Volume Fraction Of Large Particles Research Articles

Tortuosity variation in a low density binary particulate bed

The importance of particle size ratio and particle composition in the properties of a mixed bed is well known. Nevertheless, the dependence of the bed channel tortuosity T on the porosity ɛ in the form T = 1/ ɛ n , where n is assumed to be a constant, shows that the value of n depends on the properties of the packed bed. For loose packing, experimental data for binary mixtures of glass beads of a size ratio from 1 up to 53.8 was analysed in terms of porosity, tortuosity and permeability. The packing procedure was performed without intensive compacting methods e.g. vibration, etc. Obtained results show that the parameter n is a function of the volume fraction of large particles x D and, for spherical particles, lies in the range 0.4–0.5. The explanation for this variation is (1) a distortion effect on the small particles arrangement occurring near the large particle surface; (2) in the region of minimum porosity, near contact points of large particles, the occurrence of dead zones that are free of small particles. A relationship accounting for this effect is proposed that may be useful for the analysis of transport phenomena in granular bed filters, chromatographic columns, etc.

Rheological behavior and microstructure of bimodal suspensions of core-shell structured swollen particles

The rheological behavior and microstructure of bimodal suspensions of core-shell structured swollen particles have been examined with changing volume ratio of two different sized particles. As the volume fraction of large particles increases, the viscosity, degree of shear-thinning, and the critical shear stress σc decreases, while the interparticle distance ξ of the microstructure increases. The suspensions exhibit single mode rheological behavior and have a single diffraction peak in the SAXS profiles. These results suggest that the bimodal suspensions of the core-shell structured swollen particles behave likely to unimodal suspensions of hard spheres with alloy like single mode microstructure composed of hypothetical intermediate size particle. The relationship between σc and ξ can be represented as σc = 3kT/4πξ3, which corresponds to the dynamics of the Brownian hard sphere model with ξ being the particle diameter. These findings indicate that the shear-thinning of the suspensions can be attributed to dynamical competition between the thermal motion and the hydrodynamic motion under shear flow and that the mechanism can be applied to bimodal suspensions of the swollen particles as well as unimodal suspensions of hard spheres. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 102: 2212–2217, 2006

Isostatic compaction of bimodal powder mixtures and composites

We study the effect of using a mixture of particles of two different sizes for the compaction of spherical metallic powders by discrete element method simulations (DEM). The study focuses on large size ratios (4 and 8) for which a wide range of volume fractions of large particles is investigated (from 0% to 80% volume). The bimodality of the powder is shown to affect all stages of powder compaction. The relative density of the powder when no significant load is applied (tap density) is a function of both the size ratio and the volume fraction of large particles. Furthermore, we show that bimodal compacts exhibit a stiffer response during isostatic plastic compaction compared to the monomodal case. The important practical application of a mixture of soft deformable particles (metallic) with hard particles (ceramic) is also studied. Following compaction, the unloading of the compact and the resulting tensile strength (green strength) are also shown to depend on the bimodality of the compact.

Interparticle Potential and the Phase Behavior of Temperature-Sensitive Microgel Dispersions

Molecular-thermodynamic models assisted with experimental measurements are applied to correlate and predict the volume transition and structural ordering of poly(N-isopropylacrylamide) (PNIPAM) microgel particles dispersed in pure water. The effective pair potential between PNIPAM particles is represented by a Sutherland-like potential where the size and energy parameters are correlated with particle radius and the solution osmotic second virial coefficients attained from static and dynamic light scattering experiments. Using a first-order perturbation theory for the fluid phase and an extended cell model for the crystalline solid, the calculated phase diagram indicates that an aqueous dispersion of PNIPAM particles may freeze at both high and low temperatures. At low temperature, the freezing occurs at large particle volume fraction, similar to that in a hard-sphere system, while at high temperature, the freezing is driven by strong van der Waals attraction due to the increase in the Hamaker constant of the microgel particles when they collapse. The phase diagram of PNIPAM dispersions predicted from the molecular-thermodynamic models agrees favorably with experimental observations.

Viscosity of concentrated noncolloidal bidisperse suspensions

At the same solid volume fraction (Φ) the relative viscosity (η r ) of a concentrated noncolloidal bidisperse suspension of hard spherical particles is lower than that of a monodisperse suspension. In this paper a semi-analytical viscosity model of noncolloidal bidisperse suspensions is derived using an integration method. In this model the random loose packing density obtained by computer simulation is taken as the limit of solid volume fraction Φ m which depends upon both the diameter ratio (λ) of large to small particles and the volume fraction of large particles (ξ=Φ l /Φ). This model shows that at high solid volume fraction, Φ > 0.40, both λ and ξ significantly influence η r . For example, at Φ=0.5, it predicts that for monodisperse suspensions η r =70, while for bidisperse suspensions (λ=2 and ξ=0.7) η r =40. Comparison shows that, at high solid volume fraction (0.4–0.5), the relative viscosity predicted by this model is in good agreement with that predicted by the work of Shapiro and Probstein (1992) and of Patlazhan (1993), but is higher than that predicted by the work of others.

Kinetic modelling of binder burnout for optimisation of slurry–powder manufacturing process of Ti/SiC composites

A slurry–powder metallurgy method is currently under development as a low cost production route for Ti/SiC composites. One of the critical steps in the process is the complete removal of a fugitive binder used to form the powder slurry. A diffusion-controlled, shrinking-core model has been developed for the prediction of the binder burnout kinetics in a metal powder compact with relatively large particles. This model is suitable for a polymeric binder that decomposes mainly to a monomer. The model considers the degradation of the polymer and the diffusion of the monomer in the core that contains a powder structure filled with a liquid polymer–monomer solution. It is found that the dominant mechanism is the liquid diffusion of monomer and the burnout time increases significantly with the compact size. The model also predicts a longer burnout time for a larger particle volume fraction.

Computer simulation of random packing of unequal particles.

A Monte Carlo simulation model for the random packing of unequal spherical particles is presented in this paper. With this model, the particle radii obeying a given distribution are generated and randomly placed within a cubic packing domain with high packing density and many overlaps. Then a relaxation iteration is applied to reduce or eliminate the overlaps, while the packing space is gradually expanded. The simulation is completed once the mean overlap value falls below a preset value. To simulate the random close packing, a "vibration" process is applied after the relaxation iteration. For log-normal distributed particles, the effect of particle size standard deviation, and for bidisperse particles, the effects of particle size ratio and the volume fraction of large particles on packing density and on coordination number are investigated. Simulation results show good agreement with that obtained by experiments and by other simulations. The randomness, homogeneity, and isotropy, which have not been evaluated before for packing of distributed particles, are also examined using statistical measures.

The Equilibrium Properties and Microstructure of Mixtures of Colloidal Particles with Long-Range, Soft Repulsions

Osmotic pressure and elastic moduli of bimodal suspensions of particles experiencing long-range, soft repulsions were measured. At fixed osmotic pressure, the total suspension volume fraction, φ, varies linearly as the mixing ratio φl/φ is increased from 0 to 1. Here φlis the volume fraction of large particles based on total suspension volume. This result suggests the suspensions studied here are phase separated into domains containing primarily small and primarily large particles and is not expected for hard sphere suspensions where, at fixed osmotic pressure, φ passes through a maximum as φl/φ is increased. Elastic moduli are well described by a model based on a composite microstructure where the domains of pure large and small particles must have the same osmotic pressure which fixes the local particle volume fraction and hence the elastic modulus in each phase. The existence of phase separation is supported by electron micrographs taken on samples prepared by rapidly drying suspensions with volume fractions near 0.6.

A Mathematical Model for Intercalation Electrode Behavior: I. Effect of Particle‐Size Distribution on Discharge Capacity

A mathematical model is presented to study the effect of the particle size distribution (PSD) on the galvanostatic discharge behavior of the lithium/separator/intercalation electrode system. A recently developed packing theory has been incorporated into a first‐principles model of an intercalation electrode to provide a rational basis for including the effect of PSD on packing density. The model is used to investigate how binary mixtures of spherical particles affect electrode capacity. The electrode capacity of an insertion electrode is calculated for various parameters including applied current density, thickness of the electrode, and volume fraction, size, and size ratio of the particles. The model shows that an electrode comprised of two different sized particles can have a significantly higher capacity than an electrode consisting of single‐sized particles. However, increasing the packing density increases the liquid‐phase diffusion resistance. As a result of the trade‐off between packing density and liquid‐phase diffusion resistance, discharge capacity can be optimized by adjusting the particle size, volume fraction of large and small particles, and the size ratio. Pulse discharge of an intercalation electrode comprised of two different sized particles shows a marked difference in transient behavior from that of an electrode which has single‐sized particles. Since there are many parameters which control the performance of the electrode, use of this model should aid greatly in making superior electrodes.

シリカ粒子充てんエポキシ樹脂の強度特性に及ぼす粒子充てん量の影響と破壊メカニズムの検討

Epoxy resins for encapsulating integrated circuit (IC) devices are filled with silica particles to reduce the thermal expansion coefficient and to improve thermal conductivity. Recently, the size of chips mounted in a package has increased rapidly with advances in large-scale integration technology. This trend creates a problem : increased mechanical stress in the package, which sometimes causes cracking in the encapsulation resin under temperature cycling. Hence, evaluation of the fracture properties of these materials has become an important issue in package design. This study reports the effects of the filler particle volume fraction on the static strength of smooth specimens and fracture toughness of silica-particulate -filled epoxy resins for IC encapsulation. The smooth specimen strength and fracture toughness were measured, respectively, by the three-point bending test and the double torsion test. It was found that the fracture toughness increased with increasing volume fraction. The static strength of epoxy resins with a small amount of silica particulate was smaller than that of unfilled resins. The crack propagation in resins containing 30% volume fraction of large size particles was unstable. At larger than 45% volume fraction of particles, the crack propagation was stable. These crack propagation properties have been related to the plastic zone size of matrix and particle spacing.

Metal matrix composite layer formation with 3 μm SiC p powder on IMI318 titanium alloy surfaces through laser treatment

Metal surface modification is frequently carried out to increase the life and performance of engineering components that undergo severe service conditions such as wear, erosion and corrosion, without the cost of treating the entire component. The development of a suitable high performance surface layer on substrate materials can combat many surface degradation mechanisms. The formation of an in-situ surface layer MMC by injecting ceramic particulates on laser melted surfaces can, in particular, be used in applications requiring a localised treatment without changing the properties of the bulk material. Using a high volume fraction (25–60vol%) of large (50–150μm) ceramic particles (TiC, SiC) on titanium surfaces, the surface hardness was found to increase between 1.1 to 4 times the base hardness (150 Hv). In the present work, a 5kW continuous wave carbon dioxide laser was used under both helium and nitrogen environments to introduce a smaller volume fraction of 3 μm SiC p particles using the powder preplacement technique on a laser melted IMI318 titanium alloy (Ti-6Al-4V) surface. By changing the laser processing parameters, graded microstructures with hardness gradients were obtained over a melt depth of about 1 mm. The tracks produced surface cracks, but of low intensities (0.1 to 0.3 No./mm). However, in some glazing conditions cracks were absent. Under a helium environment, most of the ceramic particles dissolved in the melt pool, and the microstructure consisted mainly of thread-like particles; some dendrites were also present near the surface and at the edges of the melt pool. Under a nitrogen environment, the tracks produced mostly dendritic structure with no SiC p particles in the melt zone. The hardness developed from a base hardness of 350 Hv to the range 600 to 1200 Hv and 600 to 1450 Hv for tracks processed in helium and nitrogen atmospheres respectively.

Multiple cracks in transformation toughened ceramics

The problem of a collinear array of cracks in a transformation toughened ceramic under monotonically increasing load is analyzed by the theory of complex potentials and dislocation formalism. The analysis is applicable to both a homogeneous material containing multiple cracks and a brittle matrix ceramic reinforced by distributed transformable particulates. The detrimental effect of transformation at the onset of crack growth is generally found to be amplified by crack tip interactions. For the particulate reinforced ceramic the maximum relative strengthening is achieved for moderate volume fractions of large particles.

Mechanical properties and microstructure of cast oxide-dispersion-strengthened aluminum

Oxide-dispersion-strengthened aluminum containing 25 vol.%, 0.28 μm, alumina dispersoids was fabricated by pressure infiltration. The mechanical properties at room and elevated temperature are presented for both as-cast, coarse-grained materials and extruded, fine-grained materials. Although the room temperature yield strength is low (about 60 MPa), the 0.2% proof stress and ultimate tensile stress are much higher (about 200 MPa and 330 MPa respectively) as a result of the very high strain hardening rate. However, the initially high strain hardening rate decreases with strain. This behavior is explained by extending a model by Ashby for dilute dispersion-strengthened metals to the case of a matrix containing a large volume fraction of large particles, whereby the interaction of primary glide dislocations with secondary loops punched by dispersoids is considered.

Crack front trapping in transformation-toughened ceramics

A theoretical study is made of the trapping of a crack front in brittle matrix ceramic reinforced by dispersed transformable zirconia particles. The trapped discontinuous crack front is modelled by a collinear array of microcracks interspersed by transformable particles. The effect of trapping of the macrocrack front is approximated by a closing pressure on a bridged zone. The maximum closing pressure and the critical opening of the macrocrack are related to the volume (area) fraction and size of the transformable particles. It is found that the maximum toughening due to trapping occurs at moderate volume (area) fractions of large particles. This is in agreement with available theoretical and experimental results.

High-frequency viscosity of a dilute polydisperse colloidal suspension

Abstract We consider a dilute polydisperse suspension of spherical colloidal particles and obtain an expression for the high frequency (short time) effective viscosity of the suspension. We show that the Huggins coefficient for such a suspension is sensitive to the degree and nature of the polydispersity. We present numerical calculations for hard sphere particles and for droplets to show that size polydispersity can either decrease or increase the Huggins coefficient of such a suspension relative to its value for a monodisperse system of the same type of particles. For suspensions of hard spheres or droplets with internal viscosity much different from that of the suspending liquid, the effect can be significant when there is a distribution of particle sizes such that there are appreciable volume fractions of both large and small particles. By choice of the spectrum of particle sizes and of the volume fraction of each size the Huggins coefficient can be tuned over an appreciable range.

Radiative Transfer With Dependent Scattering by Particles: Part 1—Theoretical Investigation

Dependent radiation scattering for which the independent scattering theory fails to predict the scattering properties is important in analyzing radiative transfer in packed and fluidized beds. In this paper the dependent scattering properties have been derived assuming the Rayleigh–Debye scattering approximation for two cases: two identical spheres and a cloud of spherical particles. The two-sphere calculated results compare well with the exact solutions in the literature, giving confidence in the present analytical approach. The gas model and packed-sphere model have been employed to calculate dependent scattering properties for a cloud of particles of small and large particle volume fraction, respectively. The calculated dependent scattering efficiencies for a cloud of particles are smaller than the independent scattering efficiencies and decrease with increasing particle volume fraction. A regime map for independent and dependent scattering has been constructed and compared with existing empirical criteria.