A theoretical interpretation of self-similar right-skewed particle size distributions in Ostwald ripening of cementite in ferrite

A multi-particle approach of Ostwald ripening in two-phase systems based on direct interactions is developed which successfully explains the stationary right-skewed shape of the particle size distribution found in coarsening experiments of cementite in ferrite at a volume fraction of about 0.07. To reproduce such an evidence the mean field hypothesis of the classical LSW theory has been replaced by a topological framework where any particle exchanges solutes with all its neighbours within an interaction volume proportional to its size. Then, an effective diffusion distance depending on the current average size in the system and on volume fraction of the second phase has been introduced.     

Effects of particle/matrix interface and strengthening mechanisms on the mechanical properties of metal matrix composites

A randomly distributed multi-particle model considering the effects of particle/matrix interface and strengthening mechanisms introduced by the particles has been constructed. Particle shape, distribution, volume fraction and the particles/matrix interface due to the factors including element diffusion were considered in the model. The effects of strengthening mechanisms, caused by the introduction of particles on the mechanical properties of the composites, including grain refinement strengthening, dislocation strengthening and Orowan strengthening, are incorporated. In the model, the particles are assumed to have spheroidal shape, with uniform distribution of the centre, long axis length and inclination angle. The axis ratio follows a right half-normal distribution. Using Monte Carlo method, the location and shape parameters of the spheroids are randomly selected. The particle volume fraction is calculated using the area ratio of the spheroids. Then, the effects of particle/matrix interface and strengthening mechanism on the distribution of Mises stress and equivalent strain and the flow behaviour for the composites are discussed.     

Influence of Al3Ni crystallisation origin particles on hot deformation behaviour of aluminium based alloys

Abstract

Binary Al–Ni, Al–Mg and ternary Al–Mg–Ni alloys containing various dispersions and volume fraction of second-phase particles of crystallisation origin were compressed in a temperature range of 200–500 °C and at strain rates of 0.1, 1, 10, 30 s^?1 using the Gleeble 3800 thermomechanical simulator. Verification of axisymmetric compression tests was made by finite-element modelling. Constitutive models of hot deformation were constructed and effective activation energy of hot deformation was determined. It was found that the flow stress is lowered by decreasing the Al₃Ni particle size in case of a low 0.03 volume fraction of particles in binary Al–Ni alloys. Intensive softening at large strains was achieved in the alloy with a 0.1 volume fraction of fine Al₃Ni particles. Microstructure investigations confirmed that softening is a result of the dynamic restoration processes which were accelerated by fine particles. In contrast, the size of the particles had no influence on the flow stress of ternary Al–Mg–Ni alloy due to significant work hardening of the aluminium solid solution. Atoms of Mg in the aluminium solid solution significantly affect the deformation process and lead to the growth of the effective activation energy from 130–150 kJ/mol in the binary Al–Ni alloys to 170–190 kJ/mol in the ternary Al–Mg–Ni alloy.     

浓悬浮液中渗透性颗粒的扩散特性研究

本文利用浓悬浮液中渗透性颗粒的短时扩散动力学数值模拟的结论,并结合Cohen-de Schepper近似和Percus-Yevick近似,研究了不同粒径渗透性颗粒的有效扩散系数随体积分数和渗透率的变化关系. 结果表明:对于浓悬浮液中一定粒径的渗透性颗粒,其扩散系数随渗透率的增加而增加,随体积分数的增加而减少;具有相同粒径与流体动力学屏蔽深度比值且波数较大的渗透性颗粒,其粒径对扩散的影响可以忽略. 关键词： 渗透性颗粒 有效扩散系数 体积分数 布朗运动短时区域     

Modelling of the influence of dihedral angle,volume fractions,particle size and coordination on the driving forces for sintering of dual phase systems

The equilibrium shape of solid particles in an aggregate immersed in a liquid or in a gas results from the minimization of interface energy. A model is developed for expressing the dependence of the solid–solid and solid–second phase interface areas on the system parameters: phase volume fractions, dihedral angle, particle size and coordination. The model aims at allowing quantitative assessment of the role of these parameters on the driving force for sintering. The representative volume element is a cone of which the apex angle accounts for the average particle coordination. In order to comply with the uniformity of interface curvature, the solid–second phase interfaces are described using the mathematics of the Delaunay surfaces. The results are compared with the solutions obtained by approximating the interface shape by the revolution of an arc of circle around the cone axis. This approximation does not involve a significant loss of precision.     

Brownian dynamic simulation for the prediction of effective thermal conductivity of nanofluid

Nanofluid is a colloidal solution of nanosized solid particles in liquids. Nanofluids show anomalously high thermal conductivity in comparison to the base fluid, a fact that has drawn the interest of lots of research groups. Thermal conductivity of nanofluids depends on factors such as the nature of base fluid and nanoparticle, particle concentration, temperature of the fluid and size of the particles. Also, the nanofluids show significant change in properties such as viscosity and specific heat in comparison to the base fluid. Hence, a theoretical model becomes important in order to optimize the nanofluid dispersion (with respect to particle size, volume fraction, temperature, etc.) for its performance. As molecular dynamic simulation is computationally expensive, here the technique of Brownian dynamic simulation coupled with the Green Kubo model has been used in order to compute the thermal conductivity of nanofluids. The simulations were performed for different concentration ranging from 0.5 to 3 vol%, particle size ranging from 15 to 150 nm and temperature ranging from 290 to 320 K. The results were compared with the available experimental data, and they were found to be in close agreement. The model also brings to light important physical aspect like the role of Brownian motion in the thermal conductivity enhancement of nanofluids.     

Estimation of the Effective Measuring Volume of Single-Fibre Reflection Probes for solid volume concentration measurements

The working principle of the single-fibre reflection (SFR) probe is that light emitted by a laser diode is guided into the measuring volume by the same fibre which receives the proportion of light reflected by the particles in the vicinity of the probe tip and transmits it back to a photosensitive element. In contrast to other configurations of fibre optical probes, the SFR probe is characterized by an unambiguous calibration graph over the entire range of solid volume concentration values. SFR probes have been successfully applied to different kinds of multiphase flow systems, e.g. fluidized beds, pneumatic conveying lines, elutriators and thickeners. A particular question for the interpretation of measurements has always been the effective size of the measuring volume, which is mainly determined by the solid volume concentration. In this paper a simplified mathematical model of the signal generation by backscattering of the emitted light at the particle surfaces is given. The theory takes into account the average optical properties of the solids and their particle size distributions. The particle properties are determined on the basis of this model, which finally delivers the shape, size and depth of the effective measuring volume. For particle sizes between 30 and 120 μm the depth of the measuring volume of a 600-μm fibre probe is between 0.2 mm for solid concentrations near the fixed-bed state and approximately 4 mm for solid volume concentrations as low as 0.1 vol.-%.     

Some general features of limited coalescence in solid-stabilized emulsions

We produce direct and inverse emulsions stabilized by solid mineral particles. If the total amount of particles is initially insufficient to fully cover the oil-water interfaces, the emulsion droplets coalesce such that the total interfacial area between oil and water is progressively reduced. Since it is likely that the particles are irreversibly adsorbed, the degree of surface coverage by them increases until coalescence is halted. We follow the rate of droplet coalescence from the initial fragmented state to the saturated situation. Unlike surfactant-stabilized emulsions, the coalescence frequency depends on time and particle concentration. Both the transient and final droplet size distributions are relatively narrow and we obtain a linear relation between the inverse average droplet diameter and the total amount of solid particles, with a slope that depends on the mixing intensity. The phenomenology is independent of the mixing type and of the droplet volume fraction allowing the fabrication of both direct and inverse emulsion with average droplet sizes ranging from micron to millimetre.Received: 4 April 2003, Published online: 8 July 2003PACS: 82.70.-y Disperse systems; complex fluids - 82.70.Kj Emulsions and suspensions - 68.15.+e Liquid thin films     

Mixing and segregation of granular materials in chute flows

Mixing of granular solids is invariably accompanied by segregation, however, the fundamentals of the process are not well understood. We analyze density and size segregation in a chute flow of cohesionless spherical particles by means of computations and theory based on the transport equations for a mixture of nearly elastic particles. Computations for elastic particles (Monte Carlo simulations), nearly elastic particles, and inelastic, frictional particles (particle dynamics simulations) are carried out. General expressions for the segregation fluxes due to pressure gradients and temperature gradients are derived. Simplified equations are obtained for the limiting cases of low volume fractions (ideal gas limit) and equal sized particles. Theoretical predictions of equilibrium number density profiles are in good agreement with computations for mixtures of equal sized particles with different density for all solids volume fractions, and for mixtures of different sized particles at low volume fractions (nu<0.2), when the particles are elastic or nearly elastic. In the case of inelastic, frictional particles the theory gives reasonable predictions if an appropriate effective granular temperature is assumed. The relative importance of pressure diffusion and temperature diffusion for the cases considered is discussed. (c) 1999 American Institute of Physics.     

Implementation of an advanced fixed sectional aerosol dynamics model with soot aggregate formation in a laminar methane/air coflow diffusion flame

An advanced fixed sectional aerosol dynamics model describing the evolution of soot particles under simultaneous nucleation, coagulation, surface growth and oxidation processes is successfully implemented to model soot formation in a two-dimensional laminar axisymmetric coflow methane/air diffusion flame. This fixed sectional model takes into account soot aggregate formation and is able to provide soot aggregate and primary particle size distributions. Soot nucleation, surface growth and oxidation steps are based on the model of Fairweather et al. Soot equations are solved simultaneously to ensure convergence. The numerically calculated flame temperature, species concentrations and soot volume fraction are in good agreement with the experimental data in the literature. The structures of soot aggregates are determined by the nucleation, coagulation, surface growth and oxidation processes. The result of the soot aggregate size distribution function shows that the aggregate number density is dominated by small aggregates while the aggregate mass density is generally dominated by aggregates of intermediate size. Parallel computation with the domain decomposition method is employed to speed up the calculation. Three different domain decomposition schemes are discussed and compared. Using 12 processors, a speed-up of almost 10 is achieved which makes it feasible to model soot formation in laminar coflow diffusion flames with detailed chemistry and detailed aerosol dynamics.     

Elasticity,fracture and thermoreversible gelation of highly filled physical gels<Superscript>⋆</Superscript>

We describe a physically associating triblock copolymer-based gel that exhibits a reversible transition between solid and liquid states at a temperature of approximately 55^°C. The thermal transition of the gel enables us to compare the properties of liquid suspensions and elastic composites with identical particle loadings, with particle volume fractions as large as 0.55. The suspension viscosity and the composite elasticity scale in a similar manner with the overall particle volume fraction, a result that is rationalized in terms of an effective strain amplification factor that depends only on the particle loading. Measured values of the strain amplification factor are in good agreement with the expected form for well-dispersed spheres. We also find that the elastic composites are exceptionally strong, with fracture strengths that exceed the modulus of the base gel by a factor of 100 or more. Deviations from purely elastic behavior became important for high particle volume fractions, and were probed by stress relaxation experiments.     

Qualitative evaluation of the effect of morphology,spatial distribution and coherent interfaces on the coarsening kinetics and size distribution of particles during Ostwald ripening

ABSTRACT

By exploiting the simple structure of the recently developed Multi-Particle model of Ostwald ripening based on pairwise interactions, the effect of extra factors affecting the coarsening process, such as the morphology of particles, the topology of their spatial distribution and the presence of elastic fields surrounding coherent precipitates, is analysed from a qualitative viewpoint.

Two observables disclose the presence of deviations with respect to the behaviour of a system of spherical and incoherent precipitates: the absolute value of the kinetic coarsening constant, together with its evolution with the volume fraction, and the shape of the asymptotic particle size distribution (PSD) for a given volume fraction of second phase.

By using a parametrised ‘rounded cube’ ideal solid it is shown that, as the shape of precipitates flattens, the coarsening constant decreases reaching in some condition values as low as about 20% that of a system of spheres with the same fraction.

Consequently, the curve of the relative kinetic constant with the volume fraction has a slower increase above 0.7 compared to spherical particles and this permits to explain accurately the experimental data on dense systems in the whole range of volume fractions.

It is also shown how the shape of the PSD is influenced by regular arrangements of particles in the space and by interfacial stresses in the matrix surrounding coherent precipitates. In both cases the model predicts a sharpening of the PSD, whose shape tends to become more symmetrical and somehow similar to that of the classical LSW theory.     

Modelling soot formation in a premixed flame using an aromatic-site soot model and an improved oxidation rate

An updated rate of O₂ oxidation of one to four ring polyaromatic hydrocarbons in premixed flames is presented based on density function theory simulations of oxygen attack at different radical sites on various PAHs. The rate is in agreement with other rates found in the literature; however, it is several orders of magnitude lower than the currently accepted oxidation rate of multi-ring aromatic species, including soot. Simulations are presented of a premixed flame using this improved rate and a new advanced soot particle model, which is developed in this paper. This model includes unprecedented detail of the particles in the ensemble, including the aromatic content, C/H composition and primary-particle aggregate structure. The O₂ oxidation rate calculated in this paper is shown to give a better prediction of particle number density and soot volume fraction for a premixed flame. The predicted particle size distributions are shown also to describe better the experimental data. Predicted C/H ratio and PAH size distributions are shown for the flame. Computed TEM-style images are compared to experimental TEM images, which show that the aggregate structure of the particles is well predicted.     

Energy spectra and charge fractions for keV hydrogen and helium backscattered from silicon

Energy spectra and charge fractions for hydrogen and helium backscattered from silicon targets are reported. The primary energy of the incident particle varies from 5 to 15 keV. The backscattered energy distributions are measured down to 500 eV and the results are compared to a Monte-Carlo computer simulation. Good agreement is found between the theoretical model and the experimental data. Charge fractions are measured by differentiating between scattered ions and neutrals. For hydrogen, neutralization occurs primarily at the surface for the backscattered particles and no depth effects are found. Helium shows a large peak in the ion yield for surface scattering with a much reduced ion yield for particles scattered from within the solid.     

An Incompressible Three-Dimensional Multiphase Particle-in-Cell Model for Dense Particle Flows

A three-dimensional, incompressible, multiphase particle-in-cell method is presented for dense particle flows. The numerical technique solves the governing equations of the fluid phase using a continuum model and those of the particle phase using a Lagrangian model. Difficulties associated with calculating interparticle interactions for dense particle flows with volume fractions above 5% have been eliminated by mapping particle properties to an Eulerian grid and then mapping back computed stress tensors to particle positions. A subgrid particle, normal stress model for discrete particles which is robust and eliminates the need for an implicit calculation of the particle normal stress on the grid is presented. Interpolation operators and their properties are defined which provide compact support, are conservative, and provide fast solution for a large particle population. The solution scheme allows for distributions of types, sizes, and density of particles, with no numerical diffusion from the Lagrangian particle calculations. Particles are implicitly coupled to the fluid phase, and the fluid momentum and pressure equations are implicitly solved, which gives a robust solution.     

界面润湿性及固相体积分数对颗粒粗化动力学影响的相场法研究

利用多相场模型模拟了液-固两相体系中固相颗粒的粗化过程, 分析了界面润湿性及固相体积分数对粗化指数、粗化速率及颗粒尺寸分布的影响.结果表明, 不同固相体积分数下粗化指数基本不变, 但粗化速率常数及尺寸分布与固相体积分数及界面润湿性密切相关.在完全润湿条件下, 随着固相体积分数的增加, 粗化速率常数逐渐增大; 而非完全润湿条件下, 随着固相体积分数的增加, 粗化速率常数增大速度变缓, 且当润湿性较低、 固相分数较大时, 粗化速率常数还将随体积分数的增加而下降. 此外, 模拟结果表明各种润湿条件下颗粒的尺寸分布均随着固相分数增加而变宽, 分布峰值降低, 但非完全润湿条件下峰值下降变缓.模拟结果为理解不同实验观测结果之间的分歧提供了依据. 关键词： 粗化 相转变 相场法 润湿性     

On-Line Characterization of the Shape and Size of Particles

An image analysis system for extracting on-line quantitative geometric and densitometric information from images of ore samples is described. The apparatus employs a pulsed semiconductor laser as the light source for illuminating of a flowing stream of particles and a non-interlaced solid-state TV camera as size measurement device in a shadowgraph imaging system. The problem of the sampling volume is discussed and several size distributions of solid particulates are presented. The particle size measurement range is 2–400 μm.     

Radiation properties of soot from diffusion flames

The spectral extinction coefficients k_λ of soot from flame transmission data are obtained for small pool diffusion flames of various fuels including solid polystyrene and plexiglas; foam polystyrene and polyurethane; and liquid isooctane and toluene. Good agreement between experimental and predicted k_λ from Mie theory and soot optical properties throughout the visible and infrared ranges substantiates the general applicibility of these optical properties. On the other hand, the determination of soot sizes and volume fractions from visible range data and optical properties requires the form of the size distribution be known. The effect of using different size distributions on these soot results is evaluated by using the three-parameter distribution for the particle number density N(r) = ar^b exp (?br/r_m), with b varied to create different functional dependence on radius r. The most probable radius r_m is found to increase by about 80% as b is changed from 2 to 6, while the volume fraction changes by less than 10%. Hence, the most probable radius is rather sensitive to this functional dependence, while the volume fraction is only slightly affected.     

Brownian dynamics of polydisperse colloidal hard spheres: Equilibrium structures and random close packings

Recently we presented a new technique for numerical simulations of colloidal hard-sphere systems and showed its high efficiency. Here, we extend our calculations to the treatment of both 2- and 3-dimensional monodisperse and 3-dimensional polydisperse systems (with sampled finite Gaussian size distribution of particle radii), focusing on equilibrium pair distribution functions and structure factors as well as volume fractions of random close packing (RCP). The latter were determined using in principle the same technique as Woodcock or Stillinger had used. Results for the monodisperse 3-dimensional system show very good agreement compared to both pair distribution and structure factor predicted by the Percus-Yevick approximation for the fluid state (volume fractions up to 0.50). We were not able to find crystalline 3d systems at volume fractions 0.50–0.58 as shown by former simulations of Reeet al. or experiments of Pusey and van Megen, due to the fact that we used random start configurations and no constraints of particle positions as in the cell model of Hoover and Ree, and effects of the overall entropy of the system, responsible for the melting and freezing phase transitions, are neglected in our calculations. Nevertheless, we obtained reasonable results concerning concentration-dependent long-time selfdiffusion coefficients (as shown before) and equilibrium structure of samples in the fluid state, and the determination of the volume fraction of random close packing (RCP, glassy state). As expected, polydispersity increases the respective volume fraction of RCP due to the decrease in free volume by the fraction of the smaller spheres which fill gaps between the larger particles.     

In Situ Charge Characterization of TiO<Subscript>2</Subscript> and Cu–TiO<Subscript>2</Subscript> Nanoparticles in a Flame Aerosol Reactor

Charge distribution characteristics were investigated for nanoparticles synthesized in a diffusion flame aerosol reactor. The nanoparticles considered were pristine TiO₂ and Cu–TiO₂, with Cu dopant concentrations ranging from 1 to 5 wt% with particle size from 25 to 60 nm. In situ measurements were conducted by integrating a tandem differential mobility analyzer (TDMA) experimental setup with the flame aerosol reactor. A charging model was used to identify the important parameters that govern the two charging mechanisms (diffusion and thermo-ionization) in the flame and their relative importance at different operating parameters. The results indicate that TiO₂ and Cu–TiO₂ nanoparticles carry single as well as double unit charges. The charged fraction depends on particle size as well as on dopant concentration. The charged fraction increased with increasing particle size and decreased with copper dopant concentration. Measured charged fractions were similar for both the polarities at different mobility diameters. Based on the flame operating parameters, the calculations indicate that diffusion charging is dominant in the flame, which is consistent with the experimental results.