Effect Of Particle Interactions Research Articles

High-shear granulation modeling using a discrete element simulation approach

This work develops a method for prediction of dynamic changes in particle size distributions (PSD) of high-shear granulation systems using a discrete element simulation technique. This method allows for direct evaluation of particle interactions based on multi-dimensional descriptions of particle parameters. Pouw et al. [38] [G.A. Pouw, D. Verkoeijen, G.M.H. Meesters, B. Scarlett, Population balances for particulate processes—a volume approach. Chemical Engineering Science 57 (2002) 2287–2303] proposed the use of a volume-based Population Balance Equation (PBE) model with the volume of solid, liquid, and gas in each particle as internal parameters to predict result of particle interactions. This paper extends on the work of Pouw et al. by using a discrete element simulation approach rather than direct application of population balance equations to determine the evolution of particle size distributions. This is accomplished by simulating the effects of particle interactions based on physically significant coalescence criteria. Three granule modification mechanisms are used in the proposed method: coalescence, consolidation, and breakage. Two types of coalescence are modeled in this simulation. In Type I coalescence, granules are stopped solely by viscous dissipation of the binder layer before the granule solid surfaces touch, whereas Type II coalescence occurs when deformable granules come into contact with their solid surfaces and the granule surfaces then bind together. Consolidation, the escape of air from granules due to compaction following collisions, is described by an exponential relationship related to the porosity of each individual simulated particle. One may assume that breakage will occur when there is sufficient externally applied kinetic energy to deform and shear a granule. Breakage can be determined based on whether the Stokes deformation number for a particle exceeds a critical value. One objective of this work is to move toward modeling and simulation methods that allow for dynamic changes in operating conditions at any time in a batch run. Current empirically based coalescence kernels used in population balance based models are generally developed using static operating conditions, limiting the model validity for online control applications. The main contribution of this work lies in the observation that when using this type of simulation model, the physics of the granulation system can be altered more easily than modeling the granulation process using traditional population balance. Systems exhibiting a wide range of yield strength can be modeled to determine boundaries for Type I coalescence, Type II coalescence, or rebound events based on physical arguments rather than extrapolation of empirically based coalescence kernels. Using similar initial and operating conditions, the discrete element simulation is shown to produce results similar to population balance results. To examine the extended flexibility of the new modeling method, several open-loop simulations using this method are presented in this paper to display how a process would dynamically react to changes in operating conditions.

Biocompatible superparamagnetic iron oxide nanoparticles used for contrast agents: a structural and magnetic study

The magnetic properties of different biocompatible magnetic iron oxide nanoparticles (MION) are presented. Dextran-coated, magnetite (Fe 3O 4) MIONs were studied as supplied and after lyophilization, to disentangle the effects of particle interactions. All samples showed superparamagnetic behavior at room temperature, with blocking transitions at T B∼40–56 K (at 100 Oe), depending on the particle interactions. The dynamics of the thermally activated blocking process reveals that the effect of dipolar interactions is to increase the energy barriers of the individual particles.

Flow properties of hard structured particle suspensions

A class of structured particles is developed such that the effects of particle interactions are adjusted enabling suspension mechanics to be studied without the influence of interparticle forces other than volume exclusion, Brownian and hydrodynamic interactions. Three grades of these near-hard structured particles are developed from fumed silica. These particles have the same structure as measured by the mass fractal dimension. Stress dependent viscosities and diffusivity measurements are reported as a function of particle concentration, providing an opportunity to determine the scaling behavior of these properties with the two characteristic sizes: the primary particle and aggregate sizes. Except at stresses exceeding the critical value demarking the onset of shear thickening, flow curves superimposed with each other and with hard sphere suspensions compared at the same effective packing fraction, φ/φm.

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.

Continuum modelling of transformation hysteresis in a metal hydride system

Charging many metal films or powders with hydrogen results in the growth of second-phase metal hydride particles. A large volume difference between hydride and metal can induce plastic deformation and result in a significant hysteresis upon removal of the hydrogen. For a palladium hydride system (with an 11% volume change), we estimate this hysteresis with calculations of the elastic and plastic works of multiple forward and reverse transformations using a two-dimensional finite-element model and find reasonable agreement between finite-element estimates and experimental observations. We also use a three-dimensional phase-field model to determine the effects of particle interactions, but for the isotropic dilation in the Pd/PdH system, these interactions do not apparently have a significant effect.

Thermodiffusion of interacting colloids. I. A statistical thermodynamics approach.

The thermal diffusion coefficient of colloids consists of two additive contributions, one related to specific interactions between the surfaces of colloidal particles with solvent molecules, and a contribution due to interactions between the colloidal particles. In the present paper, the effect of intercolloidal particle interactions on their thermodiffusive behavior is discussed within a statistical thermodynamics framework. Transport coefficients are expressed in terms of the interaction potential between the colloidal spheres. A special feature of macromolecular systems is that this interaction potential is a potential of mean force, which is temperature dependent. It is shown that under certain conditions this implicit temperature dependence gives rise to negative Soret coefficients, that is, to diffusion of macromolecules to hot regions.

Effect of particle interactions on sedimentation field-flow fractionation of a binary suspension

The effect of particle interactions on sedimentation field-flow fractionation of a binary suspension is studied on the basis of a phenomenological model. The solvent fluid is regarded as a background medium mediating the effective interactions between solute particles. A binary suspension with large and small particles is considered. Equilibrium profiles of both species are calculated from an approximate expression for the Helmholtz free energy of a hard sphere mixture. The effect of solute particles on suspension viscosity is taken into account via a semi-empirical relationship. It is found that retention factors of both species depend strongly on the two mean volume fractions. The ratio of the two retention factors is nearly independent of the concentration of the large particles and first decreases, but then increases significantly with the concentration of the small ones.

The effect of particle interactions on the sedimentation process of non-cohesive particles

The sedimentation process of solid particles in a two-dimensional channel with an initially homogeneous, square configuration is numerically investigated at Reynolds numbers up to 10. The Lattice Boltzmann method is used to simulate the hydrodynamic interactions between fluid and particles. During the process the dispersion of particles in the horizontal direction fluctuates around zero, while the dispersion in the vertical direction (along the gravity direction) increases almost linearly. The increasing rate heavily depends on the initial symmetry of the suspension. The simulations show that the process of sedimentation encompasses three stages. In the first stage, the initial particle configuration plays a major role on the average velocity of the particles. A V-shape or W-shape front may be formed by the particles. During the second stage, the concentration is lower, strong particles interactions occur and the formation and destruction of particle clusters play a major role in the process. The sedimentation velocity depends to a large extent on the number of clusters formed and the velocity field developed. During the third stage, the concentration becomes low and the particle clusters are stable. The wakes generated by particle and clusters, especially of the leading cluster becomes important in the process. Average and fluctuation velocity have been obtained in the simulations and are reported in this paper.

Collective diffusion and self-diffusion coefficients comparison to separate interactions and micellar size effects on ionic micelle diffusivities: Cylindrical micelles of sodium taurodeoxycholate

Collective and self-diffusion coefficients of sodium taurodeoxycholate (NaTDC) and taurocholate (NaTC) D2O micellar solutions were measured, as a function of ionic strength (0–0.6 M NaCl added) and bile salt concentration, by means of quasielastic light-scattering and 1H pulse-gradient-spin-echo nuclear magnetic resonance measurements. A data analysis, performed by using a simple model of monodisperse Brownian particles with hydrodynamic interaction and hard-core repulsion, allowed us to separate the effect of micellar size and particle interactions at low ionic strength. An estimation of the hydrodynamic radius and of the Debye–Hückel interaction strength was obtained without extrapolating the data to the critical micellar concentration. A discussion based on a hard-body interacting cylinder model suggests that attractive interactions influence the NaTDC diffusivities at high NaCl concentration. With respect to NaTC, at the same ionic strength, greater effective charge and size characterize the NaTDC micellar aggregates that, moreover, show a more extended growth as a function of NaCl and bile salt concentration.

Exponential formula for computing effective viscosity

An exponential model is proposed for evaluating the effective viscosity of a particle–fluid mixture. First, theoretical consideration is restricted to the dilute condition without effects of dynamic particle interactions and fluid turbulence. This leads to a power series expressed in terms of particle concentration, which can be viewed as an extension of the Einstein's formula. The derivation is then extended using an exponential model for the condition of high particle concentrations. The exponential formula obtained, which is not subjected to the maximum particle concentration, is found comparable to various empirical formulas available in the literature.

Electric conductivity of a suspension of charged colloidal spheres with thin but polarized double layers

An analytical study of the effective electric conductivity of a homogeneous suspension of identical, charged, spherical particles in the solution of a symmetrically charged electrolyte is presented. 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 two neighboring particles, but the effect of polarization of the mobile ions in the diffuse layer is taken into account. The effects of interactions among individual particles are taken into explicit account by employing a unit cell model that is known to provide good predictions for the sedimentation of monodisperse suspensions of spherical particles. The appropriate equations of conservation of electrochemical potential energies of ionic species are solved for each cell, in which a spherical particle is envisaged as surrounded by a concentric shell of the suspending fluid. Analytical expressions for the electric conductivity are obtained in closed form as functions of the volume fraction of the particles and other characteristics of the suspension. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made. The effects of particle interactions on the effective conductivity can be quite significant in general cases.

Electrophoretic Mobility and Electric Conductivity of Suspensions of Charge-Regulating Colloidal Spheres

An analytical study of electrophoresis and electric conduction in a monodisperse suspension of spherical charge-regulating particles with an arbitrary thickness of the electric double layers is presented. The charge regulation due to association/dissociation reactions of ionogenic functional groups on the particle surface is approximated by a linearized regulation model, which specifies a linear relationship between the surface charge density and the surface potential. The effects of particle interactions 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 electric potential profile, the ionic concentration distributions, and the fluid flow field in the electrolyte solution surrounding the particle in a unit cell are linearized assuming that the system is only slightly distorted from equilibrium. Using a regular perturbation method, these linearized equations are solved with the equilibri...

Thermophoretic interactions of aerosol particles with constant temperatures

This paper presents an analytical study of the thermophoretic motion of two free aerosol spheres with constant temperatures by using a method of reflections. The particles are allowed to differ in radius, in temperature, and in surface properties. The Knudsen numbers are assumed small so that a continuum model describes the fluid flow with a thermal creep and a hydrodynamic slip at the particle surfaces. The method of reflections is based on an analysis of the thermal and hydrodynamic disturbances produced by a single sphere with constant temperature placed in an arbitrarily varying temperature field. The results for two-sphere interactions are correct to O( r 12 −7), where r 12 is the distance between the particle centers. For the special situation of two identical spheres, the effect of particle interactions will drive the pair system approaching each other if the particle temperature is less than the temperature of the surrounding. While the temperature of the particles is higher than the surrounding temperature, the thermophoretic force obtains a repulsive effect between the particles. Based on a microscopic model the results for two-particle interactions are applied to find the effect of particle concentration on the average thermophoretic velocity in a bounded suspension. In general, the effect of interactions on thermophoretic coagulation of particles with constant temperatures can be stronger than that on sedimentation.

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.

Low‐frequency oscillations and transport processes induced by multiscale transverse structures in the polar wind outflow: A three‐dimensional simulation

Multiscale transverse structures in the magnetic‐field‐aligned flows have been frequently observed in the auroral region by FAST and Freja satellites. A number of multiscale processes, such as broadband low‐frequency oscillations and various cross‐field transport effects are well correlated with these structures. To study these effects, we have used our three‐dimensional multifluid model with multiscale transverse inhomogeneities in the initial velocity profile. Self‐consistent generation of the low‐frequency mode driven by local transverse gradients in the field‐aligned ion flow and associated transport processes were simulated. Effects of particle interaction with the self‐consistent time‐dependent three‐dimensional wave potential have been modeled using a distribution of test particles. For typical polar wind conditions it has been found that even large‐scale (∼ 50 – 100 km) transverse inhomogeneities in the flow can generate low‐frequency oscillations that lead to significant flow modifications, cross‐field particle diffusion, and other transport effects. It has also been shown that even small‐amplitude (∼ 10 – 20%) short‐scale (∼ 10 km) modulations of the original large‐scale flow profile significantly increases low‐frequency mode generation and associated cross‐field transport, not only at the local spatial scales imposed by the modulations but also on global scales. Note that this wave‐induced cross‐field transport is not included in any of the global numerical models of the ionosphere, ionosphere‐thermosphere, or ionosphere‐polar wind. The simulation results indicate that the wave‐induced cross‐field transport not only affects the ion outflow rates but also leads to a significant broadening of particle phase‐space distribution and tranverse particle diffusion.

Sedimentation Velocity and Potential in a Suspension of Charge-Regulating Colloidal Spheres

Body-force-driven migration in a homogeneous suspension of spherical charge-regulating particles with electrical double layers of arbitrary thickness is analyzed. The charge regulation due to association/dissociation reactions of functional groups on the particle surface is approximated by a linearized regulation model, which specifies a linear relationship between the surface-charge density and the surface potential. The effects of particle interactions are taken into account by employing a unit cell model. The overlap of the 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 ionic concentration distributions, the electrostatic 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 regular perturbation method, these linearized equations are solved for a symmetrically charged electrolyte with the equilibrium surface potential of the particle as the small perturbation parameter. Closed-form formulas for the settling velocity of the charge-regulating spheres and for the sedimentation potential in the suspension are derived. Our results show that the charge regulation effects on the sedimentation in a suspension appear starting from the leading order of the equilibrium surface potential, which is determined by the regulation characteristics of the suspension.

Approach for Particle Sizing in Dense Polydisperse Colloidal Suspension Using Multiple Scattered Light

Direct particle sizing of colloidal suspensions at high solid concentrations is difficult due to confounding effects of multiple scattering and particle interactions. In this work, the frequency domain photon migration (FDPM) technique, based upon multiple light scattering, is extended for particle sizing of colloidal suspensions at high volume fractions by combining an appropriate model to account for particle interactions. FDPM measurements of isotropic scattering coefficients were conducted to assess the effect of particle interactions of polydisperse polystyrene samples at high volume fractions ranging from 1% to 40%. The isotropic scattering coefficients were then compared with the theoretical predictions which include the full polydisperse hard sphere Percus−Yevick (HSPY) model as well as the decoupling approximation and the local monodisperse approximation models to account for excluded volume effects. Results show that the polydisperse HSPY model is suitable for accounting for particle interactions which predominately arise from volume exclusion effects and which influence light scattering. Upon use of the polydisperse HSPY model to predict static structure factors, the particle size distribution (PSD) of polydisperse polystyrene suspensions was recovered at high volume fractions up to 40% at two different wavelengths. Our inversion results agree well with PSD measured by dynamic light scattering at a diluted sample of the same suspensions (∼0.01% volume of solids).

The Electrophoretic Mobility and Electric Conductivity of a Concentrated Suspension of Colloidal Spheres with Arbitrary Double-Layer Thickness

The electrophoresis in a monodisperse suspension of dielectric spheres 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, and the overlap of the double layers of adjacent particles is allowed. The electrokinetic equations, which govern the ionic concentration distributions, the electric 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 electrophoretic mobility of the colloidal sphere in closed form correct to O(ζ) are obtained. Based on the solution of the electrokinetic equations in a cell, a closed-form formula for the electric conductivity of the suspension up to O(ζ2) is derived from the average electric current density. Comparisons of the results of the cell model with different conditions at the outer boundary of the cell are made for both the electrophoretic mobility and the electric conductivity.

Momentum Distribution for an Inhomogeneous Bose Fluid at T = 0 with Both Confinement and Particle Interactions Modelled as Harmonic

Because of experimental interest in the effects of particle interactions in Bose condensates, such as a dilute atomic vapour of 87Rb, we have worked out the momentum distribution in an N-Boson many-body assembly at T = 0, for which both confinement and interbosonic interactions are modelled as purely harmonic. The half-width of the Gaussian momentum distribution is displayed as a function of N and of the strength and sign of the harmonic interactions. The bosonic kinetic energy is finally treated.

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(r12−7), where r12 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.