scholarly journals How size ratio and segregation affect the packing of binary granular mixtures

Soft Matter ◽  
2020 ◽  
Vol 16 (39) ◽  
pp. 9094-9100
Author(s):  
Salvatore Pillitteri ◽  
Eric Opsomer ◽  
Geoffroy Lumay ◽  
Nicolas Vandewalle
Keyword(s):  
Packing Fraction ◽  
Size Ratio ◽  
Granular Mixtures ◽  
Granular Segregation ◽  
Small Grains

For reaching high packing fractions, grains of various sizes are often mixed together allowing the small grains to fill the voids created by the large ones. However, in most cases, granular segregation occurs leading to lower packing fractions. We show how a layered packing or a gradient segregation affects the global packing fraction.

Density difference-driven segregation in a dense granular flow

2013 ◽  
Vol 717 ◽  
pp. 643-669 ◽  
Author(s):  
Anurag Tripathi ◽  
D. V. Khakhar
Keyword(s):  
Distinct Element ◽  
Tracer Particle ◽  
Packing Fraction ◽  
Heavy Particles ◽  
Drag Forces ◽  
Fluctuation Dissipation ◽  
Granular Mixtures ◽  
Inclination Angles ◽  
Tangential Forces ◽  
Dense Granular Flow

AbstractWe consider the segregation of spheres of equal size and different density flowing over an inclined plane, theoretically and computationally by means of distinct element method (DEM) simulations. In the first part of the work, we study the settling of a single higher-density particle in the flow of otherwise identical particles. We show that the motion of the high-density tracer particle can be understood in terms of the buoyancy and drag forces acting on it. The buoyancy force is given by Archimedes principle, with an effective volume associated with the particle, which depends upon the local packing fraction, $\phi $. The buoyancy arises primarily from normal forces acting on the particle, and tangential forces have a negligible contribution. The drag force on a sphere of diameter $d$ sinking with a velocity $v$ in a granular medium of apparent viscosity $\eta $ is given by a modified Stokes law, ${F}_{d} = c\pi \eta dv$. The coefficient ($c$) is found to decrease with packing fraction. In the second part of the work, we consider the case of binary granular mixtures of particles of the same size but differing in density. A continuum model for segregation is presented, based on the single-particle results. The number fraction profile for the heavy particles at equilibrium is obtained in terms of the effective temperature, defined by a fluctuation–dissipation relation. The model predicts the equilibrium number fraction profiles at different inclination angles and for different mass ratios of the particles, which match the DEM results very well. Finally, a complete model for the theoretical prediction of the flow and number fraction profiles for a mixture of particles of different density is presented, which combines the segregation model with a model for the rheology of mixtures. The model predictions agree quite well with the simulation results.

scholarly journals Forced segregation in binary granular mixtures

2021 ◽  
Vol 249 ◽  
pp. 02001
Author(s):  
Salvatore Pillitteri ◽  
Geoffroy Lumay ◽  
Éric Opsomer ◽  
Nicolas Vandewalle
Keyword(s):  
Experimental Data ◽  
Analytical Solutions ◽  
Physical Interpretation ◽  
Packing Fraction ◽  
Granular Mixtures ◽  
Large Particles ◽  
Granular Particles

Mixing granular particles of di erent sizes is a common way of increasing the packing fraction. Recently, a model predicting the packing fraction, taking into account the inhomogeneity of the mixed small and large particles, has been proposed by S. Pillitteri et al. Under certain conditions, this model can be simpli ed and analytical solutions can be found. We present here these solutions, compared to experimental data, and the physical interpretation they can bring.

scholarly journals JAMMING DYNAMICS IN GRAIN MIXTURES: AN EXTENDED HYDRODYNAMIC APPROACH

2007 ◽  
Vol 07 (02) ◽  
pp. L163-L167
Author(s):  
SUPURNA SINHA
Keyword(s):  
Binary Mixture ◽  
Mixture Model ◽  
Hard Sphere ◽  
Point Of View ◽  
The Novel ◽  
Hydrodynamic Approach ◽  
Granular Mixtures ◽  
Small Grains ◽  
Extended Hydrodynamics

We study jamming in granular mixtures from the novel point of view of extended hydrodynamics. Using a hard sphere binary mixture model we predict that a few large grains are expected to get caged more effectively in a matrix of small grains compared to a few small grains in a matrix of larger ones. A similar effect has been experimentally seen in the context of colloidal mixtures.

Optimum formulation derivation for the ultimate packing fraction using monodispersed particle sizes when optimizing suspension viscosities

2019 ◽  
Vol 48 (1) ◽  
pp. 45-56
Author(s):  
Richard D. Sudduth
Keyword(s):  
Particle Size ◽  
Average Particle Size ◽  
Packing Fraction ◽  
Size Ratio ◽  
Average Particle ◽  
Particle Sizes ◽  
Monodisperse Particle ◽  
Content Type ◽  
Particle Size Ratio ◽  
Minimum Number

Purpose The importance of maximizing the particle packing fraction in a suspension by maximizing average particle size ratio of D5/D1 has been adequately shown to be important as previously reported in the literature. This study aims to extend that analysis to include the best formulation approach to maximize the packing fraction with a minimum number of monodisperse particle sizes. Design/methodology/approach An existing model previously developed by this author was modified theoretically to optimize the ratio used between consecutive monodisperse particle sizes. This process was found to apply to a broad range of particle configurations and applications. In addition, five different approaches for maximizing average particle size ratio D̅5/D̅1 were addressed for blending several different particle size distributions. Maximizing average particle size ratio D̅5/D̅1 has been found to result in an optimization of the packing fraction. Several new concepts were also introduced in the process of maximizing the packing fraction for these different approaches. Findings The critical part of the analysis to maximize the packing fraction with a minimum number of particles was the theoretical optimization of the ratio used between consecutive monodisperse particle sizes. This analysis was also found to be effectively independent of the maximum starting particle size. This study also clarified the recent incorrect claim in the literature that Furnas in 1931 was the first to generate the maximum theoretical packing fraction possible for n different particles that was actually originally developed in conjunction with the Sudduth generalized viscosity equation. In addition, the Furnas generated equation was also shown to give significantly different results from the Sudduth generated equation. Research limitations/implications Experimental data involving monodisperse particles of different blends with a minimum number of particle sizes that are truly monodisperse are often extremely difficult to obtain. However, the theoretical general concepts can still be applicable. Practical implications The expanded model presented in this article provides practical guidelines for blending pigments using a minimum number of monodisperse particle sizes that can yield much higher ratios of the particle size averages D̅5/D̅1 and thus potentially achieve significantly improved properties such as viscosity. Originality/value The model presented in this article provides the first apparent guidelines to control the blending of pigments in coatings by the optimization of the ratio used between consecutive monodisperse particle sizes. This analysis was also found to be effectively independent of the maximum starting particle size.

Influence of particle size on vertical plate penetration into dense cohesionless granular materials (large-scale DEM simulation using real particle size)

2019 ◽  
Vol 21 (4) ◽  
Author(s):  
Shinichiro Miyai ◽  
Murino Kobayakawa ◽  
Takuya Tsuji ◽  
Toshitsugu Tanaka
Keyword(s):  
Particle Size ◽  
Granular Materials ◽  
Vertical Plate ◽  
Plate Thickness ◽  
Shear Bands ◽  
Penetration Resistance ◽  
Packing Fraction ◽  
Size Ratio ◽  
Two Dimensional ◽  
The Mean

Abstract The influence of the particle size on the vertical plate penetration into dense cohesionless granular materials was numerically investigated. Simulations were performed in quasi-two-dimensional conditions by changing the mean particle diameters d50 but maintaining the plate thickness B from B/d50 = 63–2.6. The initial bulk packing fraction was kept high, irrespective of the particle size. In the smallest particle size case (B/d50 = 63), the size ratio reached almost the same level as that in the laboratory experiments using natural sand particles. The results demonstrated that the mean penetration resistance force acting on the plate tip surface increases with a decrease of B/d50, while the tangential force acting on the side surfaces does not change with B/d50. Tip resistances increase linearly with the penetration depth, while the tangential resistances increase with the square of the depth regardless of B/d50. The behavior of the resistance fluctuations changes qualitatively between B/d50 = 31 and 21. For all cases, we confirmed the formation of a wedge-shaped flow with a high forward velocity in front of the plate tip. The wedge flow width was larger than the plate thickness by almost a mean particle diameter, and was responsible for the increase in the mean resistance depending on the particle size. For the large B/d50 cases only, the resistance exhibited quasi-periodic fluctuations, which was attributable to the intermittent nucleation and disappearance of the shear bands. Moreover, we investigated the dependence of B/d50 on the band evolutions by analyzing the band thickness. Graphic abstract The influence of the particle size on the vertical plate penetration into dense cohesionless granular materials was numerically investigated using DEM. Simulations were performed in quasi-two-dimensional conditions by changing the median particle diameters d50 but maintaining the plate thickness B. The initial bulk packing fraction was kept high, irrespective of the particle size. Upper and lower figures show the result of small (B/d50 = 63) and large particle size case (B/d50 = 21), respectively. In the small particle size case (B/d50 = 63), the size ratio reached almost the same level as that in the laboratory and the dynamics of 35.5 million particles was considered. Right and left figures illustrate instantaneous shear strain rate and local packing fraction distributions, respectively. Large qualitative change in the granular behaviors as well as penetration resistance was observed between B/d50 = 31 and 21. The intermittent nucleation and disappearance of the shear bands were clearly observed only for large B/d50 cases.

scholarly journals DEM modeling of segregation and stratification in pouring heaps of bidispersed mixtures of rounded particles

2021 ◽  
Vol 249 ◽  
pp. 03049
Author(s):  
Tristan Vuilloz ◽  
David Cantor ◽  
Carlos Ovalle
Keyword(s):  
Statistical Analysis ◽  
Granular Media ◽  
Contact Dynamics ◽  
Mass Ratio ◽  
Open Problems ◽  
Granular Mixtures ◽  
Element Approach ◽  
Numerical Tools ◽  
Small Grains ◽  
2D And 3D

This study aims to assess and analyse the patterns of segregation and stratification in pouring heaps of granular mixtures composed by binary sized and uniformly shaped particles. We present 2D and 3D simulations which respectively build deposits of poured disks and spheres by means of a discrete-element approach known as contact dynamics (CD). In order to identify preferable conditions for segregation and stratification, we try several deposition scenarios varying the pouring flow rate, injection height, heap’s width and mass ratio between large and small grains in our binary samples. Although some authors assert that shape dispersity might not be necessary to obtain stratification, the phenomenon seems hard to seize with mono-shaped granular media as it appears to require a close control on pouring conditions. The introduction of our DEM models and statistical analysis intend to provide examples of what could constitute efficient numerical tools to study the remaining open problems related to heap segregation patterns prediction.

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