Volume Fraction Of Solid Phase Research Articles

Investigation of the mechanism of low‐density particle and liquid mixing process in a stirred vessel

AbstractIn order to investigate the mechanism of the low‐density solid particle and liquid mixing process, a specialised agitator structure was used. Both computational fluid dynamics simulation and experiments were carried out to study the two‐phase mixing characteristics in the stirred vessel. The mixing process was captured by snapshots. The flow field and solid phase volume fraction evolution were analysed. Experimental and numerical results agreed well with each other. Solid particles floating on the liquid surface were gradually transported to the bottom through the centre of the vessel and the mixing time was predicted and tested. Results indicate that the agitator structure used in this study is able to form an obvious axial circulation in the vessel and then achieve a good performance in low‐density solid and liquid mixing operations. The study provides a valuable reference for the design and optimisation of solid–liquid mixing equipment. © 2011 Canadian Society for Chemical Engineering

鉛直管内固液二相上昇流の体積率の相関式

A correlation based on the drift-flux model is proposed to estimate volume fraction of solid-phase in developed steady liquid-solid upward two-phase flows in vertical pipes. The distribution parameter and the drift velocity in the model are expressed by the six non-dimensional groups composed of input physical quantities and others. Their fundamental frames are given as follows: VS = JS/αS = Co(JL+JS) − {1-(dS/D)2}αLs VST Co=A1(dS/D)a{JL/(JL+JS)}b{JS/(JL+JS)}e(ρS/ρL)f{(JL+JS)/(gD)0.5}h {ρLD(JL+JS)/μL}j + B1 αL=A2(dS/D)k{JL/(JL+JS)}m{JS/(JL+JS)}n(ρS/ρL)p{(JL+JS)/(gD)0.5}q {ρLD(JL+JS)/μL}r + B2By using these new expressions, the volume fraction of solid-phase can be estimated with higher precisions than the author's previous correlation and Bankoff-type correlation.

PDA experiments and CFD simulation of a lab-scale oxidation ditch with surface aerators

Though hydrodynamic characteristic is an important parameter for the optimization of reactors, very little research deals with the hydrodynamics of oxidation ditches. This paper focuses on the hydrodynamics of an oxidation ditch from the point of view of both experiments and simulations. The three-dimensional flow field in the oxidation ditch aerated with surface aerators like inverse umbrella is simulated with computational fluid dynamics (CFD). The two-fluid model and the standard k– ɛ model are used for the turbulent solid–liquid two-phase flow. The distributions of liquid velocity and volume fraction of solid phase are obtained. Experiments are performed in a lab-scale oxidation ditch with particle dynamic analyser (PDA). The comparison between simulations and PDA experiments confirms that the results and the methods employed in this paper are reliable. The liquid and solid have similar flow velocity, while the vertical velocity of solid phase is slightly lower than that of liquid. With the increase of aerator speed, the velocity increases and solid phase disperses more evenly. The flow in the oxidation ditch has noticeable three-dimensional features, especially between the circular channel and the straight channel. And solid phase is ready to settle in these regions. All these results form the basis for the optimization and deep research of oxidation ditches.

Model of thermal conductivity in powder beds

Heat transfer between contacting solid particles in gas is localized about the points of contact because of the low thermal conductivity of gas. This suggests the model of a network of discrete thermal resistances. Thermal interaction of two particles in the zone of contact between them includes thermal conductivity in the solid phase as well as heat transfer through a gas gap between the particles, where the conductive heat transfer at higher distances from the center of the contact changes to the transition transfer and free molecular transfer near the contact center. In the framework of this approach the effective thermal conductivity depends on three dimensionless morphological parameters: the volume fraction of solid phase, the mean coordination number, and the ratio of the size of necks between particles to the size of particles. The physical properties of the phases are specified by the thermal conductivities of the solid and the gas, the adiabatic exponent of the gas, and the Knudsen number. The proposed model agrees with the experimental S curves of the effective thermal conductivity versus the logarithm of gas pressure. It also describes the experimental tendencies of increasing the effective thermal conductivity with the particle size and the volume fraction of solid. The model can be applied to powder beds with micron-sized particles as well as to packed beds with millimeter-sized particles in gas. Free molecular and transient regimes of heat transfer in the gas filling pores can be important even for millimeter-sized particles at atmospheric pressure when the Knudsen number is as low as ${10}^{\ensuremath{-}5}$. These rarefied gas phenomena are responsible for such a complicated behavior of the considered heterogeneous media. Their quantitative description gives the model, which does not contain fitting parameters.

On the problem of taking viscous effects into account in the macroscopic description of flow through a porous medium

The problem of the need to take the viscous stresses in the fluid phase into account in the continuum description of flow through a porous medium is discussed. In order quantitatively to estimate the fluid viscosity effect on the macroscopic velocity field, the problem of flow in a channel filled with a model porous medium, a set of spherical particles positioned at the nodes of a cubic lattice, is considered. This problem is solved by direct numerical simulation on the basis of the Navier-Stokes equations. From the data of numerical experiments the fluid velocity profiles and the viscous dissipation are found for four lattices with different solid-phase volume fractions. The results obtained indicate that in the continuum description the viscous fluid stresses can be neglected even for small (several per cent) solid phase volume fractions.

Preparation of Silicon Nitride Ceramics with High Wear Resistance by Aqueous Colloidal Process

Advanced silicon nitride ceramics with high wear resistance were fabricated by colloidal process.Orthogonal design was utilized to optimize the process parameters.The change of Zeta potential for Si_3N_4 particles after adding dispersant was analyzed.Furthermore,the microstructure,mechanical properties and wear resistance of silicon nitride ceramics were investigated.The results indicate that the green body with high density can be formed when the volume fraction of solid phase of silicon nitride slurry is equal to 45%.And silicon nitride ceramics with fracture toughness of 7.21MPa.m~(1/2),hardness of 9.30GPa is obtained in the optiinum condition.The friction and wear tests show that silicon nitride ceramics happen to crisp rupture and break off in the dry condition;while in the water-lubricated condition,the film of Si(OH)_4 is formed on the friction surface,and the wear mechanism is mainly chemical fretting wear.

Mechanical properties of thixomolded AZ91D magnesium alloy

Tensile properties of thixomolded AZ91D alloy were studied to investigate the fracture mechanism by the microstructure and decohesion surfaces of tensile specimens which were manufactured at different processing conditions including barrel temperature, shot velocity, mold temperature and screw rotation speed. The results revealed that mechanical properties of thixomolded AZ91D mainly depended on porosity level, the size and volume fraction of primary solid phase and the size of α-Mg and β-Mg 17Al 12 in liquid phase. The increase in barrel temperature and shot velocity would cause the increase of both strength and ductility, while increasing mold temperature or improving screw rotation speed was coupled by the reduction of tensile properties. The tensile behaviors for different processing parameters were reasonably interpreted through the dependant factors during the deformation.

Design of a Plug Formation Detector Based on the Capacitance Measurement Technique

A measurement system has been developed to non-invasively detect plug formation in density pneumatic conveying. This plug formation detection system yields quantitative information that is validated by comparison to an electrical capacitance tomography (ECT) system. Both the plug detection system and the ECT system were applied to a horizontal pipeline (50 mm inner diameter) in density pneumatic conveying. The experimental conditions were varied for different heights of the initial particle dense layer and air volume flow rates. For all cases, the results obtained from the plug detector and ECT show similar patterns. This good agreement suggests that, where feasible, this plug detector can be used in place of the ECT system, which is advantageous since plug detection systems are often less expensive and faster than ECT systems. The factors influencing plug formation are discussed in detail. As a result, it can be seen that the height of the initial particle dense layer and the air volume flow velocity contribute to the nature of the plug formation rather than the solid-phase volume fraction in the dense layer.

Multi-variable optimization of PEMFC cathodes using an agglomerate model

A comprehensive numerical framework for cathode electrode design is presented and applied to predict the catalyst layer and the gas diffusion layer parameters that lead to an optimal electrode performance at different operating conditions. The design and optimization framework couples an agglomerate cathode catalyst layer model to a numerical gradient-based optimization algorithm. The set of optimal parameters is obtained by solving a multi-variable optimization problem. The parameters are the catalyst layer platinum loading, platinum to carbon ratio, amount of electrolyte in the agglomerate and the gas diffusion layer porosity. The results show that the optimal catalyst layer composition and gas diffusion layer porosity depend on operating conditions. At low current densities, performance is mainly improved by increasing platinum loading to values above 1 mg cm −2, moderate values of electrolyte volume fraction, 0.5, and low porosity, 0.1. At higher current densities, performance is improved by reducing the platinum loading to values below 0.35 mg cm −2 and increasing both electrolyte volume fraction, 0.55, and porosity 0.32. The underlying improvements due to the optimized compositions are analyzed in terms of the spatial distribution of the various overpotentials, and the effect of the agglomerate structure parameters (radius and electrolyte film) are investigated. The paper closes with a discussion of the optimized composition obtained in this study in the context of available experimental data. The analysis suggests that reducing the solid phase volume fraction inside the catalyst layer might lead to improved electrode performance.

Viscosity of Highly Basic Slags

The viscous behavior of CaO–SiO2–FeO–MgO slags saturated with dicalcium silicate (2CaO·SiO2) with 8 mass% MgO at 1873 K, and CaO–SiO2–FeO–Al2O3–MgO slags are measured under the conditions of highly basic slag compositions with regard to the fluidity of BOF slag and slag coating technology. The experiment shows that slag viscosities increase with decreasing temperature for almost all the slags that have been investigated over a range of temperature range, and the slag viscosity has exhibited different behavior in the temperature range lower and higher than 1773 K. The viscosity of the present slag systems has decreased with increasing FeO content. The viscosities depended on Al2O3 and FeO contents more strongly than on MgO content. The slag basicity has a more significant effect on increasing slag viscosity. A thermodynamic approach for the constants of the Einstein–Roscoe equation has resulted in a reasonable relationship between the relative viscosity and the volume fractions of solid phases estimated from the slag compositions. Thus, the present study confirms that the viscosities of highly basic slags can be estimated in terms of the slag compositions by predicting the fraction of solid phases in the slags for the stable BOF operation and the reliable coating of vessel lining.

Microstructural development and evolution of liquid phase sintered Cr-Cu composites

Features of the microstructure formation of Cr-Cu composites under impregnation followed by liquid phase sintering of reduced and electrolytic chromium powders at 1200?C in a vacuum of (2-4)?10-3Pa have been studied. The refractory component particle size distribution in the microstructure of samples with reduced chromium sintered for 60 min is shown to obey a normal logarithmic law; with distribution parameters being sensitive to the volume fraction of the refractory particles. The calculated values of the dihedral angle are close to the value of one of the modes in the experimental dihedral angle distribution for the microstructure of electrolytic chromium based samples (115?). The interfacial and interparticle surface energies ratio ?sl/?ss>0.5 is shown to correspond to theory for the Crs-Cul system in equilibrium, which indicates the presence of skeleton structure elements in the course of composition formation under liquid phase sintering (including the case of excess liquid phase). Experimentally determined interparticle and interfacial surface areas, solid particle contiguity and continuity are discussed in terms of concurrent diffusion-controlled particle coarsening (in Lifshitz, Slyozov and Wagner theory) and particle coalescence (in German?s model). The kinetics of shrinkage for the composites with 50...55 % solid-phase volume-fractions at heating and isothermal sintering in a vacuum at a temperature of 1200?C in terms of linearly viscous rheological theory are discussed.

Spherical Cell Approach for the Effective Viscosity of Suspensions

In the present paper, the spherical cell approach is employed for addressing the effective viscosity of suspensions of spherical particles. The proposed derivation is based on the only assumption which constitutes the essence of the spherical cell approach: a representative part of the suspension is a spherical cell which contains a particle surrounded by the continuous phase. In contrast with the previous studies on this topic, no additional assumptions are used in the present analysis. The general method of derivation and the final result, which represents the effective viscosity as a function of the solid-phase volume fraction, are compared with earlier studies where the spherical cell approach was applied for describing the effective viscosity.

Scale‐related topology optimization of cellular materials and structures

AbstractThe integrated optimization of lightweight cellular materials and structures are discussed in this paper. By analysing the basic features of such a two‐scale problem, it is shown that the optimal solution strongly depends upon the scale effect modelling of the periodic microstructure of material unit cell (MUC), i.e. the so‐called representative volume element (RVE). However, with the asymptotic homogenization method used widely in actual topology optimization procedure, effective material properties predicted can give rise to limit values depending upon only volume fractions of solid phases, properties and spatial distribution of constituents in the microstructure regardless of scale effect. From this consideration, we propose the design element (DE) concept being able to deal with conventional designs of materials and structures in a unified way. By changing the scale and aspect ratio of the DE, scale‐related effects of materials and structures are well revealed and distinguished in the final results of optimal design patterns. To illustrate the proposed approach, numerical design problems of 2D layered structures with cellular core are investigated. Copyright © 2006 John Wiley & Sons, Ltd.

Grain growth of Al-4Cu-Mg alloy during isothermal heat treatment

Abstract The microstructure of an Al-4Cu-Mg alloy during isothermal heat treatment in the Strain Induced Melt Activation (SIMA) process was investigated and the kinetics of grain growth was analyzed. The grain growth during isothermal heat treatment of the Al-4Cu-Mg alloy coincided with the Ostwald ripening theory. During isothermal heat treatment, both grain shape and the high volume fraction of solid phase have significant effects on grain growth. Therefore, a new grain growth model based on the Ostwald ripening theory was proposed taking into consideration the grain shape and the volume fraction of solid phase. By comparing the calculated results with the experimental results, it was confirmed that the present model could be applied to grain growth during isothermal heat treatment of the Al-4Cu-Mg alloy in the SIMA process.

Deposition Behaviors of Solid Phases in Liquid-Solid Two-Phase Particles in High Velocity Oxy-Fuel Spraying

Three types of composite coatings were deposited by high velocity oxy-fuel (HVOF) spraying using metal-clad WC-18Co and SiC-50Co cermet powders, and sintered-crushed Al2O3-75Ni composite powders. Liquid-solid two-phase state of the sprayed particles with two different structures was achieved prior to their impingement on the substrate. The effects of particle structure and HVOF spraying parameters on volume fraction of the solid phase were investigated. The distribution of ceramic particle size inside coatings was also clarified. Scanning electron microscopy was employed to characterize the microstructure of HVOF sprayed cermet coatings. The volume fraction of solid particles and the distribution of particle size in the three types of coatings were estimated using a quantitatively metallographic approach from the microstructure of the coatings. The volume fraction of the solid phase in the coating made from Al2O3-Ni powders was increased with increase in the fuel gas flow. The maximum volume fraction of the Al2O3 phases reached about 64% of the original powder. On the other hand, the volume fraction of solid phase in the clad cermet coatings was decreased with increasing the fuel gas flow. The volume fraction of the solid phase dropped significantly from 72.2% in the original WC-18Co particle to 8.5% in the coating. The limited retention of the solid phase from spray particle to subsequent coating is due to rebounding off of large solid particle upon impacting. [doi:10.2320/matertrans.47.1684]

Microstructure development and solute redistribution in aluminium alloys under low and moderate shear rates during rheo processing

Microstructural features and microsegregational behaviour of solute are studied in shear or stir-cast aluminium alloys under low and moderate shear rates. Alloys studied are Al–6.2% Cu, Al–7.3% Si and Al–13.2% Mg. In all the cases, microstructures of the primary pre-quench solid for stir-cast samples show rosette or ellipsoidal morphologies. Volume fractions of pre-quenched solid phase show significantly higher values for stir-cast alloys as compared to calculated. Microsegregation studies by microprobe analysis along the grains of the samples solidified under different treatment conditions show that stir casting changes the segregation pattern significantly. Except for Al–13.2% Mg alloys lower values than those calculated by Scheil's microsegregation equation are observed for other systems. A model for microstructure evolution during stir casting is presented. The microsegregation patterns have been discussed in terms of interaction between the diffusing solute and the vacancies migrating from solid into liquid.

Plant–water relations and the fibre saturation point

This review is about the behaviour of water in cell walls. The aim is to introduce to biologists the concept of the fibre saturation point (FSP), and the related research of material scientists and engineers on the thermodynamics and chemistry of water in timber and wood. In the review, we first summarise what the FSP is, why it is important and how the FSP is routinely used by engineers and material scientists to estimate the volume fractions of solid, liquid and gas phases in bulk timber. We then show that the FSP can be intuitively understood using equilibrium thermodynamics. That analysis shows that the FSP is based on the concept that a certain (and repeatable) amount of water is chemically bound to cellulose and other substances in wood. That water, sometimes called bound water, exists in a water-cell wall mixture. The noted physical chemist and wood scientist, A. J. Stamm, called this mixture a 'solid solution'. In timber, the 'solid solution' is considered a separate phase from adjacent water in either a pure liquid phase or a vapour phase. Following that, we examine the FSP and wood-water dynamics at the molecular and cellular level. Despite differences between timber and living trees, we conclude that the FSP-based framework long used by material scientists and engineers is likely to be useful to biologists.

Capture of particles of dust by convective flow

Interaction of particles of dust with vortex convective flows is under theoretical consideration. It is assumed that the volume fraction of solid phase is small, variations of density due to nonuniform distribution of particles and those caused by temperature nonisothermality of medium are comparable. Equations for the description of thermal buoyancy convection of a dusty medium are developed in the framework of the generalized Boussinesq approximation taking into account finite velocity of particle sedimentation. The capture of a cloud of dust particles by a vortex convective flow is considered, general criterion for the formation of such a cloud is obtained. The peculiarities of a steady state in the form of a dust cloud and backward influence of the solid phase on the carrier flow are studied in detail for a vertical layer heated from the sidewalls. It is shown that in the case, when this backward influence is essential, a hysteresis behavior is possible. The stability analysis of the steady state is performed. It turns out that there is a narrow range of governing parameters, in which such a steady state is stable.

Examination of factors influencing the bond strength of high velocity oxy-fuel sprayed coatings

Several types of Ni and Co based composite coatings were deposited by high velocity oxy-fuel (HVOF) spray process using WC–Co, SiC–Co, TiC–Co (or Ni), Al 2O 3–Ni, W–Ni composite powders and large metallic powders in order to examine the factors influencing the bond strength of HVOF coatings. The bond strength of coatings was measured with the pull-off test method according to ASTM C-633-79 standard. It was found that the conventional state parameters of spray particles including temperature, velocity and momentum were not directly correlated with the bond strength of HVOF coatings. The physical properties of the non-melting phases in a two-phase particle significantly influence the bond strength of HVOF coatings. The effective mass of non-melting phases in a spray particle, which is defined as the product of density and square of volume fraction of solid phase in the two-phase particle, is proposed to give a good correlation with the bond strength of the coatings. It was found that the bond strength of HVOF coatings is correlated well with the parameter proposed.

DTA‐Measurements to Determine the Thixoformability of Steels

Semi‐solid metallurgy (SSM), also known as “thixoforming” or “thixoprocessing”, is of special interest as a new potential manufacturing technology for components in the automobile, machine and electronic industries. The aim of this technology is to produce complex shapes which cannot be produced with conventional processing methods.An important process step of semi‐solid processing (SSP) is the reheating and isothermal holding of the billet within the solid‐liquid range in order to obtain the required fraction liquid content and the desired globular microstructure. Aside from the investigation of billet heating and the development of a suitable tool design, the development and evaluation of adequate microstructures over a wide temperature area is very important. The focus of this paper is to determine the semi‐solid area of different steels through Differential Thermal Analysis (DTA) measurements. To determine a process window for handling the alloys in the semi‐solid state, the DTA‐results can be combined with microstructure parameters. Subsequent quenching experiments show the development of the microstructure parameters (e.g. grain size, phase distribution, volume fraction, shape factor, matrix character, contiguity, and particle density of the primary solid and liquid phases). A comparison of the slopes of the determined solid‐liquid areas for different steels show the width of the melting or freezing intervals to evaluate the possible process windows. DTA‐experiments performed at different heating rates show the influence of faster heating and cooling rates on the solidus‐liquidus interval. To evaluate the suitability for the thixoforming processes, this paper describes, and then compares, the semi‐solid intervals of different steel grades, which have been investigated in the Department of Ferrous Metallurgy at the RWTH Aachen University. The tool steel HS 6‐5‐3 and the cold work tool steel X210CrW12 have a wide semi‐solid area, which can be explained due to the dissolution of different carbides. In contrast to this, the steels C45, 42CrMo4, 16MnCr5, 34CrNiMo4, 100Cr6, X220CrVMo13‐4 and the Alloy 33 show a much smaller semi‐solid area.