Interparticle Contact Area Research Articles

Prediction of effective thermal conductivity of packed beds of polyhedral particles

In packed beds, particle shape influences the heat transfer considering different particle-particle contacts and pore morphology. This paper extends a predictive model for effective thermal conductivity, the Zehner, Bauer and Schlünder (ZBS) model for various shapes. Thus, real structures were studied parallel with numerically generated packings and thermal simulations were performed in FEM solver. ZBS model parameters, porosity, shape factor and interparticle contact area ratio were derived. FEM and ZBS results were compared over a wide range of particle-to-gas conductivity ratios. ZBS model predicted well for lower conductivity particles with the newly introduced sphericity term. In the mid-range of particle conductivity, the results are shape factor sensitive, model predicts well with experimental validation. New correlations were built for ZBS model parameters, extending the model for irregular, non-spherical particles. Prospectively, particle-particle heat transfer coefficients for the discrete element method (DEM) can be derived from the effective thermal conductivity of such particles.

Multiphysics Simulation and Experimental Investigation of the Densification of Metals by Spark Plasma Sintering

Multivariant experimental investigations and multiphysics microstructural modeling of the spark plasma sintering process of metallic powders have been performed up to a relative density of approximately 80%. In comparison, the effect of sintering temperature, pressure, and particle size on the interparticle contact area growth and axial shrinkage of cylindrical specimens of copper and nickel particles is measured in laboratory scaled tests. Herein, for the first time all relevant for sintering phenomena are considered simultaneously: the fully coupled thermo‐electro‐mechanical modeling of the spark plasma sintering processes, additionally taking into account for lattice, grain boundary, surface diffusion, electromigration, and thermomigration, has been carried out. The computational analysis of various physical phenomena allows to identify dominant and insignificant mechanisms. The two‐level numerical simulation includes the modeling of the sintering setup at the macroscopic level and the neck formation process in particle chain systems at the microscopic level. The results of the numerical simulations show a very good agreement with the experimental data. Therefore, the impact of electrical and mechanical loads as well as of particle size on microscopic distribution of temperature, inelastic strain, and on densification has been studied by the finite element simulations.

Investigation of consolidation mechanisms induced by applied electric/electromagnetic fields during the early stages of spark plasma sintering

This work aims at investigating the role of the electric/electromagnetic fields generated by the pulsed current applied during Spark Plasma Sintering (SPS) process on the sintering mechanisms. The selected model material was a metallic granular medium composed of microsized particles of pre-oxidized copper. Its electrical behavior and correlated microstructural modifications were studied in two complementary enclosures. First, a demonstrator equipped with a modulable pulsed electric current generator has allowed analyzing, at low temperature and without mechanical loading, the effects related to the application of an electric wave, by controlling and modulating its characteristics (i.e. shape, frequency, amplitude). An abrupt electrical transition, named “Branly effect” from an insulating to a conductive state, is observed in the granular copper medium. The increase of pulses frequency is shown to strongly reduce the critical time to generate the electrical transition. Moreover, a commercial SPS device, with specific electrical and thermal instrumentation, was implemented by varying applied stress and using conductive and insulating dies. The analysis of the electrical behavior coupled with post-mortem microstructural observations allowed to highlight that the coupling between pulsed current and mechanical stress promotes specific mechanisms in SPS. Under high stress, interparticle contact area increase and the insulating oxide layer is damaged by microcracking. The coupling with the flow of the pulsed current involves local overheating and dielectric breakdown, favoring ignition of Branly effect. Micro-welds are formed between particles, creating privileged paths of the pulsed current and initiating densification at low temperature (250 °C).

Effective thermal conductivity of packed beds made of cubical particles

This work addresses the parameterization of the Zehner-Bauer-Schlünder model (ZBS), a standard model for the determination of the effective thermal conductivity of packed beds, based on thermal simulations in ANSYS. Data are presented for the effective thermal conductivity of packed beds of cubical particles, obtained from simulations of heat conduction in particle systems generated by rigid body dynamics using the open-source software Blender. The particle-to-gas thermal conductivity ratio is varied over many orders of magnitude in these simulations. Punctual validation is provided by heat conduction measurements with cubes made of plastic and aluminum in air. Structural results are validated by micro-computed X-ray tomography. Emphasis is set on bed porosity and on the relative interparticle contact area. Comparisons elucidate ZBS behavior at the limit of non-conducting particles. In the region of medium particle-to-fluid conductance, ZBS shape factor is for the first time evaluated for cubes. At high solid conductance, the effective thermal conductivity of the bed is dominated by areal contacts between particles. Such contacts are large with cubes, but they are also shown not to be thermally perfect. Contact imperfection limits the increase in bed conductivity with increasing particle conductivity and requires the introduction of an additional empirical parameter in the ZBS model. In total, a full parametric setting of ZBS is provided for cubical particles. Several sets of this kind would help to generalize the model for applicability to particles of arbitrary shape.

Tailoring microstructures of carbon fiber reinforced carbon aerogel-like matrix composites by carbonization to modulate their mechanical properties and thermal conductivities

The microstructure evolution of carbon fiber reinforced carbon aerogel-like matrix (C/CA) composites with carbonization temperature and its influence on their properties were investigated. The removal of residual organo-functional groups of the C/CA precursors is dominant when carbonized at 600–750 °C with a large volume shrinkage difference by 17–22% as compared to that at 1200 °C, while the rearrangement of novolac structures is dominant at 900–1200 °C with a slight volume shrinkage fluctuation of 6%. Resultantly, the amount of micropore first increases and then decreases, while the particle size experiences an opposite change. The microstructure correspondingly transforms from a completely amorphous state to a partially amorphous state with graphite crystallites in low-angle misorientation, and then with graphite-like entangling ribbons. Due to the reduced residual tensile stress and increased interfacial bonding, the resulting composites with a variable bulk density of 0.58–0.64 g cm−3 have much higher compressive strengths of 45.8–96.9 MPa than other reported carbon foams or aerogels with similar bulk densities. The increase of strength and modulus with carbonization temperature is mainly due to the smaller tensile stress, higher particle packing compactness, larger microcrystallite size and less residual organo-functional groups. The composites also present a relatively low thermal conductivity of 0.12–0.59 W m−1 K−1. The increase of thermal conductivity with temperature is related to the synergistic effect of reduced phonon scattering associated with smaller specific surface area, larger microcrystallite size and less organo-functional groups and improved phonon transfer associated with increased inter-particle contact area.

Experimental Investigations on the State-Dependent Thermal Conductivity of Sand-Rubber Mixtures

Soil-rubber mixtures are potential construction materials for use in civil engineering applications such as the thermal insulation layer for buried pipelines in the permafrost zone and underground energy storage systems. Currently, however, the thermal conductivity of soil-rubber mixtures in various stress, saturation, and void ratio conditions is not fully understood. In this study, a stress-controlled apparatus based on the thermal needle probe technique was developed. It was employed to study the influence of the aforementioned factors on the thermal conductivity of sand-rubber mixtures. Thirty-four tests were completed with a wide range of net stresses (0–600 kPa), initial degrees of saturation (0%–100%), void ratios (0.45–0.95), and rubber contents (0%, 10%, and 20%). Three replicates were used in each condition. The results showed that the thermal conductivity was strongly dependent not only on void ratio, rubber content, and degree of saturation but also on net stress. For instance, the thermal conductivity of a dry sand-rubber mixture increased by 30% when the stress increased from 0 to 600 kPa. This increase in thermal conductivity can mainly be attributed to an increase in interparticle contact area, accounting for about 25% of the 30% increase; the reduction in void ratio played a minor role. A semiempirical equation was proposed to calculate the thermal conductivity of sand-rubber mixtures at different stress levels.

Estimation of thermal conductivity of cemented sands using thermal network models

Effective thermal conductivity of soils can be enhanced to achieve higher efficiencies in the operation of shallow geothermal systems. Soil cementation is a ground improvement technique that can increase the interparticle contact area, leading to a high effective thermal conductivity. However, cementation may occur at different locations in the soil matrix, i.e. interparticle contacts, evenly or unevenly around particles, in the pore space or a combination of these. The topology of cementation at the particle scale and its influence on soil response have not been studied in detail to date. Additionally, soils are made of particles with different shapes, but the impact of particle shape on the cementation and the resulting change of effective thermal conductivity require further research. In this work, three kinds of sands with different particle shapes were selected and cementation was formed either evenly around the particles, or along the direction parallel or perpendicular to that of heat transfer. The effective thermal conductivity of each sample was computed using a thermal conductance network model. Results show that dry sand with more irregular particle shape and cemented along the heat transfer direction will lead to a more efficient thermal enhancement of the soil, i.e. a comparatively higher soil effective thermal conductivity.

Advances in the understanding of mesoporous transition aluminas: Unveiling the correlation between morphology and thermostability

The thermostabilities of mesoporous γ-Al2O3 samples with similar initial surface areas and average pore radii, but significantly different pore volumes, were studied in detail. The results show that γ-Al2O3 with highest initial pore volume converts to α-Al2O3 at a significantly higher temperature, along with larger residual surface area and pore volumes after aging. These observations are directly related to the morphologies of the individual particles and the resulting aggregate structures, which were studied by automated crystallite orientation mapping (ACOM-TEM). Large particles with well-developed plate-like morphologies preferentially form dense stacks by assembly via the {110} main basal planes (pseudo-cubic lattice). This arrangement favors sintering and the formation of α-Al2O3 at comparatively low temperatures. Aluminas with higher proportions of the lateral {100} and {111} facets tend to form aggregate structures with higher porosities and lower interparticle contact areas, thus explaining their superior thermostabilities. These findings highlight the importance of the aggregate structure for the purposeful development of alumina-supported catalysts.

The influence of calcium lignosulphonate addition on non-isothermal pyrolysis and gasification of demineralised bituminous coal fines

• Coal fines were demineralised using acid de-ashing treatment. • CaLS added to the coal fines and demineralised coal in different proportion showed an increase in compressive strength. • CaLS blended samples showed higher reactivity when compared to the demineralised coal and coal fines. • 5% CaLS addition did not influence coal gasification rate significantly. • An increase in CaLS blends correlates with an increase in reactivities. Amorphous calcium lignosulphonate (CaLS), a by-product of the paper industry, was evaluated as an adhesive to bind demineralised bituminous coal fines in various weight percentage ratios. Sequential acid (HCl, HF, HCl) leaching was used to reduce mineral matter content in the coal fines. The pyrolysis and gasification of the samples were investigated in laboratory-scale experiments to determine the effect of the CaLS addition on the pyrolysis and gasification reactivities. Coal-CaLS blends consisting of 5, 10, and 15% calcium lignosulphonate were prepared, compressed into pellets, and characterised using proximate, X-ray diffraction, and X-ray fluorescence analyses. An increase in binder concentration increases the mechanical strength of the pellets due to the increased interparticle contact area. The relative coal gasification reaction reactivity (1/T max and 0.5/T 50 ), which was determined from the derivative thermogravimetry curves, increases with CaLS addition. The experimental results revealed that these wastes (coal fines and calcium lignosulphonate) could be utilised in thermochemical processes. Utilising these wastes will reduce the environmentally unfriendly volumes of amorphous calcium lignosulphonate and coal fines particles.

Development and validation of an analytical method for tensile strength determination of fibrous bulk solids

The increasing significance of products consisting of elongated particles or fibres along with a lack of understanding flow properties of fibrous bulk solids in processes urge for appropriate test procedures.Therefore, a tensile tester was designed with respect to the special needs in terms of test techniques of those bulk solids. The procedure of tensile strength determination was tested with regard to several possible influencing factors. Following from that, the manner of filling and filling height were identified to have the greatest influence on results. Furthermore, it is shown that the developed load system is capable of improving the repeatability of test results for fibrous bulk solids.Based on the derived standard procedure, systematic tests were carried out on beech and spruce chips in three different fractions each as well as model materials such as polypropylene fibres and differently sized bunches of glass fibres. The biomass materials have been characterised by dynamic image analysis prior to and after experiments resulting in particle size and shape factor distributions. It is found that tensile strength is affected by particle shape, size, roughness and interparticle contact area.

Numerical modeling of effective thermal conductivity of hollow silica nanosphere packings

Hollow silica nanosphere packings (HSNSPs) can significantly suppress heat conduction through solid and gas phases due to the voids, small interparticle contact areas, and nanosized pores, showing promising potentials towards energy-efficient building applications. The HSNSPs display a two-level structure, where the solid silica nanoparticles form the shells of hollow spheres, and the accretion of hollow spheres form the porous powder packing structures. Investigating thermal transport in HSNSPs helps to understand the fundamental thermal transport processes and to guide the design of their geometric structures. Herein, we developed a numerical model based on the two-level structure of HSNSPs to explore their effective thermal conductivities. The developed numerical model considers the geometric parameters such as sphere size, shell thickness, interparticle contact resistance, and the gas pressure inside and outside the hollow spheres. The developed numerical model was validated by the measured thermal conductivities of HSNSPs fabricated via the sacrificial template method. The results show that the effective thermal conductivity of HSNSPs can be reduced by decreasing sphere diameter, contact area and shell thickness. The influence of ratio of contact diameter to sphere diameter on the effective thermal conductivity becomes weaker as the hollow sphere size decreases (e.g., < 200 nm). Besides, we also show that reducing gas pressure outside the hollow spheres can effectively decrease the thermal conductivity of HSNSPs. This work provides a guideline for the structural design and optimization of HSNSPs.

Thermo-electro-mechanical modeling of spark plasma sintering processes accounting for grain boundary diffusion and surface diffusion

In the present research, a numerical modeling approach of the initial stage of consolidation during spark plasma sintering on the microscopic scale is presented. The solution of a fully coupled thermo-electro-mechanical problem also accounting for grain boundary and surface diffusion is found by using a staggered way. The finite-element method is applied for solving the thermo-electro-mechanical problem while the finite-difference method is applied for the diffusion problem. A Lagrange-based non-linear formulation is used to deal with the detailed description of plastic and creep strain accumulation. The numerical model is developed for simulating the structural evolution of the involved particles during sintering of powder compacts taking into account both the free surface diffusion of the particles and the grain boundary diffusion at interparticle contact areas. The numerical results obtained by using the two-particle model—as a representative volume element of the powder—are compared with experimental results for the densification of a copper powder compact. The numerical and experimental results are in excellent agreement.

Effect of particle proximity on changing of diffusion mechanism of 3Y-TZP nanoparticles at the initial stage of sintering

In order to evaluate the effect of interparticle contact area on the sintering behavior of 3Y-TZP nanopowder, the shrinkage of powder samples, compacted at different pressures were measured under constant rates of heating. Compaction of zirconia NPs at different pressures allowed to increase the contact area between particles and determined the critical parameters when the volume diffusion mechanism is changing on the grain boundary diffusion. It was found that the volume diffusion mechanism is the dominant densification mechanism at the initial stage of sintering for 3Y-TZP nanopowders at a low relative density of green ceramics, when there are few contacting particles, and the grain boundary diffusion mechanism cannot be realized due to the large diffusion path. The domination of the grain boundary diffusion mechanism during initial stage of sintering of 3Y-TZP nanoparticles was detected in case the contact area between particles increased up to 56%.

Characterization of Spray Dried Particles Through Microstructural Imaging

Spray drying is commonly used to produce amorphous solid dispersions (ASD) to improve the bioperformance of poorly water-soluble drugs. In this study, imaging techniques such as focused ion beam-scanning electron microscopy (FIB-SEM) and X-ray microcomputed tomography (XRCT) were used to study the microstructure of spray dried (SD) particles. Spray drying at higher outlet temperature (Tout) was found to produce more spherical hollow particles with smooth surface and thinner walls, while more raisin-like particles with thicker walls were generated at lower Tout. For the first time, an artificial intelligence–facilitated XRCT image analysis tool was developed to make quantitative analysis of thousands of particles individually possible. The particle size distribution through XRCT image analysis is generally in line with what is measured by laser diffraction. The image analysis reveals envelope density as a more sensitive physical attribute for process change than conventional bulk/tap density. Further, the tensile strength of SD particle compacts correlates with the particle wall thickness, and this is likely caused by the larger interparticle contact area generated by more deformation of particles with thinner walls. The knowledge gained here can help enable SD particle engineering and drug product with more robust process and optimized performance.

Melting at the inter-particle contacts during Spark Plasma Sintering: Direct microstructural evidence and relation to particle morphology

During Spark Plasma Sintering (SPS), electric current passing through the sample can cause specific effects not observed in the absence of current. We present microstructural evidence of the formation of melt at the inter-particle contacts during SPS of mechanically milled Ti–C–3Cu mixtures transforming into TiC–Cu composites. The shape of the composite particles acquired after ball milling is related to inter-particle melting during SPS. Particles with higher width/length ratios show a greater tendency to melt at the contacts. The reinforcing effect of TiC inclusions plays a key role in preserving the initial inter-particle contact areas small, as plastic flow at high temperatures was inhibited.

Effect of Nanopowder Addition on the Sintering of Water-Atomized Iron Powder

A promising method of improving the densification of powder metallurgical steel components is to blend nanopowder with the otherwise typically used micrometre-sized powder. The higher surface-to-volume ratio of nanopowder is hypothesized to accelerate the sintering process and increase the inter-particle contact area between the powder particles. This is supposed to enhance the material transport and improve the densification. In the present investigation, water-atomized iron powder (− 45 μm) was mixed separately with pure iron and low-carbon steel nanopowder, each at a ratio of 95 to 5 pct. These powder mixes were compacted at different pressures (400, 600 and 800 MPa) and then sintered at 1350 °C in a pure hydrogen atmosphere. The sintering behavior of the powder blend compacts was compared to that of the compact with micrometre-sized powder only. Densification commenced at much lower temperatures in the presence of nanopowder. To understand this, sintering at intermittent temperatures such as 500 °C and 700 °C was conducted. The fracture surface revealed that the nanopowder was sintered at between 500 °C and 700 °C, which in turn contributed to the densification of the powder mix at the lower temperature range. Based on the sintering experiments, an attempt was made to calculate the activation energy and identify the associated sinter mechanism using two different approaches. It was shown that the first approach yielded values in agreement with the grain-boundary diffusion mechanism. As the nanopowder content increased, there was an increase in linear shrinkage during sintering.

A dilatometry study of the influence of green density on anisothermal and isothermal shrinkage of plain iron green parts

ABSTRACT The influence of green density between 6.5 and 7.3 g cm−3 on the anisothermal and isothermal shrinkage of atomized plain iron was investigated by dilatometry. The geometrical activity deriving from the extension of the interparticle contact areas and the structural activity provided by the defectiveness of the interparticle contacts promote anisotropic anisothermal shrinkage starting from 500°C up to the bcc to fcc iron transformation. It displays a minimum at 6.9 g cm−3, resulting from the combined effects of the thermodynamic driving force and of geometrical and structural activity. Anisothermal shrinkage is caused by an anisotropic increase in the internal radius of the neck. Anisotropic isothermal shrinkage is smaller than the anisothermal one and is almost independent on green density. No anisothermal shrinkage was observed on the tapped powder, demonstrating that anisothermal shrinkage in green specimens is due to geometrical and to structural activity introduced by prior cold compaction.

Network analysis of heat transfer in sphere packings

Porosity-dependent models can be used to predict the effective thermal conductivity (ETC) of particulate materials. However, they cannot directly account for microstructural features such as particle connectivity and interparticle contact area. Complex network theory can be used to extract network features as microstructural characteristics. However, these features have not been used to study heat transfer. In this work, both contact network and thermal networks are constructed for mono-disperse and poly-disperse sphere packings. Network features are extracted using complex network theory and machine learning techniques are applied to investigate the correlation between these features and the ETC. The most relevant thermal and contact network features for predicting thermal conductivity are identified. The network features capturing both interparticle connectivity and contact quality, such as “weighted degree”, show high correlation with ETC. Furthermore, random forest regression results show that involving multi-network features in a model enhances the accuracy in predicting ETC.

Geotechnical characteristics of polystyrene treated sand

Many polymeric materials are recently used in geotechnical practice for enhancing the engineering properties of soils. Among the various polymers, this study aims at investigating the geotechnical properties of silica sand coated with polystyrene(PS), which is rarely studied in geotechnical engineering. The polystyrene coated sand was prepared by polymerizing styrene monomer on the surface of silanized sand with median diameter of 0.467 mm. Testing specimens were prepared at 3 different initial relative densities (30, 50 and 70%) by air pluviation. Comprehensive experiments, including one-dimensional compression test with bender elements and triaxial test, were performed to observe the change in geotechnical properties due to the coating of PS on sand surface. The results demonstrate that the adsorbed polymer plays different roles according to strain levels. At very small strain, the polymer on the sand surface may increase the interparticle contact area by applying additional adhesion force between soil particles, leading to an increase in Gmax. However, with an increase in strain level, the polymer will act as the lubricant between sand particles; therefore, the coated sand can show increased compression index and decreased friction angle.

Sintering shrinkage of uniaxial cold compacted iron: a new shrinkage kinetic equation accounting for the microstructure of green parts

ABSTRACTA new shrinkage kinetic equation accounting for the extension of the interparticle contact areas is proposed. The mass transport mechanism responsible for shrinkage is bulk diffusivity. Shrinkage increases on increasing the internal neck radius that represents the geometrical activity in sintering of prior cold compacted powders.