non-Newtonian fluids in parallel plates

Walls can exert a retardation effect on particles settling in bounded fluid media. In this work, the parallel plate retardation effect was studied for particles falling in non-Newtonian fluids along the centreline of parallel plate ducts. The eccentric effect was also investigated for those particles which approached the wall. For spheres settling in sodium carboxymethylcellulose (CMC) solutions, the variation in wall factors against the size ratio of the sphere’s diameter to the parallel plate wall spacing shows a non-linear trend; the particle settling velocity is independent at small size ratio, and then decreases quickly with increase in size ratio. A new correlation was presented covering a wider range of size ratios (0.02 < λ < 0.83) in the flow region of 0.0011 < Re < 9.75. When particles settle in polyacrylamide solutions, the fluid elasticity reduces the wall-retardation effect and it can be deduced that the drag reduction mechanism of some polyacrylamide solutions may weaken the wall retardation effect. As the spheres settling in the CMC solutions approach the wall, the neighbouring wall exerts no retardation effect at small size ratios (≤ 0.8). Then the settling velocity reduces sharply, while the effect is negligible for polyacrylamide solutions. In comparison with cylinders, the actuating range of the neighbouring wall is smaller for parallel plates.     

Effect of small particles on the near-wall dynamics of a large particle in a highly bidisperse colloidal solution

We consider the hydrodynamic effect of small particles on the dynamics of a much larger particle moving normal to a planar wall in a highly bidisperse dilute colloidal suspension of spheres. The gap h(0) between the large particle and the wall is assumed to be comparable to the diameter 2a of the smaller particles so there is a length-scale separation between the gap width h(0) and the radius of the large particle b>h(0). We use this length-scale separation to develop a new lubrication theory which takes into account the presence of the smaller particles in the space between the larger particle and the wall. The hydrodynamic effect of the small particles on the motion of the large particle is characterized by the short time (or high frequency) resistance coefficient. We find that for small particle-wall separations h(0), the resistance coefficient tends to the asymptotic value corresponding to the large particle moving in a clear suspending fluid. For h(0)>a, the resistance coefficient approaches the lubrication value corresponding to a particle moving in a fluid with the effective viscosity given by the Einstein formula.     

Sedimentation velocity and potential in concentrated suspensions of charged porous spheres

The body-force-driven migration in a homogeneous suspension of polyelectrolyte molecules or charged flocs in an electrolyte solution is analyzed. The model used for the particle is a porous sphere in which the density of the hydrodynamic frictional segments, and therefore also that of the fixed charges, is constant. The effects of particle interactions are taken into account by employing a unit cell model. The overlap of the electric double layers of adjacent particles is allowed and the relaxation effect in the double layer surrounding each particle is considered. The electrokinetic equations which govern the electrostatic potential profile, the ionic concentration (or electrochemical potential energy) distributions, and the fluid velocity field inside and outside the porous particle in a unit cell are linearized by assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved for a symmetrically charged electrolyte with the density of the fixed charges as the small perturbation parameter. An analytical expression for the settling velocity of the charged porous sphere is obtained from a balance among its gravitational, electrostatic, and hydrodynamic forces. A closed-form formula for the sedimentation potential in a suspension of identical charged porous spheres is also derived by using the requirement of zero net electric current. The dependence of the sedimentation velocity and potential of the suspension on the particle volume fraction and other properties of the particle-solution system is found to be quite complicated.     

Sedimentation Velocity and Potential in Concentrated Suspensions of Charged Spheres with Arbitrary Double-Layer Thickness

The sedimentation in a homogeneous suspension of charged spherical particles with an arbitrary thickness of the electric double layers is analytically studied. The effects of particle interactions are taken into account by employing a unit cell model. Overlap of the double layers of adjacent particles is allowed, and the polarization effect in the double layer surrounding each particle is considered. The electrokinetic equations that govern the ionic concentration distributions, the electric potential profile, and the fluid flow field in the electrolyte solution in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved for a symmetrically charged electrolyte with the surface charge density (or zeta potential) of the particle as the small perturbation parameter. An analytical expression for the settling velocity of the charged sphere in closed form is obtained from a balance among its gravitational, electrostatic, and hydrodynamic forces. A closed-form formula for the sedimentation potential in a suspension of identical charged spheres is also derived by using the requirement of zero net electric current. Our results demonstrate that the effects of overlapping double layers are quite significant, even for the case of thin double layers. Copyright 2000 Academic Press.     

Particle Interactions in Diffusiophoresis and Electrophoresis of Colloidal Spheres with Thin but Polarized Double Layers

The diffusiophoretic and electrophoretic motions of two colloidal spheres in the solution of a symmetrically charged electrolyte are analyzed using a method of reflections. The particles are oriented arbitrarily with respect to the electrolyte gradient or the electric field, and they are allowed to differ in radius and in zeta potential. The thickness of the electric double layers surrounding the particles is assumed to be small relative to the radius of each particle and to the gap width between the particles, but the effect of polarization of the mobile ions in the diffuse layer is taken into account. A slip velocity of fluid and normal fluxes of solute ions at the outer edge of the thin double layer are used as the boundary conditions for the fluid phase outside the double layers. The method of reflections is based on an analysis of the electrochemical potential and fluid velocity disturbances produced by a single dielectric sphere placed in an arbitrarily varying electrolyte gradient or electric field. The solution for two-sphere interactions is obtained in expansion form correct to O(r(12)(-7)), where r(12) is the distance between the particle centers. Our analytical results are found to be in good agreement with the available numerical solutions obtained using a boundary collocation method. On the basis of a model of statistical mechanics, the results of two-sphere interactions are used to analytically determine the first-order effect of the volume fraction of particles of each type on the mean diffusiophoretic and eletrophoretic velocities in a bounded suspension. For a suspension of identical spheres, the mean diffusiophoretic velocity can be decreased or increased as the volume fraction of the particles is increased, while the mean electrophoretic velocity is reduced with the increase in the particle concentration. Generally speaking, the particle interaction effects can be quite significant in typical situations. Copyright 2000 Academic Press.     

Startup of electrophoresis in a suspension of colloidal spheres

The transient electrophoretic response of a homogeneous suspension of spherical particles to the step application of an electric field is analyzed. The electric double layer encompassing each particle is assumed to be thin but finite, and the effect of dynamic electroosmosis within it is incorporated. The momentum equation for the fluid outside the double layers is solved through the use of a unit cell model. Closed‐form formulas for the time‐evolving electrophoretic and settling velocities of the particles in the Laplace transform are obtained in terms of the electrokinetic radius, relative mass density, and volume fraction of the particles. The time scale for the development of electrophoresis and sedimentation is significantly smaller for a suspension with a higher particle volume fraction or a smaller particle‐to‐fluid density ratio, and the electrophoretic mobility at any instant increases with an increase in the electrokinetic particle radius. The transient electrophoretic mobility is a decreasing function of the particle volume fraction if the particle‐to‐fluid density ratio is relatively small, but it may increase with an increase in the particle volume fraction if this density ratio is relatively large. The particle interaction effect in a suspension on the transient electrophoresis is much weaker than that on the transient sedimentation of the particles.     

Rigorous calculations of linearized Poisson-Boltzmann interaction between dissimilar spherical colloids and osmotic pressure in concentrated dispersions

We present computational results on the static properties of concentrated dispersions of bidisperse colloids. The long-range electrostatic interactions between dissimilar spherical colloids are determined using the singularity method, which provides rigorous solutions to the linearized electrostatic field. The NVT Monte Carlo simulation is applied to the bulk suspension to obtain the radial distribution function for the concentrated system. The increasing trend of osmotic pressure with increasing total particle concentration is reduced as the concentration ratio between large and small particles is increased. The increase of electrostatic interaction between similarly charged particles caused by the Debye screening effect provides an increase in the osmotic pressure. From the estimation of total structure factor, we observe the strong correlations developed between dissimilar spheres, and the small spheres are expected to tend to fit into the spaces between the larger ones. As the particle concentration increases at a given ionic strength, the magnitude of the first peak in structure factors increases and also moves to higher wavenumber values.     

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.     

Taylor dispersion in systems of sedimenting nonspherical Brownian particles : II. Homogeneous ellipsoidal particles

An Aris-type moment scheme is applied to calculate the Taylor-Aris dispersion tensor for the sedimentation of small homogeneous ellipsoidal (and other orthotropic) particles settling under the influence of gravity in a quiescent viscous fluid and undergoing rotational and translational Brownian motions. This generalizes to triaxial particles a prior dispersion result for centrally symmetric bodies of revolution, such as spheroids. An independent Langevin-type dispersivity calculation is shown to yield results identical to those obtained by the moment scheme. The components and of the transversely isotropic dispersion dyadic, parallel and perpendicular, respectively, to the direction of the gravitational field, are shown to be given by the Taylor—Aris-type formulasHere, is the mean settling velocity of the particle, and and

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and (d₁,d₂,d₃) respectively the appropriate diffusivity components along the principal axes of the particle. The dimensionless coefficient γ, which is of order unity, is given by the formulaThis anisometric parameter vanishes identically for spherical particles and other hydrodynamically isotropic particles (e.g., cubes, tetrahedra, octahedra, etc.) whose translational and rotational hydrodynamic resistances are independent of the orientation of the particle relative to the directions of its linear and angular velocity vectors. Upon utilizing the translational and rotational Stokes-Einstein equations, explicit numerical values of and are furnished for ellipsoids of revolution of various aspect ratios and sizes when settling in water. Physical restrictions pertaining to sedimentation-vessel apparatus size and the requirement of reasonable sedimentation times greatly restrict the range of particle sizes whose anisometric properties may be experimentally investigated by this new particle-shape characterization technique.     

Effective velocity and effective dispersion coefficient for finite-sized particles flowing in a uniform fracture

In this work we derive expressions for the effective velocity and effective dispersion coefficient for finite-sized spherical particles with neutral buoyancy flowing within a water saturated fracture. We considered the miscible displacement of a fluid initially free of particles by another fluid containing particles of finite size in suspension within a fracture formed by two semi-infinite parallel plates. Particle spreading occurs due to the combined actions of molecular diffusion and the dispersive effect of the Poiseuille velocity profile. Unlike Taylor dispersion, here the finite size of the particles is taken into account. It is shown that because the finite size of a particle excludes it from the slowest moving portion of the velocity profile, the effective particle velocity is increased, while the overall particle dispersion is reduced. A similar derivation applied to particles flowing in uniform tubes yields analogous results. The effective velocity and dispersion coefficient derived in this work for particle transport in fractures with uniform aperture are unique and ideally suited for use in particle tracking models.     

Surface Potential of Coal Particles in Coal-Oil Mixture and Control of Settling Stability Under Gravity

This work deals with the problem of settling under gravity for coal-oil mixtures when the concentration of particles is large. The repulsive force necessary to ensure stability of coal particle is vital. The net forces acting on the particle include gravity, buoyancy, viscous drag force, and electrostatic repulsive force. Accordingly, the equation at the terminal velocity at settling is obtained along with a critical surface potential to prevent settling under gravity.     

Particle interactions in electrophoresis due to inertia

The inertial forces acting on two cylinders and two spheres have been calculated. The cylinders or spheres are of the same radius and zeta potential, and arbitrarily oriented in an electric field. It is found that when two particles are aligned perpendicular to the direction of the electric field, the force between them along the line of the centers is attractive. When they are along the direction of the electric field, the force between them along the line of the centers is repulsive. On a pair of arbitrarily oriented particles, the force perpendicular to the line of the centers tends to rotate the particles around the midpoint between the particle centers such that the pair is aligned normal to the applied electric field. The stable equilibrium orientation of a pair of particles and the attractive interaction forces between the particles when they are stably orientated may give rise to aggregation of particles during electrophoretic motion of a suspension.     

Numerical Modeling in Radio Frequency Suspension Plasma Spray of Zirconia Powders

A comprehensive model was developed to investigate the suspension spraying for a radio frequency (RF) inductively coupled plasma torch. Firstly, the electromagnetic field is solved with the Maxwell equations and validated by the analytical solutions. Secondly, the plasma field with different power inputs is simulated by solving the governing equations of the fluid flow coupled with the RF heating. Then, the suspension droplets embedded with nano particles are modeled in a Lagrangian manner, considering feeding, collision, heating and evaporation of the suspension droplets, as well as tracking, acceleration, melting and evaporation of the nano or agglomerate particles. The non-continuum effects and the influence of the evaporation on the heat transfer are considered. This particle model predicts the trajectory, velocity, temperature and size of the in-flight nano- or agglomerate particles. The effects of operating conditions and intial inputs on the particle characteristics are investigated. The statistical distributions of multiple particles’ size, velocity, temperature are also discussed for the cases with and without consideration of suspension droplets collision.     

Diffusiophoresis in a concentrated suspension of colloidal spheres in nonelectrolyte gradients

The diffusiophoretic motion of a homogeneous suspension of identical spherical particles is considered under conditions of small Reynolds and Peclet numbers. The effects of interaction of the individual particles are taken into explicit account by employing a unit cell model which is known to provide good predictions for the sedimentation of monodisperse suspensions of spherical particles. The appropriate equations of conservation of mass and momentum are solved for each cell, in which a spherical particle is envisaged to be surrounded by a concentric shell of suspending fluid, and the diffusiophoretic velocity of the particle is calculated for various cases. Analytical expressions of this mean particle velocity are obtained in closed form as functions of the volume fraction of the particles. Comparisons between the ensemble-averaged diffusiophoretic velocity of a test particle in a dilute suspension and our cell-model results are made. Received: 30 June 1999 Accepted: 8 December 1999     

悬浮-乳液复合聚合聚苯乙烯-聚甲基丙烯酸甲酯复合粒子的颗粒特性和成粒机理

采用在苯乙烯 (St)悬浮聚合过程中滴加甲基丙烯酸甲酯 (MMA)乳液聚合组分的悬浮 乳液复合聚合方法 ,制备大粒径聚苯乙烯 聚甲基丙烯酸甲酯 (PS PMMA)复合粒子 .研究聚合物粒径分布和颗粒形态的变化发现 ,在St悬浮反应中期滴加MMA乳液聚合组分后 ,聚合体系逐渐由悬浮粒子与乳胶粒子并存向形成单峰分布复合粒子转变 ,最终形成核 壳结构完整的大粒径PS PMMA复合粒子 ;在St悬浮反应初期滴加MMA乳液聚合组分 ,St与MMA一起分散成更小液滴 ,反应后期凝并成非核 壳结构复合粒子 ;在St悬浮反应后期滴加MMA乳液聚合组分 ,PMMA乳胶粒子与PS悬浮粒子基本独立存在 .根据以上结果 ,提出了St MMA悬浮 乳液复合聚合的成粒机理 .     

Diffusiophoresis in a suspension of spherical particles with arbitrary double-layer thickness

The diffusiophoresis in a homogeneous suspension of identical dielectric spheres with an arbitrary thickness of the electric double layers in a solution of a symmetrically charged electrolyte with a constant imposed concentration gradient is analytically studied. The effects of particle interactions (or particle volume fraction) are taken into account by employing a unit cell model, and the overlap of the double layers of adjacent particles is allowed. The electrokinetic equations that govern the ionic concentration distributions, the electrostatic potential profile, and the fluid flow field in the electrolyte solution surrounding the charged sphere in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Using a perturbation method, these linearized equations are solved with the surface charge density (or zeta potential) of the particle as the small perturbation parameter. Analytical expressions for the diffusiophoretic velocity of the dielectric sphere in closed form correct to the second order of its surface charge density or zeta potential are obtained from a balance between its electrostatic and hydrodynamic forces. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made.     

Modeling Elastic Pore Sensors for Quantitative Single Particle Sizing

An empirically derived model of how the dimensions of an elastic size-tunable pore sensor change with applied membrane stretch is presented. Quantitative modeling of the pore dimensions, in conjugation with a simplified pore resistance model, enabled particle size and translocation velocity profiles to be calculated from the individual particle 'pulse' events, at any membrane stretch. Size analysis of a trimodal suspension, composed of monodisperse 220, 330 and 410 nm particles, gave rise to 3 distinguishable particle peaks with coefficient of variances below 8.2% and average size values within 2.5% of single modal dynamic light scattering measurements. Particle translocation velocity profiles, over the approximate 12 μm pore sensing zone, showed that particles entering the small pore were initially accelerated to velocities approaching 5,000 to 6,000 μm/s. They then rapidly decelerated due to the pore geometry affects on the forces driving particle translocation, being the electric field strength and fluid flow.