Volume Fraction Of Small Particles Research Articles

Wall-resolved large eddy simulation of mixed-size sand-laden flow

Most of the existing numerical studies on wind-blown sand flow simplify sands into single-size particles, whereas natural wind-blown sand flow is a two-phase flow with mixed-size particles, thus, the simulation of mixed-size sand-laden flow is necessary. In the present work, wall-resolved large eddy simulations of mixed-size sand-laden flows are realized. Each sand in the wind field is tracked using the Lagrangian point-particle model. The transport characteristics of sand particles in mixed-size sand-laden flow are investigated under the premise of considering bed erosion. Considering the significant influence of sand-bed collision on simulation, the splash function is modified in the present simulation according to the previous experimental results. It reveals that in mixed-size sand-laden flow, the fraction of rebound sand particles in all the saltation particles is approximately 0.6, which is twice times of the ejected sand particles, and the modification of the sand rebound angle greatly affects the simulation results of mixed-size sand-laden flow. Meanwhile, the mean size of the saltation sand particles decreases with height and is 20% lower at the top of the saltation layer than that near the sand bed in the present simulation. Further analysis by grouping of sands with their size shows that the sand transport intensity of small sands decreased more rapidly with increasing height. The volume fraction and sand transport intensity of small sand particles exceed those of medium and large sand particles at heights y/δ = 0.05 and y/δ = 0.1.

An experimental approach to investigate the viscoelastic and rheological behavior of polydisperse glass suspensions

Polydispersity is an essential factor in characterizing suspensions, specifically in industrial processes. In the present work, we report the viscosity of non-colloidal polydisperse glass suspensions for the first time and study the predictability of log-transformed quadratic viscosity equations over a wide range of blending ratios at a constant total volume fraction of solid particles. The viscosity and viscoelasticity measurement of multimodal suspensions was carried out by mixing three monomodally distributed solid particle suspensions with a relatively narrow size distribution to prepare bidisperse and tridisperse suspensions. The results showed a good agreement between experimental and predicted viscosity data for multimodal suspensions, making the generalized model a good alternative to describe the viscosity of polydisperse mixtures. The diameter ratio of large-to-small particles and the volume fraction of small particles in bidisperse systems strongly affected the viscoelastic behavior of multimodal suspensions. In addition, the dynamic rheology measurement showed that the storage modulus was independent of frequency, while a linear frequency dependence of loss modulus was observed for multimodal suspensions. In the case of polydisperse suspensions, this yield stress and dimensionless elastic modulus increased by declining the particle size ratio and increasing the volume fraction of small particles in bidisperse subsystems.

Determination of parameters for self-stratification in bimodal colloidal coatings using Raman depth profiling

In waterborne mixtures of colloidal particles with differing sizes, the spontaneous stratification of one species of particle in a coating – driven by diffusiophoresis - offers the possibility to tailor the surface properties. However, despite strong research interest in stratification in recent years, the acceptable range of experimental parameters has not been fully explored, and the extent of stratification that is achievable has not yet been quantified. Here, we study the stratification of bimodal mixtures of waterborne polyurethane particles mixed with larger acrylic particles. We use ultra-low angle microtoming to prepare cross-sections of coating samples and analyse compositions quantitatively with Raman mapping. We use this method to obtain high-resolution depth profiles of the polyurethane phase in the coating with spacing between measurements corresponding to a few tens of nm. We experimentally test a model of diffusiophoresis and observe stratification when the processing parameters (evaporation rates, film thickness, and volume fraction of small particles) fall within the required range. Samples that exhibit stratification have top layer thicknesses on the order of tens of μm, which is a significant depth for exploitation in coatings aiming to modify surface properties. To guide the design of coatings in applications, we draw on the model to define the range of parameters in which self-stratification is expected. Our results provide a fundamental understanding that will enable the fabrication of tailored coatings in which the properties of the surface differ from the bulk material.

The influence of Einstein's effective viscosity on sedimentation at very small particle volume fraction

We investigate the sedimentation of identical inertialess spherical particles in a Stokes fluid in the limit of many small particles. It is known that the presence of the particles leads to an increase of the effective viscosity of the suspension. By Einstein's formula this effect is of the order of the particle volume fraction ϕ. The disturbance of the fluid flow responsible for this increase of viscosity is very singular (like |x|−2). Nevertheless, for well-prepared initial configurations and ϕ→0, we show that the microscopic dynamics is approximated to order ϕ2|log⁡ϕ| by a macroscopic coupled transport-Stokes system with an effective viscosity according to Einstein's formula. We provide quantitative estimates both for convergence of the densities in the p-Wasserstein distance for all p and for the fluid velocity in Lebesgue spaces in terms of the p-Wasserstein distance of the initial data. Our proof is based on approximations through the method of reflections and on a generalization of a classical result on convergence to mean-field limits in the infinite Wasserstein metric by Hauray.

Numerical simulation of electric field in cylindrical silo based on non-uniform electrostatic charge distribution caused by particle segregation

Size-induced particle segregation during the silo filling process greatly changes the electrostatic charge distribution, influencing the occurrence of the incendiary electrostatic discharge. However, few studies concern the electric field distribution in this condition. In this work, the non-uniform space charge density distribution obtained in DEM simulation of the particle segregation was used for simulating the electric field. A comparison between the electric fields of segregation and uniform cases was conducted. Results show that the electric field of the segregation case is similar to that of the uniform case in the monopolar charging system. While in the bipolar charging system, the electric field of the segregation case can become different from that of the uniform case due to the bipolar space charge density in particle layers. The neutralization of the charges carried on large and small particles can result in the decline of the electric field. In the case with low net charges, the probability of the electrostatic discharge can be more than three times higher than that in uniform cases once the particle segregation happens. Moreover, the enhancement effect of the particle segregation on the electrostatic discharge can be stronger when the volume fraction of small particles is less than 75%. Reducing the charging efficiency of particles and the repose angle and avoiding particle segregation are preferable approaches to lower the risk of the electrostatic discharge.

Analysis of Tortuosity in Compacts of Ternary Mixtures of Spherical Particles.

Herein, an approach is proposed to analyze the tortuosity of porous electrodes using the radical Voronoi tessellation. For this purpose, a series of particle compacts geometrically similar to the actual porous electrode were generated using discrete element method; the radical Voronoi tessellation was constructed for each compact to characterize the structural properties; the tortuosity of compact porous structure was simulated by applying the Dijkstra’s shortest path algorithm on radical Voronoi tessellation. Finally, the relationships were established between the tortuosity and the composition of the ternary particle mixture, and between the tortuosity and the radical Voronoi cell parameters. The following correlations between tortuosity values and radical Voronoi cell parameters were found: larger faces and longer edges of radical Voronoi cell leads to the increased fraction of larger values of tortuosity in the distribution, while smaller faces and shorter edges of radical Voronoi cell contribute to the increased fraction of smaller tortuosity values, being the tortuosity values more uniform with narrower distribution. Thus, the compacts with enhanced diffusion properties are expected to be obtained by packing particle mixtures with high volume fraction of small and medium particles. These results will help to design the well-packed particle compacts having improved diffusion properties for various applications including porous electrodes.

Rheology, packing and sintering behavior in dense suspension of multimodal spherical silica

Pursuing the limit of solid volume fraction of suspension and packing density of compacts is an important issue in industry such as ceramic processing. In present manuscript, the experiment results show that a very high solid volume content (82%) in suspension and a high packing density (92%) of compacts can be obtained, by using spherical particles to optimize particle size distribution. The proposed model can well predict the maximum solid fraction of mixtures at a given volume fraction of smaller particles. The correlation between viscosity and solid volume fraction could be expressed by an exponential equation. About the green bodies prepared from suspensions, the green density has important influence on sintered body density especially on the initial sintering stage. And dense sintered body with amorphous phase could be obtained at sintering temperature of 1100 °C.

Stress transmission in cemented bidisperse granular materials.

We analyze stress distributions in a two-dimensional bidisperse cemented granular packing for a broad range of the values of particle-size ratio, the volumes of large and small particles, and the amount of cementing matrix. In such textured porous materials, the stress concentration, which controls the fracture and fragmentation of the material under tensile loading or in grinding processes, reflects not only the porosity but also the contact network of the particle phase and the resulting stress chains. By means of peridynamic simulations under tensile loading, we show how both the texture and stress distribution depend on size ratio, volume ratio, and the amount of the cementing matrix. In particular, the volume fraction of the class of small particles plays a key role in homogenizing stresses across the system by reducing porosity. Interestingly, the texture controls not only the porosity but also the distribution of pores inside the system with its statistical variability, found to be strongly correlated with the homogeneity of stresses inside the large particles. The most homogeneous stress distribution occurs for the largest size ratio and largest volume fraction of small particles, corresponding to the lowest pore size dispersion and the cushioning effect of small particles and its similar role to the binding matrix for stress redistribution across the packing. At higher porosity, the tensile stresses above the mean stress fall off exponentially in all phases with an exponent that strongly depends on the texture. The exponential part broadens with decreasing matrix volume fraction and particle-size ratio. These correlations reveal the strong interplay between size polydispersity and the cohesive action of the binding matrix for stress distribution, which is significant for the behavior of textured materials in grinding operations.

Analysis of the effect of equal-channel angular pressing on the strength and electrical conductivity of low-alloyed alloys of the Cu-Cr-Zr system

The effect of equal-channel angular pressing (ECAP) on the strength and electrical conductivity of low-alloyed Cu-Cr-Zr alloys to identify conditions for the formation of states with high strength and electrical conductivity is considered. The increase in the content of alloying elements does not increase the strength of the alloys in the initial quenched state. After ECAP, their strength is increased by dislocations. It is shown that after ECAP of quenched samples, their specific resistances remain almost unchanged due to the increase in the length of the grain boundaries, the volume fraction of small particles of secondary phases and the segregation of alloying atoms from the matrix.

Investigation of Constant Volume and Constant Flux Initial Conditions on Bidensity Particle-Laden Slurries on an Incline

Particle-laden slurries are pervasive in both natural and industrial settings, whenever particles are suspended or transported in a fluid. Previous literature has investigated the case of a single species of negatively buoyant particles suspended in a viscous fluid. On an incline, three distinct regimes emerge depending on the particle concentration and inclination angle: settled (where particles settle and there is a pure fluid front), well-mixed (where particle concentration is constant throughout), and ridged (where a particle-rich ridge leads the flow). Recently, the same three regimes were also found for constant volume two species bidensity slurries. We extend the literature on bidensity slurries by presenting results on constant volume and a new type of initial condition: constant flux, where slurry is pumped onto the incline at a constant rate. We present front positions of the slurries and compare them to theoretical predictions. In addition, height profiles (film thicknesses) are also presented for the constant flux case, showing the distinct behavior of the ridged regime. We find that for constant flux conditions the settled regime forms for small particle volume fractions and inclination angles while the ridged regime forms for large corresponding values. Intermediate values of these two parameters are shown to produce a well-mixed regime. KEYWORDS: Thin Films; Particle-Laden Flow; Multiphase Fluids; Interfacial Flows; Particle Segregation

Suspension Taylor–Couette flow: co-existence of stationary and travelling waves, and the characteristics of Taylor vortices and spirals

Flow visualization and particle image velocimetry (PIV) measurements are used to unravel the pattern transition and velocity field in the Taylor–Couette flow (TCF) of neutrally buoyant non-Brownian spheres immersed in a Newtonian fluid. With increasing Reynolds number ($Re$) or the rotation rate of the inner cylinder, the bifurcation sequence in suspension TCF remains same as in its Newtonian counterpart (i.e. from the circular Couette flow (CCF) to stationary Taylor vortex flow (TVF) and then to travelling wavy Taylor vortices (WTV) with increasing $Re$) for small particle volume fractions ($\unicode[STIX]{x1D719}<0.05$). However, at $\unicode[STIX]{x1D719}\geqslant 0.05$, non-axisymmetric patterns such as (i) the spiral vortex flow (SVF) and (ii) two mixed or co-existing states of stationary (TVF, axisymmetric) and travelling (WTV or SVF, non-axisymmetric) waves, namely (iia) the ‘TVF$+$WTV’ and (iib) the ‘TVF$+$SVF’ states, are found, with the former as a primary bifurcation from CCF. While the SVF state appears both in the ramp-up and ramp-down experiments as in the work of Majji et al. (J. Fluid Mech., vol. 835, 2018, pp. 936–969), new co-existing patterns are found only during the ramp-up protocol. The secondary bifurcation TVF $\leftrightarrow$ WTV is found to be hysteretic or sub-critical for $\unicode[STIX]{x1D719}\geqslant 0.1$. In general, there is a reduction in the value of the critical Reynolds number, i.e. $Re_{c}(\unicode[STIX]{x1D719}\neq 0)<Re_{c}(\unicode[STIX]{x1D719}=0)$, for both primary and secondary transitions. The wave speeds of both travelling waves (WTV and SVF) are approximately half of the rotational velocity of the inner cylinder, with negligible dependence on $\unicode[STIX]{x1D719}$. The analysis of the radial–axial velocity field reveals that the Taylor vortices in a suspension are asymmetric and become increasingly anharmonic, with enhanced radial transport, with increasing particle loading. Instantaneous streamline patterns on the axial–radial plane confirm that the stationary Taylor vortices can indeed co-exist either with axially propagating spiral vortices or azimuthally propagating wavy Taylor vortices – their long-time stability is demonstrated. It is shown that the azimuthal velocity is considerably altered for $\unicode[STIX]{x1D719}\geqslant 0.05$, resembling shear-band type profiles, even in the CCF regime (i.e. at sub-critical Reynolds numbers) of suspension TCF; its possible role on the genesis of observed patterns as well as on the torque scaling is discussed.

Direct prediction of bidirectional reflectance by dense particulate deposits

To observe and study the effects of the volume packing density on polarimetric scattering by deposited particulate materials, a comparison is made between the vector radiative transport equation (VRTE) and the plane wave plane parallel (PWPP) models for the polarized bidirectional reflectance and transmittance from plane parallel layers of randomly distributed, wavelength–sized particles. Calculations have been performed on ice and mineral materials with refractive indices of m=1.31 and m=1.5+0.01i respectively. In these simulations, particle volume fraction ranges from around 0.05–0.3 for deposits consisting of spherical particles with size parameters of one and two.It is found that the PWPP model results converge to those predicted by the VRTE at small ( ∼ 5% or less) particle volume fractions. At higher volume fractions, the difference between the PWPP and VRTE results depends strongly on the particle size and refractive index, yet not so much on the optical thickness (equivalently, volume of particles per unit area of layer).PWPP simulation results of coherent backscattering effects – brightness opposition and polarization opposition effects – for ice and mineral particles are also represented. Their dependency on the particle volume fraction and particle size has been discussed.

The relationship between size-segregated particles migration phenomenon and combined membrane fouling in ultrafiltration processes: The significance of shear stress

Shear stress generated by cross flow velocity (CFV) was employed to investigate the migration of particles with varied sizes ranging from 0.5 µm to 100 µm in a laboratory flat sheet cell, which was implemented to investigate particle size segregation during the formation of combined membrane fouling. Computational fluid dynamic simulations of shear stress on the membrane surface over a range of CFV indicated that the peak value of shear stress (0.95–5.17 Pa) and average shear stress (0.267–1.873 Pa) all increased as the CFV increased (0.05–0.30 m/s). In case of the combine membrane fouling formed under short-term (6 h) filtration of mixed solution, the particle size segregation caused by shear stress was demonstrated using a laser scattering particle analyzer. In details, the volume fraction of small particles within cake layer was larger compared to that in the initial solution, whereas the large particles were susceptible to remain in the end solution. Under lower CFV, increasing shear stress could mitigate combined membrane fouling caused by organic matter and inorganic particles, however, under high CFV, increasing shear stress could enhance combined fouling, and the main reason was that higher shear stress increased the lift force exerted on particles, which could help large particles moving away from the membrane surface, leading to small particles depositing on the membrane surface and causing a severe membrane fouling. The implication is that the option of suitable hydrodynamic condition is preferable to reduce membrane fouling of mixed solution in the field of water treatment.

Effect of droplet evaporation on the flow structure and heat and mass transfer in a confined swirling gas-droplet flow downstream of a tube sudden expansion

The effect of flow swirl parameter and thermophysical properties of the droplet of water, ethanol, and acetone on the structure of turbulent flow and heat transfer in a gas-droplet flow was studied numerically. To describe the dynamics and heat and mass transfer of the two-phase flow, the Eulerian approach was used. The growth of the volume fraction of small particles on the tube axis is typical of a swirling flow because of their accumulation in the zone of reverse flows due to the turbophoresis force. It is shown that the addition of droplets leads to a signifi-cant increase in heat transfer (more than 2.5 times) at mass concentration of droplets ML1 = 0.1 in comparison with a single-phase swirling flow. Intensification of heat transfer with the use of ethanol droplets is higher than that for water droplets (approximately 10–20 %) and acetone (up to 65 %). When using the droplets of ethanol and acetone, the region of two-phase flow existence reduces, and the degree of suppression of carrier phase turbulence decreases. This is due to a more rapid evaporation of droplets of volatile liquids.

Investigating the effective interaction between silica colloidal particles near the critical point of a binary solvent by small angle neutron scattering.

An effective attractive potential can be introduced between colloidal particles dispersed in a binary solvent when the solvent condition approaches its demixing temperatures. Despite the debate of the physical origins of this effective attraction, it is widely termed as the critical Casimir force and is believed to be responsible for the colloidal stability in a wide range of particle concentration at both critical and near-critical solvent concentrations. Here, we study the effective attraction and equilibrium phase transition of charged spherical silica particles in the binary solvent of 2,6-lutidine and water as a function of the particle volume fraction and temperature at the critical solvent concentration. By analyzing our small angle neutron scattering (SANS) data, we found that at a relatively small particle volume fraction, the density fluctuation introduced attraction between silica particles can be satisfactorily explained by the function form commonly used for the critical Casimir interaction. However, at large silica particle volume fractions, an additional long range attraction has to be introduced to satisfactorily fit our SANS data and explain the large shift of the phase transition temperature. Therefore, while at relatively low volume fractions, the solvent introduced attraction may be dominated by the critical Casimir force, the physical mechanism of the effective attraction at large particle volume fractions seems to be different from the critical Casimir force. Furthermore, the range of this long range attraction is consistent with a recently proposed new theory, where the attraction can be introduced by the solvent capillary condensation between particles. We also demonstrate that the reduced second virial coefficient close to the particle phase transition is similar to the values of the binodal transition of the sticky hard sphere system.

Effect of arrangement of nano and micro barium titanate (BaTiO3) particles on the enhanced dielectric constant of high‐density polyethylene (HDPE)/BaTiO3

ABSTRACTThe aim of this study is to improve the dielectric and mechanical properties of HDPE/BaTiO3 composites by binary BaTiO3 particles, when the volume fraction of BaTiO3 is constant. In this study, it was found that the pack density of binary BaTiO3 particles in HDPE/BaTiO3 composite relies on particle ratio and volume fraction of small particles. It is found that the addition of 50 vol % 1600 nm BaTiO3 particles can boost the dielectric constant of HDPE control from 2 to 30 (14 times higher) at 40 Hz and 19 (8.5 times higher) at 40 MHz, respectively. When the particle ratio was 4, the substitution of 10 vol % 1600 nm BaTiO3 particles by 10 vol % 400 nm BaTiO3 particles can further enhance the dielectric constant of HDPE/L‐BT (10/10) from 30 to 50 (67% increase) at 40 Hz and from 19 to 42 (121% increase) at 40 MHz, respectively, without greatly influencing the volume resistivity of HDPE composites. In addition, the thermal conductivity of HDPE with binary BaTiO3 particles were all above 2.0 W/(m•K). © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018, 56, 1101–1108

Effect of particle size ratio and contribution of particle size fractions on micromechanics of uniaxially compressed binary sphere mixtures

This paper is an extension of the recent work of Wiącek (Granul Matter 18:42, 2016), wherein geometrical parameters of binary granular mixtures with various particle size ratio and contribution of the particle size fractions were investigated. In this study, a micromechanics of binary mixtures with various ratio of the diameter of small and large spheres and contribution of small particles was analyzed using discrete element simulations of confined uniaxial compression. The study addressed contact normal orientation distributions, global and partial contact force distributions and pressure distribution in packings of frictional spheres. Additionally, the effect of particle size ratio and contribution of particle size fractions on energy dissipation in granular mixtures was investigated. The particle size ratio in binary packings was chosen to prevent small particles from percolating through bedding. The bimodality of mixtures was found to have a strong effect on distribution of contact normal orientation and distribution of normal contact forces in binary mixtures. Stress transfer in binary packing was also determined by both, particle size ratio and volume fraction of small particles. Dissipation of energy was higher in mixtures with higher particle size ratios and decreased with increasing contribution of small spheres in system.

Van de Hulst Essay: The DDA, the RTE, and the computation of scattering by plane parallel layers of particles

A formulation and computational algorithm, based on the discrete dipole approximation (DDA), is presented for directly simulating the electromagnetic wave reflection, transmission, and absorption properties of plane parallel layers of random particulate media. The method is intended for situations in which the characteristic size of the particles is comparable to the radiation wavelength, yet no restriction is made regarding the concentration of the particles. In particular, the application is specifically intended for high particle concentrations characteristic of regolith, pigment layers, functional thin films, and so on. Strategies for reducing the memory and time requirements of the computations are developed. Test calculations show that the method can reproduce direct simulation predictions of hemispherical reflectance from layers of spherical particles as calculated by multiple sphere superposition solution. The method also correctly asymptotes to the radiative transport regime in the limit of small particle volume fraction. The connection of the formulation to those for discrete particle scattering, and the radiative transport equation (RTE), is discussed.

Geometrical parameters of binary granular mixtures with size ratio and volume fraction: experiments and DEM simulations

Binary mixtures represent the simplest case of polydisperse particulate systems which exhibit interesting and, in some cases, incomprehensive behavior. In this study, experimental and numerical investigations were conducted to examine the effect of particle size ratio and the ratio of volume fraction comprising small particles to the volume of all spheres (volume fraction) on geometrical properties of binary granular mixtures. The size ratio was chosen not smaller than 0.4 to prevent small particles from percolating through bedding and be trapped in the tetrahedron or octahedron made with large contacting spheres. Both, numerical tests and experiments showed an increase in the influence of the volume fraction of small particles on packing density in binary mixtures with an increasing ratio between small and large particles’ diameters. In packings with the particle size ratio not larger than 0.7, the solid fraction reached maximum when the volume fraction of small spheres was 0.6, which was not observed in samples with higher degree of particle size homogeneity. The average coordination number and packing density followed the same paths with the increasing contribution of small particles in mixtures, indicating a strong relationship between parameters. Detailed analysis of the coordination numbers for contacts between different types of particles showed that, average coordination number in binary mixtures was determined mainly by contacts between large and small particles. The composition of bidisperse samples was also found to strongly affect their spatial structure described in this study by means of the radial distribution function.

Rheology of a very dilute magnetic suspension with micro-structures of nanoparticles

The main objective of this present paper is to measure the apparent viscosity of a magnetic suspension in the presence of particle agglomerates of different sizes for several applied magnetic fields, shear rates and particle volume fractions. A secondary goal is to investigate suspension microstructure transition, when subjected to a magnetic field. We show that an employed like virial expansion of two empirical coefficients based only on the experimental data gives a good quantitative description of the magnetorheological suspension effective viscosity up to particle volume fraction less than 0.01. The observed shear rate dependence viscosity is a direct consequence of the stretching, breaking particle structures of different sizes and shapes formed by the action of magnetic attractive force between the polarized particles as observed previously in the context of dense ferrofluids. We have identified even in the limit of a very small particle volume fraction a strong non-linear behavior of the examined suspension due to formation of suspended blobs-like aggregates of different sizes and anisotropic chains of particles. These structures are induced by the presence of an external magnetic field and particle–particle magnetic interactions. A histogram of the structure size distribution is also examined. The results of this paper are important to those who are interested on the magnetorheological suspensions.