DEM simulation of binary sphere packing densification under vertical vibration

The densification of random binary sphere packings subjected to vertical vibration was modeled by using the discrete element method (DEM). The influences of operating parameters such as the vibration conditions, sphere size ratio (diameter ratio of larger versus small spheres), and composition (volume fraction of large spheres) of the binary mixture on the fractional packing density φ (defined as the volume of spheres divided by the volume of container) were studied. Two packing states, i.e., random loose packing (RLP) and random close packing (RCP), were reproduced and their micro properties such as the coordination number (CN), radial distribution function (RDF), and force structure were characterized and compared. The results indicate that properly controlling vibration conditions can realize the transition of binary packing structure from the RLP to RCP state when the sphere size ratio and composition are fixed, and the fractional packing density for RCP after vibration can reach φ_RCP?≈?0.86. Different packing characteristics from RLP and RCP identify that RCP shows much denser and more uniform structure than RLP. The current modeling results are in good agreement with those obtained from both the physical experiments and the proposed empirical models in the literature.     

Study by X-ray microtomography of the horizontal vibration effects on sand densification

X-ray microtomography experiments were performed in order to evaluate the densification of silica sand submitted to horizontal sinusoidal vibrations carried out at constant frequency (50 Hz) with controlled acceleration and deceleration \(\Gamma \). Packing homogeneity was characterized using relative density distribution through 3D images of the relaxed samples. Information obtained from the images allowed us to evaluate data at grain scale: porosity and pore size distribution, number of contacts per particle, particle shape and size distribution were evaluated and linked to the densification process. Based on the internal analysis of samples, the results confirm and extend the conclusions of previous works regarding the 3-layer densification under vibration and the proposed optimized vibration cycle to get dense and homogeneous samples. They extend them to different initial packings. Additionally, significant correlations are found between density and local particle packing characteristics such as pores size distribution, or the number of contacts per particle.     

Radial segregation of ternary granular mixtures in rotating cylinders

We carry out an experimental study of the equilibrium segregation of ternary granular mixtures in a rotating cylinder. In all the experiments, 50% of the volume of the cylinder is filled with the granular mixture and the rotational speed used ensures operation in the rolling regime of flow. Mixtures of spherical particles differing only in size and of spherical particles differing in size and density are considered, using steel balls and glass beads of different sizes. Volume fractions of the components (f{\phi}) are measured by sampling at different radial positions (r) to yield the radial volume fraction profiles (f(r){\phi(r)}). Results for mixtures differing only in size of the components indicate that the segregation process is nearly independent of the sizes of the large and middle size particles for the same size of small particles. In the case of mixtures with different size and density components, the segregation patterns depend on the direction of the resultant driving force. In many of the mixtures considered, the pattern of segregation can be qualitatively predicted by considering binary interactions between the components. However, in some mixtures, ternary interactions are found to determine the pattern obtained.     

粉体堆积密度的理论计算

考察了紧密堆积时多级理想球形颗粒混合粉体的堆积密度的理论值与粒级组分数的关系,紧密堆积时颗粒的粒度分布特征,以及堆积密度的理论值与单一粒径粉体空隙体积分数、颗粒干扰宽度的相关关系。研究表明,原始堆积密度越大,多粒级理想球形颗粒混合粉体达到相同的堆积密度所需的粒级数越少,各粒级的体积含量随着粒级的增加呈指数下降,且原始堆积密度越大,下降速度越快;其粒度分布符合对数正态分布;堆积密度的理论值与单一粉体空隙体积分数、颗粒干扰宽度的符合二元二次非线性关系。     

Computer Simulation of Random Sphere Packing in an Arbitrarily Shaped Container

Most simulations of random sphere packing concern a cubic or cylindric container with periodic boundary, containers of other shapes are rarely studied. In this paper, a new relaxation algorithm with pre-expanding procedure for random sphere packing in an arbitrarily shaped container is presented. Boundaries of the container are simulated by overlapping spheres which covers the boundary surface of the container. We find 0.4~0.6 of the overlap rate is a proper value for boundary spheres. The algorithm begins with a random distribution of small internal spheres. Then the expansion and relaxation procedures are performed alternately to increase the packing density. The pre-expanding procedure stops when the packing density of internal spheres reaches a preset value. Following the pre-expanding procedure, the relaxation and shrinking iterations are carried out alternately to reduce the overlaps of internal spheres. The pre-expanding procedure avoids the overflow problem and gives a uniform distribution of initial spheres. Efficiency of the algorithm is increased with the cubic cell background system and double link data structure. Examples show the packing results agree well with both computational and experimental results. Packing density about 0.63 is obtained by the algorithm for random sphere packing in containers of various shapes.     

牙科复合树脂中无机填料双峰混合体的堆积性能

通过测定用作牙科复合树脂中无机填料的粉体的振实密度 ,使用Mathematica和SAS/STAT软件 ,用统计学的方法得到了双组分粉体混合物的粒度分布与堆积体比容之间关系的经验公式。说明可以使用引入了粒度分布宽度作为变量的改良线性堆积模型预测双峰粉体的堆积密度。结论为双组分粉体大小粒径比相差越大 ,混合物堆积密度越高。该结论为优化牙科复合树脂的组成提供了理论依据     

Investigation on the influence of granular packing on the flow properties of cementitious suspensions

Fresh concrete can be considered as a suspension of grains of various sizes in a continuous fluid phase. The rheological properties of fresh concrete greatly depend on the physical factors, chemical and mineralogical characteristics of the fine components. Interparticle interactions occur during flow and modify the apparent rheological behaviour. Therefore, a thorough understanding of the rheological behaviour of cementitious suspensions with respect to particle packing is required. The objective of this study is to characterise the interrelationship between the flow properties and the particle packing density of the cementitious suspensions. The experimental investigation included Puntke tests for determining the packing density, and rheological tests that were performed in a rheometer for the characterisation of cement and silica fume (C + SF) as well as cement and fly ash (C + FA) mixtures. The effect of the water to powder ratio (w/p ratio) and the packing density on the flow properties of the cementitious suspensions was studied. From the study, it was observed that a good correlation exists between the w/p ratio and the yield value (g) for both C + SF and C + FA mixtures. The packing density shows a marked influence on the value of g for both mixtures, but has less influence on the value of plastic viscosity (h) for C + FA mixture.     

A hierarchical approach to simulate the packing density of particle mixtures on a computer

In many fields of materials science it is important to know how densely a particle mixture can be packed. The “packing density” is the ratio of the particle volume and the volume of the surrounding container needed for a random close packing of the particles. We present a method for estimating the packing density for spherical particles based on computer simulations only, i.e. without the need for additional experiments. Our method is particularly suited for particle mixtures with an extremely wide range of particle diameters as they occur e.g. in modern concrete mixtures. A single representative sample from such mixtures would be much larger than can be handled on present standard computers. In our hierarchical approach the diameter range is therefore divided into smaller intervals. Samples from these limited diameter intervals are drawn and their packing density is estimated from a simulated packing. The results are used to “fill” the interstices in the sample from the next larger particle interval. To account for the interaction between particles of different sizes we include larger particles into the sample of smaller ones. The larger ones act as part of the boundary during the packing. Thus we obtain more realistic estimates of how dense a fraction of particles can be packed within the whole mixture. The focus of this paper is on the divide-and-conquer approach and on how the simulation results from the fractions can be collected into an overall estimate of the packing density. We do not go into details of the simulation technique for the single packing. We compare our results to some experimental data to show that our method works at least as good as the classical analytical models like CPM without the need for any experiments.     

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 Wi?cek (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.     

填料堆积密度对SMC工艺及性能的影响

根据填料球-球双峰堆砌理论,通过激光粒度分析仪测定了几种不同比例填料复合后的粒径分布,使用连续级分法计算复合后填料的空隙率,得到了可实现密堆砌填料的类型和复合比例;通过测试树脂糊黏度、片状模塑料(SMC)试样的力学性能以及模压产品的表面波纹,研究了密堆砌填料对SMC生产的工艺性、力学性能以及模压产品表面质量的影响。结果表明,使用密堆砌的填料可实现树脂糊在初始黏度相同的情况下多加入填料30份,同时,SMC的冲击性能有明显的提高,且产品的表面质量得到了显著的改善。     

Effect of vibration direction on the packing of sphero-cylinders

Particle packing is widely encountered when coping with granular materials, while mechanical vibration is usually used for packing densification. Vibration direction has been proven to be crucial for the ordered packing of spherical particles, but there are few reports for non-spherical ones in this regard. In this study, the effect of vibration direction on the macroscopic and microscopic packing parameters of sphero-cylinders are systematically examined using discrete element method (DEM). Due to the anisotropic shapes of sphero-cylinders, their packing characteristics are much richer and also more complex than those of spheres. It is found that vibration direction affects both the packing density and the packing structure of sphero-cylinders through tuning their orientation distributions and contact modes. Moreover, vibration direction plays a significant role in determining the optimal vibration intensities for dense packing. When the sphericity of Voronoi cell decreases and/or the density increases, the Nematic order parameter increases accordingly. Besides, no obvious relationship between the packing density and the average contact number is observed.     

Mixing narrow coarse and fine coal fractions – The maximum volume fraction of suspensions

A main objective of coal-water slurry fuel (CWSF) preparation is to achieve maximum loading of coal. In the absence of a strong colloidal attractive force, the maximum loading is determined by the packing density of the particles which in turn is a function of the particle size distribution. In this study, coal fractions of different mean sizes with a narrow distribution were separated by sieving. Mixtures of different mean coarse to fine size ratios were then prepared. For each size ratio, different amounts of coarse particle contents were prepared. With these different mixtures, water was added to produce the CWSF. The maximum volume packing density, φ_max, for each mixture was determined using a rheological vane yield stress technique. The determination of φ_max involving the direct yield stress measurements of extremely high concentration suspensions is an entirely new and accurate approach. It was found that the highest φ_max was obtained when the coarse to fine ratio was ～10 located at a coarse coal content of 70 wt%. This result is consistent with that obtained by theoretical modelling of bimodal mixing of monodisperse size spheres with a size ratio of 10. At lower size ratio, φ_max obtained at the optimum coarse coal content was lower.     

Effects of particle size ratio on the macro- and microscopic behaviors of binary mixtures at the maximum packing efficiency state

The effects of particle size ratio on the mechanical behaviors of binary mixtures are investigated using three-dimensional discrete element method. The samples with three types of particle size ratios (SR, \(\hbox {SR}=3.0\), 4.5 and 6.0) are prepared at the maximum packing efficiency state, which appears at 70 % of the large particle volume content. The results demonstrate that the maxima of peak deviator stress are obtained at the sample with \(\hbox {SR}=4.5\). The initial elastic modulus, \(E_{0}\), increases with increasing SR. The value of deviator stress increases with increasing SR at the softening stage, whereas an opposite trend is observed at the critical state. The evolutions of the effective particle ratio can capture the differences among the evolutions of the deviator stress of different samples during the softening stage and the critical state to some degree. In addition, different SRs generate different packing structures of the binary mixtures and have apparent influences on the force chain networks in the binary mixtures. With increasing SR, the strong force chains become stronger, and the weak force chains become weaker. The deviator stress contributed by the contacts between large particles and between large and small particles constitutes a major part of the overall deviator stress of the binary mixtures at the maximum packing efficiency state. Furthermore, the positions of the critical state lines of binary mixtures in the \(p-q\) plane and \(v-\ln p\) plane are sensitive to SR, and the lubrication effect of small particles in the binary mixtures is enhanced with increasing SR.     

Dynamic response of well-mixed binary particulate systems subjected to low magnitude vibration

The dynamic response of well-mixed binary mixtures subjected to low magnitude vibration was investigated using a newly developed non-invasive method. An apparent mass, defined as a ratio of the base force to base acceleration, was measured when applying a sweep vibration that ranged from 10 to 2000 Hz. The method could operate more rapidly, conveniently and non-destructively for a wider range of particle packing states, including a natural packed bed, compared to previous methods. The apparent mass data exhibited several significant peaks due to the bed harmonic resonance. The first peak frequency gave the longitudinal elastic modulus of the bed via the velocity of longitudinal stress wave propagation. For loosely packed mixture beds, the mixing fraction dependence upon the elastic modulus was found to be describable by the two-phase series model. In addition, the particle packing dependence upon the elastic modulus agreed reasonably well with the fourth power scaling law in spite of the wide size distribution. Comparison of the two-phase series model and experimental data for a range of particle packing fractions was made in terms of the coefficient of the scaling law.     

Impact of powder composition on processing-relevant properties of pharmaceutical materials: An experimental study

In this work, we studied the influence of powder composition on packing density and other processing-relevant properties of binary mixtures, including powder flowability. Binary mixtures of pharmaceutical powders with different particle size ratios, α and varying fractions of large and small particles were analyzed systematically. Mixtures of three excipients and one API with different composition (2, 5, 10, 30, 50, 70, 90, 95 and 98 wt%) were prepared in a Turbula mixer. Powders with different properties and particle size distribution were chosen, in order to obtain three binary mixtures with different size ratios. Then, macroscopic powder properties including bulk (poured) and tapped density (BD and TD) were measured. A powder rheometer was used to measure the flow function coefficient (ffc), cohesion, compressibility and permeability of the binary mixtures. We considered experimentally three classes of binary mixtures, which are characterized by two critical ratios of particle diameter: the critical size ratio of entrance (α_c) and the critical size ratio of replacement (α_r), where α_c = 0.154 and α_r = 0.741. Below the critical size ratio of entrance (α_c), the particle asymmetry (ratio between large and small particle diameters) is high and small particles can fill the voids between larger ones. Between α_c and the critical size ratio of replacement (α_r), the smaller particles are too large to fit in the voids between larger particles (packing structure changes). Above α_r, the particles are more or less symmetric in size and overall packing structure does not change by mixing the particles. Our experiments show that there is a non-linear and non-monotonic dependence of all relevant properties on composition for powder mixtures that have an α < α_r. This non-linear behavior is even more significant for strongly asymmetric binary mixtures with α < α_c. We argue that this behavior is related to the composition dependence of random packing of particulate systems. Our results have relevance to pharmaceutical particle processing operations where constant powder mixture properties are needed to ensure quality standards are met; such operations include capsule or die filling during tableting, and the continuous feeding of powders via screw feeders. Our results suggest that for pharmaceutical particle processing operations, where constant powder mixture properties are a prerequisite for process robustness, the size ratio of API and excipient particles, α should not be smaller than α_r = 0.741.     

Effect of the particle size ratio on the structural properties of granular mixtures with discrete particle size distribution

In this study, the discrete element method was used to examine the structural properties and geometric anisotropy of polydisperse granular packings with discrete uniform particle size distributions. Confined uniaxial compression was applied to granular mixtures with different particle size fractions. The particle size fraction (class) was defined as the fraction of the sample composed of particles with a certain size. The threshold value of number of particle size fractions (i.e., the value above which structural properties of assemblies remain constant) was determined. The effect of heterogeneity in particle size on the critical value of number of particle size fractions was investigated for packings with different ratios between diameters of the largest and smallest grains. The threshold number of particle size classes decreased from five to three as the diameter ratio between the largest and smallest grains increased. Regardless of the diameter ratio, the critical number of particle size fractions (above which the packing density and coordination number of the granular mixtures remained constant) was determined to be five. The study has also shown an increase in packing density of binary mixtures with particle size ratio increasing up to 2.5, which was followed by decrease in density of mixtures with larger particle size ratios, which has not so far been reported in the literature.     

P, ρ, T-properties and phase equilibria in the water-n-hexane system with a low content of water

Using a piezometer of constant volume, we determined experimentally the P, ρ, and T properties and the phase equilibria for the binary water-n-hexane mixtures with 0.04, 0.05, 0.06, and 0.0673 mass fraction of H₂O over the density range of 0.067–0.607 g/cm³, temperature range of 380–680 K, at pressures up to 60 MPa. The equilibrium lines of the liquid-liquid and liquid-gas transition have been determined. The three-phase line, the line of the azeotrope, and the lower branch of the critical line (all lines are joined at the upper finite critical point) have been plotted in the work.     

Mono-sized sphere packing algorithm development using optimized Monte Carlo technique

In this paper, fuel cell catalyst layer was developed using the optimized sphere packing algorithm. An optimization technique named adaptive random search technique (ARSET) was employed in this packing algorithm. The ARSET algorithm will generate the initial location of spheres and allow them to move in the random direction with the variable moving distance, randomly selected from the sampling range (α), based on the Lennard–Jones potential and Morse potential of the current and new configuration. The solid fraction values obtained from this developed algorithm are in the range of 0.610–0.624 while the actual processing time can significantly be reduced by 5.58–34% based on the number of spheres. The initial random number sampling range (α) was investigated and the appropriate α value is equal to 0.5.     

Optimization of a Computer Simulation Model for Packing of Concrete Aggregates

A simulation algorithm was developed for modeling the dense packing of large assemblies of particulate materials (in the order of millions). These assemblies represent the real aggregate systems of portland cement concrete. Two variations of the algorithm are proposed: sequential packing model and particle suspension model. A developed multicell packing procedure as well as fine adjustment of the algorithm's parameters were useful to optimize the computational resources (i.e., to realize the trade-off between the memory and packing time). Some options to speed up the algorithm and to pack very large volumes of spherical entities (up to 10 million) are discussed. The described procedure resulted in a quick method for packing of large assemblies of particulate materials. The influence of model variables on the degree of packing and the corresponding distribution of particles was analyzed. Based on the simulation results, different particle size distributions of particulate materials are correlated to their packing degree. The developed algorithm generates and visualizes dense packings corresponding to concrete aggregates. These packings show a good agreement with the standard requirements and available research data. The results of the research can be applied to the optimal proportioning of concrete mixtures.     

CFD-DEM numerical study on air impacted packing densification of equiaxed cylindrical particles

A CFD-DEM model was developed to reproduce the packing densification process of mono-sized equiaxed cylindrical particles under air impact. The effects of operating parameters on packing density were firstly studied. Then various microscopic properties of packing structures such as coordination number (CN), contact types, particle orientations, pore features were characterized and compared. And corresponding densification mechanisms were analysed based on particle motion behaviour, local structure evolution, and forces. Results indicate that the air impact can realize the packing densification of cylindrical particles under appropriate conditions. The pore size distribution in the packing of cylindrical particles shows a tail at larger pore sizes compared with that in the packing of equal spheres. Both the size and the sphericity of the pores decrease in the final dense packing; also, more surface-surface and less surface-edge contacts between two particles therein can be formed. More cylindrical particles tend to be in parallel or perpendicular contact with each other to form more stable local structures during air impact. Most particles at higher position move down (direction of gravity/air impact) with about one particle length during the densification process and most particles exhibit translational motion to realize the local rearrangement for pore filling through air impact induced inter-particle forces.