Polydisperse Particle Systems Research Articles

Permeability estimation from pore to Darcy in cemented granular media using resolved CFD-DEM model

Permeability prediction plays a critical role in many engineering applications that involve fluid flow through porous media. Various factors including pore shape, particle size, polydispersity and compaction levels can significantly impact the flow behavior of a porous medium. Moreover, the influence of cementation should also be considered. In this work, we investigate the effect of particle cementation on the permeability using the three-dimensional resolved CFD-DEM approach. The modified cohesive contact model is utilized to simulate the cementation behavior of particles. The numerical model is initially validated by a laboratory experiment demonstrating similar results for the permeability of the sample with polydisperse particles. Results show that the permeability in both polydisperse and monodisperse particle systems decreases when the cementation of particles increases. Especially, this relationship is observed at higher porosity values. In contrast, in more compacted samples with lower porosity, the cementation effect becomes less. The numerical study also shows that the tortuosity values in both particle systems increase almost linearly with decreasing porosity. However, the strong influence of cementation on tortuosity is noticeable only in a monodisperse particle system dominated by uniform pore shapes with regular fluid paths. A study of fluid flow at different gradation levels reveals that an increase in cementation leads to a significant decrease in the permeability in a sample with larger particles. From the point of view of applying the numerical model to the real reservoir sand sample, the numerical results of permeability align well with the data reported by many studies.

A two-fluid multiphase flow model coupled with the population balance equations for the flow of a multidispersed particle system

SummaryWe present a two-fluid multiphase flow model that can be applied to the flow of polydisperse particle systems. In the model, the flow of polydisperse particle systems with different N particle sizes is considered only as two phases of fluid and particle phases, without considering the individual N phases, and the motion of particles with different diameters is represented by the motion characteristics of fluid and granular phases. The equations for the granular phase are obtained by averaging the Euler equations for the particles of different particle sizes. And the velocity of particles of different particle sizes is calculated by an explicit approximation, similar to determining the slip velocity in a mixed model of multiphase flow without solving the Eulerian momentum equation. Also, the conservation equation of particles of different particle sizes was obtained by adding the source term to the population balance equation, which is caused by the difference in the particle velocity of the particles with different particle sizes. The proposed method was compared with the results of experimental studies presented in the previous study to verify the validity of the method. The method has the advantage of not only visualizing the particle size fraction distribution but also of being stable in calculation and not increasing the computational effort significantly in studying the flow of polydisperse particle systems with particle size distribution.

Segregation flow behavior of polydisperse particle mixture with skewed distribution in a rotating drum

Industrial particle mixtures are naturally polydisperse due to the variations in size distribution during mineral processing, which makes it necessary to investigate segregation behaviors of polydisperse particle mixtures. In this work, five groups of polydisperse particle mixtures were defined separately by different skewed distributions. Based on discrete element method, the polydisperse particle segregation behaviors of in rotary drums were simulated. The results indicate that in the polydisperse particle system with normal distribution, larger particles tend to accumulate towards the both sides, while smaller particles tend to be in the middle of the drum. In this case, the medium-sized particles are uniformly distributed throughout the system. However, once the polydisperse particle mixture transitions from the coarse particle to the fine particle system, the size of medium particles exhibiting uniform distribution characteristics decreases with an increase in the skewness coefficient. Moreover, the smaller the skewness coefficient of the polydisperse particles, the slower the initial particle segregation rate, and the lower the steady particle segregation degree. Furthermore, whether the drum length to diameter (L / D) ratio or drum filling rate increases, the particle segregation rate in initial stage and the particle segregation degree in steady stage are subsequently significantly reduced, while the size of medium particles with uniform distribution characteristics remains essentially constant.

Particle clogging mechanisms in hyporheic exchange with coupled lattice Boltzmann discrete element simulations

The clogging of a stream bed has a significant impact on the exchange of water between a river and groundwater, known as hyporheic exchange. Clogging issues in orifices influenced by fluid flow have long been a concern, particularly in understanding clogging mechanisms and particle dynamics. This study focuses on investigating the behavior of poly-dispersed particle systems in the Shanghai soft soil using a coupled lattice Boltzmann method and a discrete element method (LBM-DEM). A particle-orifice model was developed based on LBM-DEM to study the clogging problem. Three different orifice diameters with the same particle size distribution were set at a microscopic scale. The simulation results indicate that the primary form of clogging is the formation of particle domes, exhibiting distinct characteristics depending on orifice size. As the orifice size increases, clogging becomes more challenging. Interestingly, the flow rate of fluid passing through clogged orifices is quite complex, as it does not decrease significantly. The formation process of the particle structure shows significant randomness, posing challenges for quantitative analysis and experimental validation. This study provides insights into the initial stages of clogging formation, leading to a better understanding of hyporheic exchange phenomena in stream bed ecosystems.

Numerical simulation for the initial state of avalanche in polydisperse particle systems

Numerical simulation is employed to investigate the initial state of avalanche in polydisperse particle systems. Nucleation and propagation processes are illustrated for pentadisperse and triadisperse particle systems, respectively. In these processes, particles involved in the avalanche grow slowly in the early stage and explosively in the later stage, which is clearly different from the continuous and steady growth trend in the monodisperse system. By examining the avalanche propagation, the number growth of particles involved in the avalanche and the slope of the number growth, the initial state can be divided into three stages: T1 (nucleation stage), T2 (propagation stage), T3 (overall avalanche stage). We focus on the characteristics of the avalanche in the T2 stage, and find that propagation distances increase almost linearly in both axial and radial directions in polydisperse systems. We also consider the distribution characteristics of the average coordination number and average velocity for the moving particles. The results support that the polydisperse particle systems are more stable in the T2 stage.

Rigid clumps in the MercuryDPM particle dynamics code

Discrete particle simulations have become the standard in science and industrial applications exploring the properties of particulate systems. Most of such simulations rely on the concept of interacting spherical particles to describe the properties of particulates, although, the correct representation of the nonspherical particle shape is crucial for a number of applications. In this work we describe the implementation of clumps, i.e. assemblies of rigidly connected spherical particles, which can approximate given nonspherical shapes, within the MercuryDPM particle dynamics code. MercuryDPM contact detection algorithm is particularly efficient for polydisperse particle systems, which is essential for multilevel clumps approximating complex surfaces. We employ the existing open-source CLUMP library to generate clump particles. We detail the pre-processing tools providing necessary initial data, as well as the necessary adjustments of the algorithms of contact detection, collision/migration and numerical time integration. The capabilities of our implementation are illustrated for a variety of examples.

Optofluidic force induction as a process analytical technology

Manufacturers of nanoparticle-based products rely on detailed information about critical process parameters, such as particle size and size distributions, concentration, and material composition, which directly reflect the quality of the final product. These process parameters are often obtained using offline characterization techniques that cannot provide the temporal resolution to detect dynamic changes in particle ensembles during a production process. To overcome this deficiency, we have recently introduced Optofluidic Force Induction (of2i) for optical real-time counting with single particle sensitivity and high throughput. In this paper, we apply of2i to highly polydisperse and multi modal particle systems, where we also monitor evolutionary processes over large time scales. For oil-in-water emulsions we detect in real time the transition between high-pressure homogenization states. For silicon carbide nanoparticles, we exploit the dynamic of2i measurement capabilities to introduce a novel process feedback parameter based on the dissociation of particle agglomerates. Our results demonstrate that of2i provides a versatile workbench for process feedback in a wide range of applications.Graphical abstract

Particle size distribution measurement based on the angular scattering efficiency factor spectra inversion-simulation and experiment.

The quantification of the particle size distribution (PSD) within a particle system is significant to various domains, including atmospheric and environmental sciences, material science, civil engineering, and human health. The scattering spectrum reflects the PSD information of the particle system. Researchers have developed high-precision and high-resolution PSD measurements for monodisperse particle systems through scattering spectroscopy. However, for polydisperse particle systems, current methods based on light scattering spectrum and Fourier transform analysis can only obtain the information of the particle component, but cannot provide the relative content information of each component. In this paper, a PSD inversion method based on the angular scattering efficiency factors (ASEF) spectrum is proposed. By establishing a light energy coefficient distribution matrix, and then measuring the scattering spectrum of the particle system, PSD can be measured in conjunction with inversion algorithms. The simulations and experiments conducted in this paper substantiate the validity of the proposed method. Unlike the forward diffraction approach that measures the spatial distribution of scattered light I(θ) for inversion, our method uses the multi-wavelength distribution information of scattered light β(λ). Moreover, the influences of noise, scattering angle, wavelength, particle size range, and size discretization interval on PSD inversion are studied. The method of condition number analysis is proposed to identify the appropriate scattering angle, particle size measurement range, and size discretization interval, and it can reduce the root mean square error(RMSE) of PSD inversion. Furthermore, the method of wavelength sensitivity analysis is proposed to select the spectral band with higher sensitivity to particle size changes, thereby improving the computational speed and avoiding the problem of diminished accuracy caused by the reduction of the number of wavelengths used.

CFD-DEM simulation of fluorination reaction in fluidized beds with local grid and time refinement method

The gas-solid reaction process with wide particle size distribution is extensively used in the chemical engineering field, especially the particle reacts with the gas gradually, such as fluorination reactions in fluidized beds. When the computational fluid dynamics-discrete element method (CFD-DEM) is used for the coupling simulation of multiphase and polydisperse particle reaction system, the grid size directly affects the accuracy of flow field information and simulation of chemical reaction. Furthermore, particle calculation time step will directly affect the efficiency of coupling calculation. In this work, a local grid and time step refinement method is proposed to simulate multiphase and polydisperse particle fluidization reaction system. In this method, the refined DEM grids are automatically generated in the computational domain around the fine particles, and the detailed fluid phase information is obtained with the interpolation algorithm. In the two-phase coupling process, particles are divided into different groups based on physical properties, each group has its own independent time step. The multistage conical-cylindrical spouted bed is proposed for the fluorination reaction process; the operating gas velocity range of the polydisperse particle system is extended by the new design while the particle size distribution changes with the gas-solid reaction process. It is demonstrated that the local grid and time step refinement method can improve the accuracy and efficiency of the traditional CFD-DEM method in the reaction process simulation, which describes a polydisperse particle system with wide particle size distribution. Aimed at improving the simulation accuracy and efficiency, this paper will be helpful for simulating the particle reaction process in the gas-solid fluidized bed and beneficial for the development of the CFD-DEM method.

Light energy distribution of submicron charged particles based on the scattering-enhancing effect

Magnetic microspheres, charged soot and other charged sub-micron particles are widely used, and the accurate measurement of their particle size is crucial to biomedical, environmental monitoring and other fields. During light scattering measurements, the light energy distribution projected onto each ring surface of the photodetector is the core data for particle size inversion calculations. When the measured particle is charged, the light energy distribution will be different from its neutral state due to the scattering-enhancing effect of surface charges. Therefore, it is necessary to confirm the extent of the scattering-enhancing effect on the light energy distribution by numerical simulation, before actual measurement. In this paper, calculation models of scattered light energy distribution are established for charged single particle, monodisperse particle system and polydisperse particle system respectively. Considering the difference between the complex refractive indices of charged particles, the forward scattering of silica and polystyrene with different monodisperse degrees are taken as an example to analyze the light energy distribution. The results show that the scattering-enhancing effect of surface charges can affect the light energy distribution of submicron particles, and the smaller the median diameter of the particle system and the lower the monodisperse degree, the more significant the effect is. At a median diameter of 0.1 μm, the light energy of charged particles with different monodisperse degrees increased by an average of about 3.5 times, near the scattering angle of 45° This research realizes the forward deduction of the light energy distribution for charged particles, and provides the necessary theoretical support for the visible light measurement of charged submicron and nanoparticles.

The effect of turbulence on the conversion of coal under blast furnace raceway conditions

The main production route for steel in Europe is still via the blast furnace. Computational fluid dynamics (CFD) can be used to analyze the process virtually and thus improve its performance. Different reducing agents can be used to (partially) substitute the coke and consequently reduce overall emissions. To analyze different reducing agents effectively using CFD, their conversion process has to be modeled accurately. Under certain conditions, coal particles can cluster as the result of turbulence effects, which further reduces the mass transfer to the coal surface and consequently the conversion rate. We analyze the effect of turbulence under blast furnace raceway conditions on the conversion of coal particles and on the overall burnout. The model is applied in RANS to polydisperse particle systems and this is then compared to the simplified monodisperse assumption. Additionally, the model is extended by adding gasification reactions. Overall, we find that the turbulent effects on coal conversion are significant under blast furnace raceway conditions and should be considered in further simulations. Furthermore, we show that an a-priori assessment is difficult because the analysis via averaged quantities is impractical due to a strong variation of conditions in the furnace. Therefore, the effects of turbulence need to be correlated to the regions of conversion.

Bubble-Based EMMS Drag Model for Particle Segregation Simulation with a Continuous Size Distribution

Particles in industrial fluidized beds are usually continuously distributed rather than monodisperse in size, and the separation of particles is a key factor in determining the performance of the fluidized reactor. In this paper, a bubble-based Energy Minimum Multi-Scale (EMMS) drag model was proposed to simulate polydisperse segregation in a gas–solid fluidized bed. Particle size distribution (PSD) was split into a sufficient class of characteristic particle sizes. Each size was treated as a solid phase, and the total drag force could be estimated by considering the influence of all solid phases and mesoscale structures. The EMMS drag model was then coupled with the Eulerian multi-fluid model (MFM) to simulate the segregation behavior of a polydisperse particle system. The effects of discrete particle size classes, different drag models, and gas velocities on the simulation results were also discussed under different operating conditions. The results showed that the present drag model was in better agreement with the experimental data in terms of axial solids concentration and mean particle size distribution than other models. In bubbling beds, the segregation patterns of polydisperse particles can be well predicted by this method.

A new GPU-based DEM simulator for polydispersed granular systems with wide size distribution and its application in the silo discharge

While discrete element method (DEM) has been successfully established in many studies, serious problems have limited its industrial-scale applications. Considerably long runtime is one of the most critical bottlenecks of the DEM simulation applicability. Despite extensive efforts on the parallelization of DEM on the CPU or GPU, DEM runtime on the current generation of computers is so long that further improvements are demanded. Moreover, while many real-world granular systems consist of polydispersed particles with a relatively wide size distribution, the majority of DEM simulation studies have assumed monodispersed particle assemblies. Few have studied the parallelization of polydispersed systems, and fewer have developed GPU-based codes for these systems. The main purpose of this study is to provide a novel solver, NP-DEM, which is optimized for GPU-based simulation of polydispersed particle systems with a wide size distribution. Silo discharge is chosen as the case study to examine the applicability of the code.

Machine Learning for heat radiation modeling of bi- and polydisperse particle systems including walls

We investigated the ability of four popular Machine Learning methods i.e., Deep Neural Networks (DNNs), Random Forest-based regressors (RFRs), Extreme Gradient Boosting-based regressors (XGBs), and stacked ensembles of DNNs, to model the radiative heat transfer based on view factors in bi- and polydisperse particle beds including walls. Before training and analyzing the predictive capability of each method, an adjustment of markers used in monodisperse systems, as well as an evaluation of new markers was performed. On the basis of our dataset that considers a wide range of particle radii ratios, system sizes, particle volume fractions, as well as different particle-species volume fractions, we found that (i) the addition of particle size information allows the transition from monodisperse to bi- and polydisperse beds, and (ii) the addition of particle volume fraction information as the fourth marker leads to very accurate predictions. In terms of the overall performance, DNNs and RFRs should be preferred compared to the other two options. For particle–particle view factors, DNN and RFR are on par, while for particle–wall the RFR is superior. We demonstrate that DNNs and RFRs can be built to meet or even exceed the prediction quality standards achieved in a monodisperse system.

Packing Fraction, Tortuosity, and Permeability of Granular‐Porous Media With Densely Packed Spheroidal Particles: Monodisperse and Polydisperse Systems

AbstractThe geometrical and topological configurations of particles have great influences on their surrounding pore tortuosity and the permeability of granular‐porous media. In this work, we develop a relaxation iteration scheme to create random dense packings of different anisotropic‐shaped spheroidal particles with monodispersity and polydispersity in sizes, which manifest the effects of particle shape, fineness, and size distribution on the random packing fraction of particles. Subsequently, we propose a direction‐guided rapidly exploring random tree (DGRRT) algorithm to probe the geometrical tortuosity of complex pore space interstitial to spheroidal particles. A non‐linear pore tortuosity prediction model that relies on the specific surface area and packing fraction of particles, is developed to suit for polydisperse and monodisperse spheroidal particle systems. We further investigate the permeability of granular‐porous media through the lattice Boltzmann method (LBM) of fluid flow. These proposed methods can accurately predict the tortuosity and permeability by comparing against available experimental, theoretical, and numerical results reported in literature. Moreover, the effects of particle packing fraction (i.e., porosity), shape, fineness, and size distribution on the pore tortuosity and permeability of granular‐porous media are evaluated. The results reveal that these microstructural configurations have important influences on the permeability and tortuosity. Our results give an intrinsic interplay between the geometrical tortuosity and permeability of monodisperse and polydisperse particle systems, which have implications for a broad range of scientific disciplines, including the properties of rocks, sandstones and soils, and the design of ultra‐high performance concrete.

Effects of beam divergence and polychromaticity on small angle x-ray scattering measurements with laser plasma sources

We explore the feasibility of small angle x-ray scattering (SAXS) measurements with intense laser-induced plasma sources. Such x-ray sources are inherently polychromatic and divergent. We simulate SAXS patterns using monochromatic and polychromatic x-ray sources with different divergences of polydisperse particle systems with different size distributions. The beam divergence is adjusted via varying x-ray source size, pinhole size, and the source-to-pinhole distance. Three typical laser plasma He-α sources (Fe, Cu, and Ge) are considered. The scattering curves are analyzed using the modified Guinier approach and the total non-negative least squares method. We demonstrate certain feasibility of SAXS measurements using laser plasma sources with a finite size, without a monochromator and additional software desmearing.

Predicting the permeability coefficient of polydispersed sand via coupled CFD–DEM simulations

Permeability is one of the most fundamental properties of soil, which governs many geotechnical engineering problems. However, among the published equations that predict the permeability coefficient k, the influence of a wide range of particle size distributions (PSDs) on k was not considered accurately. This research aims to quantify the influence of PSD on k and propose a prediction equation for k. Coupled computational fluid dynamics–discrete element method (CFD–DEM) simulations were conducted to reproduce the constant head permeability tests of different soil samples. The results show that among the various drag models implemented in the CFD–DEM, the Syamlal–O’Brien drag model leads to the highest accuracy in simulating sand permeability. The permeability coefficient is proportional to the square of the Sauter mean diameter of the polydispersed particle system. Therefore, the prediction equation for k considering the PSD of the particle system is proposed based on the particle gradation and the size characteristics Cu, Cc, and d10. The proposed equation is verified well by published experimental data. Additionally, the proposed equation can calculate the k of irregular calcareous sand by representing the effect of particle irregularity with the Kozeny–Carman (KC) constant.

Simultaneous Reciprocal and Real Space X-Ray Imaging of Time-Evolving Systems

Imaging the (sub)micron scale over large areas with high temporal resolution becomes increasingly necessary for the development and investigation of novel materials under realistic operation conditions. Small angle x-ray scattering imaging methods provide micro- and nanoscale structural information of materials. A fundamental shortcoming of such methods is the long acquisition time required to investigate macroscopic objects. In this work, we propose a single shot imaging method that allows reciprocal space sensitivity at a local level while maintaining spatial resolution for imaging macroscopic objects. We use an instrument that is sensitive to the ultrasmall angle x-ray scattering range and utilize it to image unstable polydisperse particle systems. This allows us to observe in real time the evolution of the local average particle diameter due to the stratification of the microparticles.

A novel CFD-DEM coarse-graining method based on the Voronoi tessellation

In unresolved flow CFD-DEM simulations, the porosity values for each CFD cell are determined using a coarse-graining algorithm. While this approach enables coupled simulations of representative numbers of particles, the influence of the porosity local to the particles on the fluid-particle interaction force is not captured. This contribution considers a two-grid coarse-graining method that determines a local porosity for each particle using a radical Voronoi tessellation of the system. A relatively fine, regular point cloud is used to map these local porosity data to the CFD cells. The method is evaluated using two different cases considering both disperse and tightly packed particles. The data show that the method conserves porosity data, is reasonably grid-independent and can generate a relatively smooth porosity field. The new method can more accurately predict the fluid-particle interactive force for polydisperse particle system than alternative methods that have been implemented in unresolved CFD-DEM codes.

Vaporization characteristics and aerosol optical properties of electronic cigarettes.

The aerosols generated from electronic cigarettes have a significant impact on the human respiratory system. Understanding the vaporization characteristics and aerosol optical properties of electronic cigarettes is important for assessing human exposure to aerosols. An experimental platform was designed and built to simulate the atomization process of electronic cigarette and detect the laser transmissivity of aerosols. The optical properties of single particles and polydispersed particle system for aerosols in the visible wavelength ranges of 400-780nm were analyzed based on Mie theory. The results show that a higher heating power supplied by coil results in a larger average vaporization rate of e-liquid. Meanwhile, the steady-state transmissivity of the laser beam for aerosols reduces as the heating power increases. Under the same heating power and puffing topography, the total particulate mass (TPM) of aerosols generated by the e-liquid composed of higher vegetable glycerin (VG) content decreases. The scattering efficiency factor of aerosol particle of electronic cigarette increases with an increase in particle size. The volume scattering coefficients of a polydispersed particle system of aerosols decrease as the incident visible wavelengths increase. A higher VG content in e-liquid results in decreased TPM and particle number concentration of aerosols and increased the volume scattering coefficient in the visible wavelength range. It can explain an interesting phenomenon that a lower TPM and a better visual effect brought by the aerosols generated by the e-liquid with a higher VG content could be observed concurrently. The mass indexes (e.g., TPM, average vaporization rate, average mass concentration) and optical indexes (e.g., volume scattering coefficient, laser transmissivity) are suggested to be used for the comprehensive evaluation of relative amounts of aerosols. The results have potential significances for the objective and quantitative assessments of aerosols generated from electronic cigarettes.