Particle Packing Research Articles

Enhancing sustainability of ultra-high performance concrete utilizing high-volume waste glass powder

This paper investigates the effect of recycled waste glass powder (RWGP) and particle packing optimization on the performance of UHPC. RWGP was obtained by crushing and grinding waste glass and reaching a fineness close to that of cement to study its influence on UHPC performance. UHPC mixtures were designed by optimizing the binder system based on a modified Andreasen & Andersen (MAA) particle packing model with a distribution factor (q) of 0.22 in order to reduce the required cement content (450 kg/m3). Seven different mixes have been designed, prepared, and tested with various RWGP content. Mechanical properties, durability, and microstructure of the developed concrete have been determined and evaluated. The results showed that the mixture with the inclusion of 10 % RWGP as a cement replacement achieves the highest mechanical properties at different ages. The interfacial transition zone (ITZ) is improved significantly when cement and quartz powder are replaced with RWGP. Moreover, the embodied CO2 index of RWGP50 % has been reduced to 3.7 kg/MPa/m3, while the embodied CO2 for conventional UHPC ranged to 5.75 kg/MPa/m3. Based on the environmental and economic assessment, RWGP reduces UHPC production costs and harmful environmental impacts without sacrificing the mechanical, microstructure, and durability performance significantly. Through this assessment, the effectiveness of the use of 50 C/50RWGP has been demonstrated, providing wide opportunities for the continuous future development of Eco-UHPC

A quasi-physical method for random packing of spherical particles

In this work, a quasi-physical method for the random packing of spherical particles based on the equivalent spring structure and the principle of force equilibrium is proposed. The model is inspired by a meshing method “Distmesh”. For the purpose of generating a feasible packing, the proposed model calculates the displacements of each particle based on physical principles and disregards forces that may not help with convergence, thus offering a natural and possibly fast route towards the final packing configuration. The packing densities predicted by the proposed method are in good agreement with those predicted by other methods and the experimental results. Finally, the topological properties of the packing of particles with log-normal size distributions, binary mixtures and ternary mixtures are evaluated by radical tessellation. The results show that the particle size differences and the proportions of each kind of particles have significant effect on the packing properties of the mixture. • Proposing a new quasi-physical model for the random packing of particles. • The model is inspired by a meshing method, which can more easily form force grids. • The model offers a natural and possibly fast route towards the final packing. • The particle size and volume ratio have significant effect on the packing properties.

Evaluation of three non-linear packing density models on micropowder mixtures

The formulation of powders often requires an optimized packing density of the granular skeleton which takes into account the desired properties. More accurate than the conventional linear models, three non-linear packing density models are evaluated from published data on binary or ternary mixtures of alumina powders, glass microbeads, siliceous microaggregates: the Compressible Packing Model (CPM), the 3-parameter Particle Packing Model (3PPM), the Theoretical Packing Density Model (TPDM). Depending on the models, they involve a compaction index K and certain particle interactions: the loosening effect a and possibly the critical cavity size ratio x0 from which it appears, the wall effect b and the wedging effect c. The CPM (with a, b, K), by incorporating only 2 interaction functions for a and b, reduces its versatility but is efficient for siliceous. The 3PPM (with a, b, c), by incorporating 9 interaction functions, adapts well to the various micropowders with however a lower performance for the siliceous for which the packing densities predicted in “compacted” conditions are lower than in “uncompacted” conditions. The TPDM (with a, b, K, x0) is effective for all types of micropowders and generates the best statistical indicators.

Evaluation of a Laboratory-Scale Gas-Atomized AlSi10Mg Powder and a Commercial-Grade Counterpart for Laser Powder Bed Fusion Processing.

Laser powder bed fusion (LPBF) is an additive manufacturing technology that implies using metal powder as a raw material. The powders suitable for this kind of technology must respect some specific characteristics. Controlled gas atomization and post-processing operations can strongly affect the final properties of the powders, and, as a consequence, the characteristics of the bulk components. In fact, a complete characterization of the powders is mandatory to fully determine their properties. Beyond the most used tests, such as the volume particle size distribution (PSD) and flowability, the PSD number, the Hausner ratio and the oxidation level can give additional information otherwise not detectable. The present work concerns the complete characterization of two AlSi10Mg powders: a commercial-grade gas atomized powder and a laboratory-scale gas atomized counterpart. The laboratory-scale gas atomization allows to better manage the amount of the fine particles and the oxidation level. As a consequence, a higher particle packing can be reached with an increase in the final density and tensile strength of the LPBF bulk samples.

Densest packings from size segregation of particles in geometric confinement.

A correlation between density maximization and size segregation for packings of polydisperse particles in geometric confinement has been discovered, through the derivation of a general solution for the densest-packed zigzag arrangements of polydisperse particles. This solution is a size-graded structure in which the larger a particle the closer it is located to either end of the system, such that the smaller particles in the interior are encapsulated by the larger ones away from it. Any pair of different-sized adjacent particles is a grain-boundary-like configuration that reduces the overall packing efficiency of the system, and this solution corresponds to a minimization of excess-volume contributions from grain-boundary-like configurations of different-sized particles as a result of the clustering of equal- or like-sized particles. Our findings provide new insights into how structural order of polydisperse particles emerges in confined settings.

Capacitive energy storage from single pore to porous electrode identified by frequency response analysis

Rate capability, peak power, and energy density are of vital importance for the capacitive energy storage (CES) of electrochemical energy devices. The frequency response analysis (FRA) is regarded as an efficient tool in studying the CES. In the present work, a bi-scale impedance transmission line model (TLM) is firstly developed for a single pore to a porous electrode. Not only the TLM of the single pore is re-parameterized but also the particle packing compactness is defined in the bi-scale. Subsequently, the CES properties are identified by FRA, focused on rate capability vs. characteristic frequency, peak power vs. equivalent series resistance, and energy density vs. low frequency limiting capacitance for a single pore to a porous electrode. Based on these relationships, the CES properties are numerically simulated and theoretically predicted for a single pore to a porous electrode in terms of intra-particle pore length, intra-particle pore diameter, inter-particle pore diameter, electrolyte conductivity, interfacial capacitance & exponent factor, electrode thickness, electrode apparent surface area, and particle packing compactness. Finally, the experimental diagnosis of four supercapacitors (SCs) with different electrode thicknesses is conducted for validating the bi-scale TLM and gaining an insight into the CES properties for a porous electrode to a single pore. The calculating results suggest, to some extent, the inter-particle pore plays a more critical role than the intra-particle pore in the CES properties such as the rate capability and the peak power density for a single pore to a porous electrode. Hence, in order to design a better porous electrode, more attention should be given to the inter-particle pore.

Evaluation of the microstructure and micromechanics properties of structural mortars with addition of iron ore tailings

The Interfacial Transition Zone (ITZ) between the cement paste and aggregates is a region of great interest for concretes because it is the composites' weakest region. ITZ presents a great amount of large calcium hydroxide and ettringite crystals, with the porosity being able to be up to 2.5 greater than that the rest of the paste. The microstructure, and consequently the ITZ, can be improved by mineral addition. These materials fill the pores in the composite, influence the hydration process and densify the matrix. Therefore, mineral additions, such as iron ore tailings (IOT), can modify microstructure of composites. There are few studies on the assessment of IOT heterogeneity on the microstructure and hardness of structural mortar. Thus, the present study analyzes the properties influences of four IOT types on the microstructure, porosity, and thickness of the structural mortars' Interfacial Transition Zone (ITZ) with IOT addition, by different evaluation methods. The composites were characterized through the Scanning Electron Microscope by backscattered electrons (SEM-BSE), line scan by Energy Dispersive Spectroscopy and nanoindentation. Results presented that IOT improved particle packing and tended to reduce the ITZ. The IOT improved nucleation since it reduces the amount of anhydrous cement particles and increases the amount of calcium hydroxide particles in the cement matrix. The nanoindentation showed that IOT-added matrix presented greater hardness and indentation module. It can be concluded that the IOT heterogeneity may affect microstructural properties and that the methods presented can be good ways to evaluate the parameters.

Size controllable single-crystalline Ni-rich cathodes for high-energy lithium-ion batteries.

A single-crystalline Ni-rich (SCNR) cathode with a large particle size can achieve higher energy density, and is safer, than polycrystalline counterparts. However, synthesizing large SCNR cathodes (>5μm) without compromising electrochemical performance is very challenging due to the incompatibility between Ni-rich cathodes and high temperature calcination. Herein, we introduce Vegard's Slope as a guide for rationally selecting sintering aids, and we successfully synthesize size-controlled SCNR cathodes, the largest of which can be up to 10μm. Comprehensive theoretical calculation and experimental characterization show that sintering aids continuously migrate to the particle surface, suppress sublattice oxygen release and reduce the surface energy of the typically exposed facets, which promotes grain boundary migration and elevates calcination critical temperature. The dense SCNR cathodes, fabricated by packing of different-sized SCNR cathode particles, achieve a highest electrode press density of 3.9g cm-3 and a highest volumetric energy density of 3000Wh L-1. The pouch cell demonstrates a high energy density of 303Wh kg-1, 730Wh L-1 and 76% capacity retention after 1200 cycles. SCNR cathodes with an optimized particle size distribution can meet the requirements for both electric vehicles and portable devices. Furthermore, the principle for controlling the growth of SCNR particles can be widely applied when synthesizing other materials for Li-ion, Na-ion and K-ion batteries.

Emergence of zero modes in disordered solids under periodic tiling.

In computational models of particle packings with periodic boundary conditions, it is assumed that the packing is attached to exact copies of itself in all possible directions. The periodicity of the boundary then requires that all of the particles' images move together. An infinitely repeated structure, on the other hand, does not necessarily have this constraint. As a consequence, a jammed packing (or a rigid elastic network) under periodic boundary conditions may have a corresponding infinitely repeated lattice representation that is not rigid or indeed may not even be at a local energy minimum. In this manuscript, we prove this claim and discuss ways in which periodic boundary conditions succeed in capturing the physics of repeated structures and where they fall short.

Validation and evaluation of the CPFD modeling of dense particle flow velocity: Taking particle flow around an obstacle as an example

The computational particle fluid dynamic (CPFD) method is a common approach to simulating dense particle flow, but the direct validation of the CPFD model using the particle velocity distribution is lacking. Taking particle flow around an obstacle as an example, the accuracy of the CPFD method in the simulation of the dense particle velocity field was validated and evaluated in the present study. The particle flow field was experimentally visualized using a quasi-2D flow channel and the particle velocity distribution was measured by a newly-proposed stained-particle image velocimetry technique. The simulated particle velocity using the CPFD method was compared with the measured data and the results indicated that the CPFD method was capable of accurately predicting the particle flow velocity distribution as well as the overall parameters such as the apparent mass flux if the CPFD model parameters were properly adopted. The sensitivity analysis of the simulated particle velocity to the key CPFD parameters was conducted and the results showed that the simulated particle velocity distribution was quite sensitive to the particle pack volume fraction, while the particle stress model parameters and particle-to-wall restitution coefficients show less and close sensitivity in the dense particle flow situations. The recommended model parameters were given in the present study. It is also found that multiple choices of the model parameter combinations could all give accurate overall mass flow predictions but might lead to very different flow velocity distributions with a prediction error even higher than 45%. One should directly verify the CPFD simulated flow velocity using the experimental data if the flow field study was desired.

(Digital Presentation) 3D Electrochemical Model Revealing Electrode Manufacturing Parameters’ Effects on Battery Performance

Electrode manufacturing is in the core of Li-ion battery manufacturing process. The electrode mesostructure and the associated electrochemical performance is determined by the adopted manufacturing parameters. However, in view of the strong interdependencies between these parameters, evaluating their influence on the performance is not a trivial task, and our ERC-funded ARTISTIC project1,2 is providing a theoretical framework to rationalize and optimize the manufacturing process of Li-ion battery cells. Over the years, the discussion of importance of electrode mesostructure in cell behavior has become increasingly lively. Many modeling researchers have been conducted studies to explain the influences of electrode mesostructure on its electrochemical performance3–6. However, many studies did not include manufacturing parameters as inputs, which hinders universality in regards of these electrochemical models’ application. With the aim of going into the scope of real electrode manufacturing parameters, we present here a calibrated 3D-resolved electrochemical model for NMC111-electrodes which reveals how slurry formulation and compression rate affect the electrode performance. A series of electrodes with different formulations and compression rates were manufactured. Corresponding models were built based on the basis of these manufacturing parameters, using the manufacturing process simulation workflow previously developed in ARTISTIC7. The results of simulations and experiments were compared individually. We found that one of the major factors affecting the electrode performance is the carbon-binder domain (CBD) distribution, which highly changes the conductive network within the electrode. A well-connected conductive network throughout the electrode is vital for ensuring full utilization of active material. Other features such as porosity, tortuosity factor, active material particle packing, and etc. also play important roles in different ways. This work provides systematic insights on the essence of how electrode manufacturing process takes effect on electrode performance, through a digital twin experimentally validated under multiple experimental conditions.References Artistic http://www.erc-artistic.eu/. Artistic http://www.erc-artistic.eu/scientific-production/publications.X. Lu et al., Energy Environ. Sci., 14, 5929–5946 (2021).M. E. Ferraro, B. L. Trembacki, V. E. Brunini, D. R. Noble, and S. A. Roberts, J. Electrochem. Soc., 167, 013543 (2020).X. Lu et al., Nat. Commun., 11, 2079 (2020).L. S. Kremer et al., Energy Technol., 8, 1900167 (2020).T. Lombardo et al., Batter. Supercaps, 5, e202100324 (2022).

Geopolymer: A Systematic Review of Methodologies.

The geopolymer concept has gained wide international attention during the last two decades and is now seen as a potential alternative to ordinary Portland cement; however, before full implementation in the national and international standards, the geopolymer concept requires clarity on the commonly used definitions and mix design methodologies. The lack of a common definition and methodology has led to inconsistency and confusion across disciplines. This review aims to clarify the most existing geopolymer definitions and the diverse procedures on geopolymer methodologies to attain a good understanding of both the unary and binary geopolymer systems. This review puts into perspective the most crucial facets to facilitate the sustainable development and adoption of geopolymer design standards. A systematic review protocol was developed based on the Preferred Reporting of Items for Systematic Reviews and Meta-Analyses (PRISMA) checklist and applied to the Scopus database to retrieve articles. Geopolymer is a product of a polycondensation reaction that yields a three-dimensional tecto-aluminosilicate matrix. Compared to unary geopolymer systems, binary geopolymer systems contain complex hydrated gel structures and polymerized networks that influence workability, strength, and durability. The optimum utilization of high calcium industrial by-products such as ground granulated blast furnace slag, Class-C fly ash, and phosphogypsum in unary or binary geopolymer systems give C-S-H or C-A-S-H gels with dense polymerized networks that enhance strength gains and setting times. As there is no geopolymer mix design standard, most geopolymer mix designs apply the trial-and-error approach, and a few apply the Taguchi approach, particle packing fraction method, and response surface methodology. The adopted mix designs require the optimization of certain mixture variables whilst keeping constant other nominal material factors. The production of NaOH gives less CO2 emission compared to Na2SiO3, which requires higher calcination temperatures for Na2CO3 and SiO2. However, their usage is considered unsustainable due to their caustic nature, high energy demand, and cost. Besides the blending of fly ash with other industrial by-products, phosphogypsum also has the potential for use as an ingredient in blended geopolymer systems. The parameters identified in this review can help foster the robust adoption of geopolymer as a potential “go-to” alternative to ordinary Portland cement for construction. Furthermore, the proposed future research areas will help address the various innovation gaps observed in current literature with a view of the environment and society.

Reconnoitring principles and practice of Modified Andreasen and Andersen particle packing theory to augment Engineered cementitious composite

• Engineered Cementitious Material ECC, unique composite with high resistant to crack. • Modified Andreasen and Andersen theory is employed to optimize mix proportion of ECC. • Particle packing model in accessible software (EMMA) decrease incidence of trial mixes required. • Optimization of particle packing with distribution modulus of 0.23 refines pore distribution. • From 26 trial mixes, optimal dosage of HRWRA is 2.62 percent with water binder content of 0.16. • Incorporation of 15 % silica fume, 0.16 water binder ratio enhances compressive strength to 82 MPa. Engineered Cementitious Composites (ECC) is a heterogeneous high-performance material with improved compressive strength and fatigue resistance. The nature and intensity of packing has a significant impact on the efficiency of ECC. To streamline the mix design by an improved technique the current study focuses on employing the Modified Andreasen and Andersen (MAA) theory to optimize the mixture proportions of ECC with the particle packing concept that in turn reduces lot of trial mixes. The primary input parameters are particle size distribution, density of materials, binder proportions and water content. In this case study, about series of 6 group of trail mixes with water binder ratio ranging from 0.14 to 0.24 are chosen, and the optimization is carried out using Elkem Materials Mixture Analyser (EMMA). Hence the MAA deals with the solid particle packing effect, the ratio of water and High Range Water Reducing Admixture (HRWRA) depends on the flowability test of ECC. According to the results, the optimal dosage of HRWRA is 2.62 percent with a water binder content of 0.16. It is ascertained from the case study that, A 09 mix recipe exhibits improved compressive strength of up to 82 MPa at 28 days. Some of the mix recipes exhibit higher early strength, but the strength decreases with age in some compositions of ECC. The discontinuity of hydration process due to the presence of excessive early age additives such as silica fume, lack of adaptivity between the cement and superplasticizer, inappropriate combination of mixture proportion reduces strength of ECC.

Disordered packings of binary mixtures of dimer particles

Disordered packings of non-spherical particles and their mixtures are abundant in nature, but have so far attracted only few systematic studies. Previous investigations of binary mixtures of specific convex shapes have established two generic properties: (i) the existence of a unique density maximum when shape or mixture composition of the two species are varied; (ii) the validity of an ideal mixing law indicating that the packing density is independent of the segregation state. These findings were so far only observed for mixtures of convex particles such as spherocylinders, ellipsoids, and spheres. Here, we investigate the packing properties of binary mixtures of frictionless dimer particles simulated by a gravitational pouring protocol in LAMMPS. Our results demonstrate the validity of (i, ii) also for such packings of non-convex particles. Moreover, we investigate the contact statistics of these packings to elucidate the microstructural features that underlie (i, ii). Our results show that the contact number per species also satisfies a simple mixing law and that similar microscopic rearrangements of contacts as in monodisperse dimer packings accompany the formation of the density peak in binary mixtures largely independent of the mixture composition.

Precise mix-design of Ultra-High Performance Concrete (UHPC) based on physicochemical packing method: From the perspective of cement hydration

• A physicochemical packing method to optimize the design of UHPC is proposed. • A new equivalent particle size distribution of hydrated cement is calculated. • The macro characteristics of the newly developed UHPC is evaluated. • The hydration kinetics of the newly developed UHPC is evaluated. • The microstructure development of the newly developed UHPC is evaluated. It is widely accepted that Ultra-High Performance Concrete (UHPC) could be designed by the employment of Modified Andreasen and Andersen (MAA) particle packing model. However, the traditional MAA model only takes into account that dry particles reach the dense packing status under physical conditions, without considering the chemical hydration of wet cement particles. To solve this problem, this study adopts a physicochemical packing method to optimize the mix-design of UHPC through establishing a new equivalent particle size distribution of hydrated cement by applying a multilayer spherical shell model. Based on this, the mix proportion of UHPC is redesigned and the properties of the optimized UHPC are evaluated afterwards. The results show that the optimized mix-design leads to higher particle packing density of UHPC, thereby improving the durability on the premise of guaranteeing the workability and mechanical properties. Meanwhile, the optimized mix-design can also achieve denser micro structures of UHPC matrix, which provides a valuable reference to design UHPC more scientifically and reasonably.

Experimental investigation of segregation in a rotating drum with non-spherical particles

The focus of the current investigation is to study the influence of particles’ shape on segregation of bi-disperse mixture of particles in a rotating drum. The effects of various particle parameters such as shape, size, density and size ratio are investigated along with system parameters like time, rotational speed. The results show the shape of both coarse and fine particles influence mixing. For the coarse particles, decreasing trend of extent of radial segregation as follows: sphere > oblate > prolate > elongated-needle. For the fine particle, the trend follows as sphere > cube > prolate. These trends are strongly correlated to the mono-dispersed random packing density and particle angularity. The result shows that coarse particles with higher mono-dispersed random packing density show less segregation whereas fine particles with greater angularity improves mixing. Segregation can be controlled in multiple scenarios in industries by choosing the appropriate shape of the particles. • Coarse particles with higher mono-dispersed random packing density promote mixing. • For coarse particles segregation pattern: Sphere >oblate >prolate >elongated needle. • The fine particles with greater angularity promote mixing. • For fine particles segregation pattern: Sphere >cube >prolate.

Effect of nano-metakaolin on the thixotropy of fresh cement paste

• Nano-metakaolin increases the thixotropy of fresh cement paste. • The maximum thixotropy of cement pastes occurs in the temperature range of 25–30 °C. • The thixotropy of NMK cement pastes shows an increasing trend with the hydration time. • The thixotropy of NMK cement pastes increases linearly with the yield stress. Nano-metakaolin (NMK) was used to increase the viscosity of fresh cement pastes and the mechanical properties and durability of hardened cement-based materials. However, the effect of NMK on the thixotropy of fresh cement pastes was not systematically investigated. The paper investigates the thixotropy of NMK cement pastes, the effects of superplasticizer, NMK content, hydration time, and environmental temperature were considered. The size of the flocculation structures (flocs) of the NMK cement pastes was measured, and the hysteresis loop area of the NMK cement pastes was identified. The relationships between the hysteresis loops area and yield stress, packing density, and particles spacing of the NMK cement pastes were established. The results showed that the incorporation of NMK increased the thixotropy of fresh cement pastes with and without superplasticizer addition. NMK significantly increased the thixotropy of the cement pastes with superplasticizers addition. The thixotropy of NMK cement pastes firstly increased and then decreased within 10 – 45 °C, the maximum thixotropy appeared at around 25–30 °C. The thixotropy of the NMK cement pastes exhibited an increasing trend with the hydration time. The thixotropy of the NMK cement pastes linearly increased with the yield stress. The hysteresis loop area decreased with the increase of the packing density and particles spacing.

TEMPus VoLA: The timed Epstein multi-pressure vessel at low accelerations.

The field of planetary system formation relies extensively on our understanding of the aerodynamic interaction between gas and dust in protoplanetary disks. Of particular importance are the mechanisms triggering fluid instabilities and clumping of dust particles into aggregates, and their subsequent inclusion into planetesimals. We introduce the timed Epstein multi-pressure vessel at low accelerations, which is an experimental apparatus for the study of particle dynamics and rarefied gas under micro-gravity conditions. This facility contains three experiments dedicated to studying aerodynamic processes: (i) the development of pressure gradients due to collective particle-gas interaction, (ii) the drag coefficients of dust aggregates with variable particle-gas velocity, and (iii) the effect of dust on the profile of a shear flow and resultant onset of turbulence. The approach is innovative with respect to previous experiments because we access an untouched parameter space in terms of dust particle packing fraction, and Knudsen, Stokes, and Reynolds numbers. The mechanisms investigated are also relevant for our understanding of the emission of dust from active surfaces, such as cometary nuclei, and new experimental data will help interpreting previous datasets (Rosetta) and prepare future spacecraft observations (Comet Interceptor). We report on the performance of the experiments, which has been tested over the course of multiple flight campaigns. The project is now ready to benefit from additional flight campaigns, to cover a wide parameter space. The outcome will be a comprehensive framework to test models and numerical recipes for studying collective dust particle aerodynamics under space-like conditions.

Effect of sediment form and form distribution on porosity: a simulation study based on the discrete element method

Porosity is one of the key properties of dense particle packings like sediment deposits and is influenced by a multitude of grain characteristics such as their size distribution and shape. In the present work, we focus on the form, a specific aspect of the overall shape, of sedimentary grains in order to investigate and quantify its effect on porosity, ultimately deriving novel porosity-prediction models. To this end, we develop a robust and accurate simulation tool based on the discrete element method which we validate against laboratory experiments. Utilizing digital representations of actual sediment from the Rhine river, we first study packings that are composed of particles with a single form. There, porosity is found to be mainly determined by the inverse equancy, i.e., the ratio of the longest to the smallest form-defining axis. Only for small ratios, additional shape-related properties become relevant, as revealed by a direct comparison to packings of form-equivalent but smooth ellipsoids. Since sediment naturally features form mixtures, we extend our simulation tool to study sediment packings with normally-distributed forms. In agreement with our single form studies, porosity is found to depend primarily on the inverse of the mean equancy. By supplying additional information about a second form factor and the standard deviations, we derive an accurate model for porosity prediction. Due to its simplicity, it can be readily applied to sediment packings for which some measurements of flatness and elongation, the two most common form factors, are available.Graphical abstract

Study on the stability of particle packing structure based on cells

The macroscopic mechanical property and the stability of granular mechanics system are determined by packing structure. Cells play a fundamental role in granular statistical mechanics and thus cells were utilized in this paper to research the packing structure of disk particles and gear particles in a two-dimensional cubic container. The probability distribution of cell order satisfies the exponential function distribution and is independent of intergranular friction, the size of system and vibration. Furthermore, it is observed that friction and system size are the key factors affecting the stability of particle packing structure. Significantly, the relationship between volume fraction and packing structure of disk particles is established under vibration. The experimental results reveal the characteristics of ordered packing structure of disordered particle system in mesoscale and provide data reference for perfecting the theory of particle mechanics.