Low Particle Volume Fractions Research Articles

Insights into particle dispersion and damage mechanisms in functionally graded metal matrix composites with random microstructure-based finite element model

This study investigates the impact of Al2O3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathrm {Al_2O_3}$$\\end{document} particle volume fraction and distribution on the deformation and damage of particle-reinforced metal matrix composites, particularly in the context of functionally graded metal matrix composites. In this study, a two-dimensional nonlinear random microstructure-based finite element modeling approach implemented in ABAQUS/Explicit with a Python-generated script to analyze the deformation and damage mechanisms in AA6061-T6/Al2O3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathrm{AA6061\\mbox{-}T6/Al_2O_{3}}$$\\end{document} composites. The plastic deformation and ductile cracking of the matrix are captured using the Gurson–Tvergaard–Needleman model, whereas particle fracture is modelled using the Johnson–Holmquist II model. Matrix-particle interface decohesion is simulated using the surface-based cohesive zone method. The findings reveal that functionally graded metal matrix composites exhibit higher hardness values (HRB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{HRB}$$\\end{document}) than traditional metal matrix composites. The results highlight the importance of functionally graded metal matrix composites. Functionally graded metal matrix composites with a Gaussian distribution and a particle volume fraction of 10% achieve HRB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{HRB}$$\\end{document} values comparable to particle-reinforced metal matrix composites with a particle volume fraction of 20%, with only a 2% difference in HRB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{HRB}$$\\end{document}. Thus, HRB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{HRB}$$\\end{document} can be improved significantly by employing a low particle volume fraction and incorporating a Gaussian distribution across the material thickness. Furthermore, functionally graded metal matrix composites with a Gaussian distribution exhibit higher HRB\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{HRB}$$\\end{document} values and better agreement with experimental distribution functions when compared to those with a power-law distribution.

Ionic strength effect on the structure and dynamics of colloidal dispersions with weak attractive interactions

We present a macro- and microrheological study of the effect of ionic strength on the phase behavior, structure and flow properties of colloidal dispersions stabilized by short-range repulsive interactions inferred via co-polymerization of weak acid groups. We investigated the impact of ionic strength, by varying the concentration of natrium chloride (NaCl), on dispersions with only repulsive interactions, but also when additional attractive depletion forces are present due to added non-absorbent polymer, namely polyethyleneoxide (PEO). For dispersions with only repulsive electrosteric interactions, at low particle volume fractions (ϕ < 0.4), increasing ionic strength hardly affects the relative viscosity whereas at higher particle volume fractions, a decrease in viscosity is observed due to a reduced range of electrosteric repulsion between particles, corresponding to a reduction of the effective particle volume fraction ϕeff. For dispersions including attractive interactions, at volume fractions ϕ = 0.45 below the hard sphere freezing point (ϕc=0.5), independently of the ionic strength, the bulk viscosity increases monotonically with increasing PEO concentration due to the transition from a fluid to a fluid/crystalline and finally to a gel state. However, the increase in ionic strength shifts the concentrations of both phase transitions to lower polymer concentrations, indicating that in presence of salt a weaker attraction is required to induce these transitions. At ϕ=0.52, just above ϕc, for dispersions without added salt, broadening of the fluid-crystalline coexistence regime, due to added PEO, results in a viscosity minimum corresponding to different size and packing density of the crystalline regions as observed earlier in Weis et al. [1]. When salt is added, the initial state for dispersions without PEO is a fluid state due to the reduction of ϕeff and the addition of a small amount of PEO leads to an increase in bulk viscosity due to the formation of large crystals for dispersions containing 10 mM NaCl and a network of small, dense crystals of size ≈10 µm when 100 mM NaCl is added. At ϕ=0.54, a result similar to ϕ=0.52 is obtained for dispersions without added salt, whereas in presence of salt, we find that the fluid/crystalline coexistence regime narrows down as the range of electrosteric repulsion decreases and the addition of PEO results in gel formation and gels become more uniform with increasing attraction strength. These investigations demonstrate how superimposed short range electrosteric repulsion and weak depletion attraction affect microstructure and flow behavior of colloidal dispersions.

3-D numerical simulation of the heat transfer of a fluidized bed with a horizontal tube bundle and Geldart D particles

In the present study, a numerical simulation is performed to analyse hydrodynamic and heat transfer of a fluidized bed in a vertical channel. As a novelty, MP−PIC method is applied to 3-D tube bundles immersed in a fluidized bed with Geldart D particles. The main results are compared and validated using the experimental results published in the literature.In both tube bundle distributions, the lowest heat transfer coefficients were obtained in the top region of the tube, which represents approximately 58% of the time average heat transfer coefficient of the surface tube. This behaviour differs at the bottom and sides, where particles are continuously being replaced by other particles, resulting in low particle volume fractions and higher heat transfer coefficients.Analysing each tube arrangement for the cases with the same gas velocity and particle diameter, the results numerically obtained were consistent with the experimental findings. The present study found that the time average heat transfer coefficient for the staggered arrangement was approximately 6%, 5% and 1.6% higher than that in-line, for the particle diameter of 1400, 1600 and 1850 μm, respectively. Some discrepancies can be highlighted when comparing the experimentally and numerically obtained time average heat transfer coefficients, with maximum differences close to 18%, which correspond to the cases with the highest gas velocity and particle diameter (1.71 m/s, 1850 μm).

Stress-stress correlations reveal force chains in gels.

We investigate the spatial correlations of microscopic stresses in soft particulate gels using 2D and 3D numerical simulations. We use a recently developed theoretical framework predicting the analytical form of stress-stress correlations in amorphous assemblies of athermal grains that acquire rigidity under an external load. These correlations exhibit a pinch-point singularity in Fourier space. This leads to long-range correlations and strong anisotropy in real space, which are at the origin of force-chains in granular solids. Our analysis of the model particulate gels at low particle volume fractions demonstrates that stress-stress correlations in these soft materials have characteristics very similar to those in granular solids and can be used to identify force chains. We show that the stress-stress correlations can distinguish floppy from rigid gel networks and that the intensity patterns reflect changes in shear moduli and network topology, due to the emergence of rigid structures during solidification.

Improved modelling of interfacial terms in the second-moment closure for particle-laden flows based on interface-resolved simulation data

Correlations for the interfacial terms in the fluid dissipation rate equation and Reynolds stress equations are established for particle-laden flows, based on data from the interfaced-resolved direct numerical simulations of particle sedimentation in a periodic domain at a density ratio ranging from 0.01 to 1000, a particle concentration ranging from 2.3 % to 30.2 % and a particle Reynolds number below 250. The correlations for the mean drag and the pseudo-turbulent kinetic energy are also reported, which are used for the modelling of the interfacial term in the fluid dissipation rate equation. The interfacial term correlations obtained are then incorporated in the Reynolds stress model (RSM) (i.e. second-moment closure) for the simulation of vertical turbulent channel flows laden with the finite-size particles at relatively low particle volume fractions. The results show that the RSM with new interfacial term correlations can quantitatively predict particle-induced turbulence enhancement or suppression in vertical channel flows.

The Viscosity and Self-Diffusion of Some Real Colloidal Ferrofluids

One primary concern in colloid science is understanding the relationship of its macroscopic rheology and diffusion behavior with the observed microscopic arrangements of the nanoparticles in the fluid. This manuscript addresses the study of these dynamical properties through a first-principle stochastic method. Both properties directly relate to the observed fluid structure factor, which depends on a few known material parameters. However, in the literature, this static quantity is reported up to the first prominent peak of its small momentum transfer of the scattered radiation, leading to inaccurate determination of the transport properties. Here, it is proposed to use the rescaled mean spherical approximation under the requirement of fitting the experimental data of the structure beyond the dependence of more significant wave numbers. The predicted viscosity agrees with the observed ones at a low volume fraction of particles for ferrofluids dispersed in polymer solvents. This rheological quantity is inversely related to the self-diffusion coefficient of a tracer particle.

Experimental Analysis on the Dependence of the Capacitance of Magnetorheological Fluids on Frequency

The capacitance characteristics of magnetorheological fluids (MRFs) were studied experimentally based on simulation analysis. The nonlinear relationship between the capacitance of MRFs and electric field frequency was measured by the self-made circuit device. The effects of magnetic induction intensity and particle volume fraction on the capacitance characteristics of MRFs were investigated. The results show that the nonlinear dependence of the capacitance of an MRF on frequency induced by the effect of tunnel current decreases with the increase in frequency. The capacitance of an MRF is directly related to the particle structures. The capacitance of the MRF with a chain particle structure is greater than that of the MRF with a random particle distribution. The smaller the clearance between the adjacent particles, the greater the capacitance of the MRF. The network particle structure and particle contact will reduce the capacitance of an MRF. The capacitance of an MRF increases with the increment of external magnetic field. The capacitance of an MRF with higher particle volume fraction is smaller than that of an MRF with lower particle volume fraction.

Drag model from interface-resolved simulations of particle sedimentation in a periodic domain and vertical turbulent channel flows

A drag correlation is established for laminar particle-laden flows, based on data from the interfaced-resolved direct numerical simulations (IR-DNS) of particle sedimentation in a periodic domain at density ratio ranging from 2 to 1000, particle concentration ranging from 0.59 % to 14.16 %, and particle Reynolds number below 132. Our drag decreases slightly with increasing density ratio when the other parameters are fixed. The drag correlation is then corrected to account for the turbulence effect by introducing the relative turbulent kinetic energy, from the IR-DNS data of the upward turbulent channel flows laden with the particles larger than the Kolmogorov length scale at relatively low particle volume fractions. A drift velocity model is developed to obtain the effective slip velocity from the interphase mean velocity difference for the vertical turbulent channel flow by considering the effects of particle inertia, particle concentration distribution and large-scale streamwise vortices.

Interparticle and Brownian forces controlling particle aggregation and rheology of silicate melts containing platinum-group element particles

We study the rheology of silicate melts containing platinum-group element (PGE) particles. They exhibit a shear-thinning behaviour, an intense aggregation tendency, and an anomalously high apparent viscosity in the low shear rate limit, even at very low particle volume fraction. Using a compilation of published experimental data, we analyse these effects in three steps. Firstly, we observe that the viscosities of these suspensions are much higher than those of natural silicate crystal-bearing melts for low shear rate regimes. Secondly, we demonstrate that the viscosities at low shear rate limit cannot be estimated by classical rheological models but rather may be understood as the result of particle aggregation, trapping dead fluid, and thereby increasing the effective particle volume fraction. Finally, we scale the critical shear rates for shear-thinning using a Peclet number analysis—invoking a competition between random thermal particle motion and hydrodynamic shearing motion—and, using an empirical extension, we additionally account for the particle–particle interaction energetics. We propose a framework in which the rheology of this family of particle-bearing melts can be predicted, and demonstrate that at low Peclet numbers, PGE-bearing particle aggregation is driven by interparticle forces and Brownian motion.

Magnetic susceptibility of ferrofluids determined from diffusion coefficient of a tracer

Linear response methods allow studying magnetic susceptibility relaxation in isotropic colloidal magnetic fluids. We show a relationship between the susceptibility of macroscopic magnetization at thermal equilibrium and the diffusion constant of a tracer particle. The comparison of the predicted frequency-dependent susceptibility with computer simulations shows their agreement. Besides, at a low concentration of particles, it has the expected Debye behavior. However, the initial susceptibility yields only the qualitative trends of the existing experiments at a low volume fraction of particles and its temperature dependence.

Interface design and engineering in Al matrix composite with low CTE and high strength reinforced by barium strontium titanate particles

Al matrix composites with both low coefficient of thermal expansion (CTE) and excellent mechanical property has important application value in the fields of aerocraft, precise instruments. However, obtaining both low CTE and high strength simultaneously is still a challenge. In this work, huge negative thermal expansion effect derived from ferroelectric-paraelectric phase transformation of barium strontium titanate (BST) ceramic is designed and utilized in Al matrix. Low CTE is obtained in BST/Al composite at the condition of a low volume fraction of BST particles. Annealing treatment is carried out to improve the interface bonding and to reduce residual stress, therefore the negative thermal expansion effect in the process of phase transformation of the BST particles is more thoroughly brought into play, and then the CTE of BST/Al composite is further decreased. Finally, the average CTE of BST/Al composite annealed at 600 °C for 2 h between room temperature and 250 °C reaches as low as 12.04 × 10−6 °C −1, while achieving a high compressive strength as high as 800 MPa. The microstructure around the interface and the phase transformation behavior are also investigated.

Experimental investigations on mechanical strength of concrete using nano-alumina and nano-clay

The current work aims to advance the mechanical characteristics of concrete by replacing cement with a low volume fraction of nano-alumina particles and fine aggregate with nano-clay. The initial tests had piloted on the conventional concrete using varying fractions of nano-alumina particles in order to determine the optimal nano-alumina proportions for various curing times (1 week, 4 weeks, and 8 weeks). Then, the accompanying experiments using varied volume fractions of nano-clay with the determined optimal proportion of concrete nano-mixture were conducted. The results indicated that the optical volume percentage in the concrete nano-mixture should be 2.0 percent nano-alumina particles and 3.0 percent nano-clay in order to achieve the greatest splitting tensile strength, and compressive strength. With the assistance of nano-alumina particles and nano-clay, the mechanical characteristics of the concrete were improved by around 30% effectively.

Validation of a two-layer depth-averaged model by comparison with an experimental dilute stratified pyroclastic density current

Numerical results of a two-layer depth-averaged model of pyroclastic density currents (PDCs) were compared with an experimental PDC generated at the international eruption simulator facility (the Pyroclastic flow Eruption Large-scale Experiment (PELE)) to establish a minimal dynamical model of PDCs with stratification of particle concentrations. In the present two-layer model, the stratification in PDCs is modeled as a voluminous suspended-load layer with low particle volume fractions (lesssim {10}^{-3}) and a thin basal bed-load layer with higher particle volume fractions (sim {10}^{-2}) on the basis of the source condition in the experiment. Numerical results for the suspended load quantitatively reproduce the time evolutions of the front position and flow thickness in the experimental PDC. The numerical results of the bed-load and deposit thicknesses depend on an assumed value of settling speed at the bottom of the bed load ({W}_{mathrm{sH}}). We show that the thicknesses of bed load and deposit in the simulations agree well with the experimental data, when {W}_{mathrm{sH}} is set to about 1.25times {10}^{-2} m/s. This value of the settling speed is two orders of magnitude smaller than that predicted by a hindered-settling model. The small value of {W}_{mathrm{sH}} is considered to result from decreasing in the effective deposition speed due to the erosion process accompanied by saltating/rolling of particles at the bottom of the bed load.

Experimental investigation of particle transport and distribution in a vertical nonplanar fracture

Particle transport in a vertical nonplanar fracture is a typical but poorly understood element in hydraulic fracturing. Particle-fluid flow in a nonplanar fracture with a narrowing width is investigated experimentally by a laboratory-scale slot, and the relevant transport mechanisms are compared with that in the planar slot. The effects of fluid flow rate, particle density, particle size, and particle volume fraction on particle distribution are investigated. The results indicate that the narrowing width complicates the slurry flow and lowers the bed coverage area. The vortex flow appears at the contraction of the cross-section as the bed grows to a threshold height and resuspends more particles further into the slot. An irregular bed with a descending stepped surface is formed due to non-uniform placement. Smaller size sands injected at a high flow rate and a low particle volume fraction build up a smaller bed. Larger and denser particles would reverse the trend. A rational model expressed by four dimensionless numbers is developed by the linear regression method to predict the coverage percentage of the particle bed. The model and experimental results provide directions to quantitatively evaluate the particle transport and distribution in a nonplanar fracture.

Radiative property model for non-gray particle based on dependent scattering

The radiative heat transfer of the particles has been investigated based on the gray body and the independent scattering. However, the radiative properties of the particles are strongly wavelength dependent and interact with each other with the increase of particle concentration. In order to indicate the radiative heat transfer under the high particle volume fraction, the radiation heat transfer model of non-gray particle is developed in this paper, which is based on the ideology of the weighted sum of gray gases (WSGG) model and the full-spectrum correlated k-distribution (FSCK) model, and the dependent scattering of particles is considered. For a one-dimensional plane-parallel slab system, the WSCK (the Weighted Sum of Gray Particles based on the full-Spectrum Correlated k-distribution) model is verified. Compared with the modified LBL model based on Mie theory and dependent scattering theory, the maximum errors of the dependent scattering WSCK (WSCKD) model are about 3.3% for the radiative heat flux and 11.5% for the radiative source term under non-isothermal and inhomogeneous conditions. The radiative heat flux and radiative source term by the WSCKD model and the independent scattering WSCK (WSCKI) model are almost identical for the low particle volume fraction and the calculation accuracy is higher by the WSCKD model on the industrial scale. For the high particle volume fraction, the WSCKD model is more accurate, especially for particle systems with a large percentage of small particles or a relatively high-volume fraction. In addition, the radiative heat transfers of gases, particles and gas-particle mixtures at different one-dimensional scales are examined, highlighting the crucial role of particle radiative property model in large furnaces.

Direct Numerical Simulation of Sediment Transport in Turbulent Open Channel Flow Using the Lattice Boltzmann Method

The lattice Boltzmann method is employed to conduct direct numerical simulations of turbulent open channel flows with the presence of finite-size spherical sediment particles. The uniform particles have a diameter of approximately 18 wall units and a density of ρp=2.65ρf, where ρp and ρf are the particle and fluid densities, respectively. Three low particle volume fractions ϕ=0.11%, 0.22%, and 0.44% are used to investigate the particle-turbulence interactions. Simulation results indicate that particles are found to result in a more isotropic distribution of fluid turbulent kinetic energy (TKE) among different velocity components, and a more homogeneous distribution of the fluid TKE in the wall-normal direction. Particles tend to accumulate in the near-wall region due to the settling effect and they preferentially reside in low-speed streaks. The vertical particle volume fraction profiles are self-similar when normalized by the total particle volume fractions. Moreover, several typical transport modes of the sediment particles, such as resuspension, saltation, and rolling, are captured by tracking the trajectories of particles. Finally, the vertical profiles of particle concentration are shown to be consistent with a kinetic model.

Two modes of cluster dynamics govern the viscoelasticity of colloidal gels.

Colloidal gels formed by strongly attractive particles at low particle volume fractions are composed of space-spanning networks of uniformly sized clusters. We study the thermal fluctuations of the clusters using differential dynamic microscopy by decomposing them into two modes of dynamics, and link them to the macroscopic viscoelasticity via rheometry. The first mode, dominant at early times, represents the localized, elastic fluctuations of individual clusters. The second mode, pronounced at late times, reflects the collective, viscoelastic dynamics facilitated by the connectivity of the clusters. By mixing two types of particles of distinct attraction strengths in different proportions, we control the transition time at which the collective mode starts to dominate, and hence tune the frequency dependence of the linear viscoelastic moduli of the binary gels.

Investigation on the thermal performance of a sodium sulfate CFB evaporator

To solve the serious scaling problem and low thermal performance in the evaporation process of sodium sulfate solution, a circulating fluidized bed (CFB) evaporator is designed and built to study the effect of particle type and size on its thermal performance based on our previous research. Different sizes of SiC, glass bead (GB), and polyformaldehyde (POM) particles are selected as inert particles. A series of experiments is performed with different operating parameters. Results showed that the thermal enhancement effect relates to particle type and size. At low particle volume fraction ε, the effect is in the order of SiC, POM, and GB particles. At high particle volume fraction ε, the effect is in the order of SiC, GB, and POM particles. In addition, the enhancement effect of SiC1 is less than that of SiC2. For GB particles, the enhancing factors E first decrease and then increase with the increase in particle size. For POM particles, the enhancing factors E are affected by the operating parameters. 3D diagram of enhancing factors E are established. The findings of this study may widely facilitate applying CFB technology to sodium sulfate industry.

The effects of external force and electrical field on the agglomeration of Fe3O4 nanoparticles in electroosmotic flows in microchannels using molecular dynamics simulation

Recent progress in nanoparticle construction can be seen as a breakthrough in increasing heat transfer methods. The small size of particles and low volume fraction of particles leads to solving agglomeration and pressure drop problems and reduce the cost of storing and transporting nanofluids. Molecular dynamics simulation is one of the essential branches of computational physics that can predict various structures' atomic behavior. In this study, the effects of external electrostatic force and external electrical field on the density, velocity, temperature of atomic structures, and agglomeration of Fe3O4 nanoparticles in a copper microchannel are investigated. The results of the physical properties of this structure are estimated using molecular dynamics simulation and LAMMPS software. The results show that with increasing the applied external electrostatic force the maximum velocity is converged to 0.0071 Å /ps. Also, adding an external electrical field to the simulated nanofluid, the maximum values of density, velocity, and temperature are estimated to 1.32 g/cm3, 0.0078 Å /ps, and 345 K, respectively. The external electrical field has a significant and essential role in the agglomeration process in atomic structures. Finally, it is observed that by increasing the external electrical field, the time required for the agglomeration process increases to 2.26 ns.

Enhancing High-Temperature Creep Resistance of &lt;i&gt;In Situ&lt;/i&gt; TiAl-Based Matrix Composite by Low Volume Fraction of Ti&lt;sub&gt;2&lt;/sub&gt;AlC Particles

Samples of TiAl-based matrix in-situ composite with the chemical composition Ti-46.4Al-5.1Nb-1C-0.2B (at.%) reinforced with a low volume fraction of primary Ti2AlC particles were prepared by vacuum induction melting in graphite crucibles and centrifugal casting into graphite moulds. The hot isostatic pressing (HIP) of the as-cast samples and subsequent heat treatments leads to the formation of equiaxed grains with fully lamellar α2(Ti3Al) + γ (TiAl) microstructure and uniformly distributed Ti2AlC and TiB particles. The minimum creep rates of the in-situ composite are significantly lower compared to those measured for the counterpart low carbon benchmark alloy with the chemical composition Ti-47Al-5.2Nb-0.2C-0.2B (at.%) at temperatures ranging from 800 to 900 °C and applied stress of 200 MPa. The studied in-situ composite shows also significantly improved creep resistance compared to that of some TiAl-based alloys with fully lamellar, convoluted and pseudo-duplex microstructures at a temperature of 800 °C and applied stress of 200 MPa.