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.     

Phase diagram of hard colloidal platelets: a theoretical account

We construct the complete liquid crystal phase diagram of hard plate-like cylinders for variable aspect ratio using Onsager's second virial theory and employing the Parsons–Lee decoupling approximation to account for higher-body interactions in the isotropic and nematic fluid phases. The stability of the solid (columnar) state at high packing fraction is included by invoking a simple equation of state based on a Lennard–Jones–Devonshire cell model which has proven to be quantitatively reliable over a large range of packing fractions. By employing an asymptotic analysis based on the Gaussian approximation we are able to show that the nematic–columnar transition is universal and independent of particle shape. The predicted phase diagram is in qualitative agreement with simulation results.     

The role of interfacial layers in the enhanced thermal conductivity of nanofluids: A renovated Hamilton–Crosser model

We previously developed a renovated Maxwell model for the effective thermal conductivity of nanofluids and determined that the solid/liquid interfacial layers play an important role in the enhanced thermal conductivity of nanofluids. However, this renovated Maxwell model is limited to suspensions with spherical particles. Here, we extend the Hamilton--Crosser model for suspensions of nonspherical particles to include the effect of a solid/liquid interface. The solid/liquid interface is described as a confocal ellipsoid with a solid particle. The new model for the three-phase suspensions is mathematically expressed in terms of the equivalent thermal conductivity and equivalent volume fraction of anisotropic complex ellipsoids, as well as an empirical shape factor. With a generalized empirical shape factor, the renovated Hamilton--Crosser model correctly predicts the magnitude of the thermal conductivity of nanotube-in-oil nanofluids. At present, this new model is not able to predict the nonlinear behavior of the nanofluid thermal conductivity.     

A discrete model of Ostwald ripening based on multiple pairwise interactions

A discrete multi-particle model of Ostwald ripening based on direct pairwise interactions is developed for particles with incoherent interfaces as an alternative to the classical LSW mean field theory. The rate of matter exchange depends on the average surface-to-surface interparticle distance, a characteristic feature of the system which naturally incorporates the effect of volume fraction of second phase. The multi-particle diffusion is described through the definition of an interaction volume containing all the particles involved in the exchange of solute. At small volume fractions this is proportional to the size of the central particle, at higher volume fractions it gradually reduces as a consequence of diffusion screening described on a geometrical basis. The topological noise present in real systems is also included. For volume fractions below about 0.1 the model predicts broad and right-skewed stationary size distributions resembling a lognormal function. Above this value, a transition to sharper, more symmetrical but still right-skewed shapes occurs. An excellent agreement with experiments is obtained for 3D particle size distributions of solid–solid and solid–liquid systems with volume fraction 0.07, 0.30, 0.52 and 0.74. The kinetic constant of the model depends on the cube root of volume fraction up to about 0.1, then increases rapidly with an upward concavity. It is in good agreement with the available literature data on solid–liquid mixtures in the volume fraction range from 0.20 to about 0.75.     

Biaxial modeling of the structure of the chevron interface in smectic liquid crystals

We have included the inherent molecular biaxiality of the smectic C phase in a model of the chevron structure. This molecular biaxiality is related to a hindered rotation about the molecular long axis which for chiral, polar molecules induces a spontaneous polarization. Through the coupling between biaxiality and the smectic cone angle, continuity of the molecular distribution at the chevron interface leads to changes in the cone angle. Under certain approximations we are able to find analytic expressions for the chevron structure and consequently estimate the width of the chevron interface. There are in fact two correlation lengths which govern variations in the cone angle and the biaxiality.     

A stochastic model for solidification

A 3-dimensional (2-space, 1-time) model relating the diffusion of heat and mass to the kinetic processes at the solid-liquid interface, using a stochastic approach is presented in this paper. This paper is divided in two parts. In the first part the basic set of equations describing solidification alongwith their analysis and solution are given. The process of solidification has a stochastic character and depends on the net probability of transfer of atoms from liquid to the solid phase. This has been modeled by a Markov process in which knowledge of the parameters at the initial time only is needed to evaluate the time evolution of the system. Solidification process is expressed in terms of four coupled equations, namely, the diffusion equations for heat and mass, the equations for concentration of the solid phase and for rate of growth of the solid-liquid interface. The position of the solid-liquid interface is represented with the help of a delta function and it is defined as the surface at which latent heat is evolved. A numerical method is used to solve the equations appearing in the model. In the second part the results i.e. the time evolution of the solid-liquid interface shape and its concentration, rate of growth and temperature are given.     

Peculiarities of heat transfer in water droplets with a solid inclusion during heating in a high-temperature gas medium

A physical model and a mathematical model of heat transfer in the conditions of inhomogeneous (with a solid inclusion—a carbon particle) liquid droplet evaporation while moving through high-temperature (800–1500 K) gases are formulated. Numerical investigations were performed using, as an example, a spherical inhomogeneous water droplet during heating in the air medium. The most probable mechanism of phase transitions in a water–carbon particle–heated air system is considered (the initial droplet size, radius, varied in the range from 0.5 mm to 1.5 mm, the inclusion radius was 0.1–1 mm). It has been found that in certain conditions, besides water evaporation from the outer (free) droplet surface, intensive vaporization is possible at the liquid–solid inclusion interface. Conditions of realization of these phase transitions in inhomogeneous water droplet–high-temperature gas medium systems are identified.     

粗化过程中颗粒界面形状演化的三维多相场法研究

利用多相场模型对液-固两相体系中固相颗粒的粗化过程进行了三维模拟,对粗化过程中的界面形状分布进行了统计分析,研究了不同固相体积分数下颗粒连接状态对界面形状演化及粗化速率的影响.模拟结果表明:当颗粒间存在大量连接时,粗化速率随固相分数的变化速率比颗粒无连接时变缓,且随着粗化进行,高曲率的双曲形界面所占比例不断降低,低曲率的椭球形界面所占比例逐渐增多;无论固相颗粒间是否发生连接,界面形状演化经历一定阶段后,三维界面形状分布均呈现自相似性,但随着固相体积分数的增加,界面形状分布呈现自相似性所需的时间延长.     

Finite size melting of spherical solid–liquid aluminium interfaces

We have investigated the melting of nano-sized cone shaped aluminium needles coated with amorphous carbon using transmission electron microscopy. The interface between solid and liquid aluminium was found to have spherical topology. For needles with fixed apex angle, the depressed melting temperature of this spherical interface, with radius R, was found to scale linearly with the inverse radius 1/R. However, by varying the apex angle of the needles we show that the proportionality constant between the depressed melting temperature and the inverse radius changes significantly. This led us to the conclusion that the depressed melting temperature is not controlled solely by the inverse radius 1/R. Instead, we found a direct relation between the depressed melting temperature and the ratio between the solid–liquid interface area and the molten volume.     

Numerical Analysis of Unsteady Magneto-Biphase Williamson Fluid Flow with Time Dependent Magnetic Field

Numerical investigation of the dusty Williamson fluid with the dependency of time has been done in current disquisition. The flow of multiphase liquid/particle suspension saturating the medium is caused by stretching of porous surface. The influence of magnetic field and heat generation/absorption is observed. It is assumed that particle has a spherical shape and distributed uniformly in fluid matrix. The unsteady two-dimensional problems are modeled for both fluid and particle phase using conservation of mass, momentum and heat transfer. The finalized model generates the non-dimensioned parameters, namely Weissenberg number, unsteadiness parameter, magnetic parameter,heat generation/absorption parameter, Prandtl number, fluid particle interaction parameter, and mass concentration parameters. The numerical solution is obtained. Locality of skin friction and Nusselt number is deliberately focused to help of tables and graphs. While inferencing the current article it is clearly observed that increment of Williamson parameter, unsteadiness parameter, magnetic parameter, volume fraction parameter, and mass concentration parameter reduces the velocity profile of fluid and solid particles as well. And increment of Prandtl number, unsteadiness parameter,volume fraction parameter, and mass concentration parameter reduces the temperature profile of fluid and solid particles as well.     

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.     

圆锥边界附近激光空泡溃灭行为的研究

为了研究刚性圆锥边界锥角对激光空泡溃灭行为的影响,文章建立了虚拟平面边界模型, 同时采用阴影摄影术、光偏转法以及数值计算的手段对边界附近空泡溃灭过程进行了研究. 结果表明边界的锥角对空泡的形状、溃灭时间以及液体射流形成均有明显影响. 空泡形状偏离球形的程度和溃灭时间均随锥角的增大而增大,且增大锥角度可以促使射流的形成. 空泡溃灭时间的实验值同理论值具有较高的一致性,验证了虚拟平面边界假设及无量纲距离修正的有效性.     

Melting of embedded anisotropic particles: PbIn inclusions in Al

Small particles embedded in the solid state can assume facetted shapes that indicate the anisotropy in interfacial free energy between the particle and the embedding phase. Previous in situ transmission electron microscopy (TEM) of Al–In has shown that such facetted nanoparticles with cubic symmetry embedded in a solid can produce a series of complex melt configurations. To determine the dependence of melt configuration on solid–solid facet energies, this work numerically calculates the equilibrium melt trajectory for a family of cuboctahedral particles parameterized by the ratio of matrix–particle interfacial free energies for orientations taken with respect to the crystal axes of the matrix, ??=?γ₁₀₀/γ₁₁₁. The calculations assume that equilibrium occurs with the minimization of the total interfacial free energy to determine the stable internal melt configuration for a fixed volume of melt confined within a member of the cuboctahedral family. At particular melt volume fractions, abrupt transitions in shape occur when a stable configuration reaches a touching or necking instability. In situ TEM of a dilute Al alloy containing embedded nanosized PbIn inclusions that gradually melt as the temperature is increased from 230 to 260°C is consistent with the results calculated for ??=?1.245.     

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.-%.     

Interfacial shape and contact-angle measurement of transparent samples with confocal interference microscopy

A model has been developed that predicts the effective optical path through a thick, refractive specimen on a reflective substrate, as measured with a scanning confocal interference microscope equipped with a high-numerical-aperture objective. Assuming that the effective pinhole of the confocal microscope has an infinitesimal diameter, only one ray in the illumination bundle (the magic ray) contributes to the differential optical path length (OPL). A pinhole with finite diameter, however, allows rays within a small angular cone centered on the magic ray to contribute to the OPL. The model was incorporated into an iterative algorithm that allows the measured phase to be corrected for refractive errors by use of an a priori estimate of the sample profile. The algorithm was validated with a reflected-light microscope equipped with a phase-shifting laser-feedback interferometer to measure the interface shape and the 68 degrees contact angle of a silicone-oil drop on a coated silicon wafer.     

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     

A model for the thermal conductivity of nanofluids – the effect of interfacial layer

A model for predicting the effective thermal conductivity of nanofluids is proposed. It has been documented that the interfacial layer at the solid (particle)/liquid interface and particle size is one of the major mechanisms for enhancing the thermal conductivity of nanofluids. Comparing with other classical models, the proposed model takes into account some additional effects including volume fraction, thickness, thermal conductivity of the interfacial layer and particle size. The proposed model is found to be better than the existing models since the predicted effective thermal conductivity of different types of nanofluids are closer to the experimental results.     

The equilibrium shape of anisotropic interfacial particles

The Wulff construction yields the equilibrium shape of a particle of fixed volume embedded in a single phase at constant temperature. When the particle attaches to an interface (boundary) between two distinct phases or grains of the same phase, the Wulff construction must be modified to account for the abutment of Wulff shapes at the boundary as well as the boundary energy that is replaced by the particle. If the boundary is non-deformable, a portion of the particle interface is constrained to replace the image (i.e. the exact position) of the boundary that is removed, and the Winterbottom construction yields the equilibrium particle shape. If the boundary can deform, the particle is not constrained to replace the image of removed boundary, and the particle shape is determined by a more general modification of the Wulff construction. In two dimensions, the particle attaches to an initially flat boundary and creates two disjoint segments that remain flat at equilibrium. In three dimensions, the boundary surrounding the particle is contiguous, and numerical calculations show that such a boundary is not necessarily flat but maintains a constant mean curvature of zero at equilibrium.     

Phase separation of bacterial colonies in a limit of high degradation

We discuss the structure of the equilibrium states of a regularized Keller-Segel model describing the chemotaxis of bacterial populations. We consider the limit of high degradation of the secreted chemical where analytical results can be obtained. Below a critical effective temperature, the system experiences a second order phase transition from a homogeneous phase to an inhomogeneous phase formed by two domains with uniform concentration separated by a thin interface (domain wall). We study the properties of the interface and determine the bifurcation between a circular shape (spot) and a rectangular shape (stripe) as a function of the control parameters. We show the analogy with the structure of Jupiter's great red spot which also consists in two phases with uniform potential vorticity separated by a thin annular jet.     

Analytic equation of state for solids with multi-exponential potential based on analytic mean field potential approach and applied to the epsilon phase of solid oxygen

The thermodynamic properties of the ε phase of solid oxygen are studied by using the analytic mean field approach （AMFP）. Analytic expressions for the Helmholtz free energy, internal energy and equation of state of solid oxygen have been derived based on the multi-exponential potential. The formulism for the case of double-exponential （DE） model is applied to the ε phase of solid oxygen. Its four potential parameters are determined through fitting the experimental compression data of the ε phase of solid oxygen. Numerical results of the pressure dependence of the volume calculated by using the AMFP are in good agreement with the original experimental data. This suggests that the AMFP is a useful approach to study the thermodynamic properties of the ε phase of solid oxygen. Furthermore, we predict the variation of the volume, lattice parameters and intermolecular distances with pressure, and some thermodynamic quantities versus volume, at several higher temperatures.