Fractal Particles Research Articles

Field measurements and modelling of climate driven hydraulic flux, water content and suction in a loess slope

Rainfall-triggered shallow slope failures are common in New Zealand loess. While often unsaturated, rainfall infiltration reduces suction in the loess as the water content increases, resulting in reduction in shear strength and increased potential for slope instability. Here the hydraulic response of an in-situ loess slope to natural rainfall and evapotranspiration is examined using long term field instrumentation. Data from a 19-month monitoring period show that the loess’ hydraulic behaviour responds to change in seasonal climatic conditions, highlighting the relationship between moisture content and suction with evapotranspiration and infiltration. To simulate the field response, a one-dimensional steady infiltration/evapotranspiration model has been developed, exploiting the unique power laws which interrelate water content, suction and hydraulic conductivity which arise from a loess’s fractal particle and pore size distributions. Hydraulic hysteresis is also accounted for. Closed form expressions are derived for the subsurface suction profile, from which profiles of moisture content, hydraulic conductivity and the suction’s contribution to strength may be obtained. Simulated subsurface water contents are in good agreement with field observations. Furthermore, fluxes across the loess surface used to obtain the modelled quantities are in general agreement with local climatic conditions and their variations during the monitoring period. Modelled and measured data are strongly correlated at shallow depths, having a Pearson correlation coefficient of 0.53.

Fractal Analysis of Particle Size and Morphology in Single-Particle Breakage Based on 3D Images

The accurate modeling of single-particle breakage based on three-dimensional (3D) images is crucial for understanding the particle-level mechanics of granular materials. This study aims to propose a systematic framework incorporating single-particle breakage experiments and numerical simulations based on a novel 3D particle reconstruction technique for fractal analysis of particle size and morphology in single-particle breakage. First, the vision foundation model is used to generate accurate particles from 3D images. The numerical approach is validated by simulating the single-particle breakage test with multiple Fujian sand particles. Then, the breakage processes of reconstructed sand particles under axial compression are numerically modeled. The relationship between 3D fractal dimensions and particle size, particle crushing strength, and morphology is meticulously investigated. Furthermore, the implications of these relationships on the particle breakage processes are thoroughly discussed, shedding light on the underlying mechanisms that govern particle breakage. The framework offers an effective way to investigate the breakage behavior of single sand particles, which will enhance understanding of the mechanism of the whole particle breakage process.

Shear Behaviors of Confined Flow: Insights for Understanding the Influences of Fractal Particle Size Distribution on High Mobility of Granular Flows

AbstractGranular flows, such as rockslide debris flows, can reach high velocities and travel vast distances, but mechanisms behind this high mobility remain elusive. Using the Discrete Element Method, we implement confined shear flow with fractal particle size distribution to study the physical mechanisms inside the highly localized basal zones. Our results show that the shear strength of confined flow decreases at large fractal dimensions, and a notable transition in shear behavior also occurs with increasing fractal dimension: large particles exhibit low granular temperature and act as solid phase within a semi‐diluted suspension, and small particles enter the rolling regime. The small particles behave as interstitial fluids and reduce the shear strength of confined flow. We suggest that the reduction of shear strength stemming from the fractal particle size distribution may provide insights into the mechanisms within the highly localized basal zones, ultimately contributing to the high mobility of granular flows.

A Roundness Calculation Method and Physical Parameter Analysis of A Porous Medium Model

The rounding degree of particles is an important index of particle morphology. It represents the degree of rounding of the original edges and corners of debris particles. To a certain extent, it can reflect the transportation and deposition process of debris particles and the source properties. Therefore, it is of great significance to explore the rounding law of gravel and the influencing factors of rounding degree for the study of geological sedimentary environment, source analysis and mass transfer process. Therefore, this paper proposes a rounding degree calculation algorithm for fractal porous media model particles with rounding characteristics. Through numerical simulation and theoretical analysis, combined with the geometric parameters of particle morphology, the relationship between particle roundness and area and perimeter parameters is discussed in detail. The results show that roundness is an important factor in the geometric parameters of particles. The change of roundness can significantly affect the geometric shape of particles, and then affect the size and area of particles. It is of great significance for understanding and optimizing the flow characteristics of porous media models.

A novel grey forecasting model with generalised fractal derivative and its optimisation

PurposeThe purpose of this paper is to propose a new grey prediction model, GOFHGM (1,1), which combines generalised fractal derivative and particle swarm optimisation algorithms. The aim is to address the limitations of traditional grey prediction models in order selection and improve prediction accuracy.Design/methodology/approachThe paper introduces the concept of generalised fractal derivative and applies it to the order optimisation of grey prediction models. The particle swarm optimisation algorithm is also adopted to find the optimal combination of orders. Three cases are empirically studied to compare the performance of GOFHGM(1,1) with traditional grey prediction models.FindingsThe study finds that the GOFHGM(1,1) model outperforms traditional grey prediction models in terms of prediction accuracy. Evaluation indexes such as mean squared error (MSE) and mean absolute error (MAE) are used to evaluate the model.Research limitations/implicationsThe research study may have limitations in terms of the scope and generalisability of the findings. Further research is needed to explore the applicability of GOFHGM(1,1) in different fields and to improve the model’s performance.Originality/valueThe study contributes to the field by introducing a new grey prediction model that combines generalised fractal derivative and particle swarm optimisation algorithms. This integration enhances the accuracy and reliability of grey predictions and strengthens their applicability in various predictive applications.

Fluorescence-Based Image Analysis of Seepage Behavior in Drip Irrigation: Exploring Varied Fractal Grading in Media Permeability

In the recycling of low-value metallic elements, heap leaching is commonly employed. The particle size distribution is a crucial parameter in heap leaching implementation, and the percolation behavior of a heap has always been a focal point in heap leaching technology. This paper utilizes a novel form of ultraviolet fluorescence image acquisition and fluorescence image analysis to investigate the percolation process with different fractal dimension particle size distributions, where the maximum particle diameter is 10 mm. The ore used was low-grade copper ore. The results indicate that the new fluorescence image analysis method can reveal different percolation regions during the heap leaching process, aiding in a better understanding of heap leaching behavior. The combined study found that under irrigation conditions of 10 mL/min, seepage was more uniform under the heap structure formed by a particle gradation with a fractal dimension of 2.2.

Shear thickening of dilute suspensions of fractal silica aggregates

The increase in viscosity under shear known as shear thickening (ST) is an inherent property of a wide variety of dense particulate suspensions. Recent studies indicate that ST systems formed by fractal particles are promising candidates for various practical applications. However, ST in fractal systems remains poorly explored. Here we experimentally study the ST behavior in suspensions of hydrophilic fumed silica (FS) particles in glycerol. Remarkably, unlike non-fractal systems, we observe a strong dependence of the onset stress for ST on the volume fraction of fractal objects and a reversible weakening of the ST response that depends strongly on the particle volume fraction as well as the properties of the FS system. Using in-situ boundary imaging, we map out the spatio-temporal flow properties during ST for different FS systems. We find that the fractal nature and structural properties like the internal branching of the particles can qualitatively explain the complex ST phase diagram of these systems.

Fractal evolution model of proton spatial distribution in low water/binder cement-based composites (LW/B-CC) during early-age hydration process

This study establishes the fractal evolution model of proton spatial distribution in low water/binder cement-based composites (LW/B-CC) based on fractal theory and low field nuclear magnetic resonance (LF NMR) technology. The results show that the fractal evolution process of gel water, capillary water and surface water distributions in LW/B-CC presents three stages: the first 4–6 h after the beginning of hydration, 4–6 h to 12 h, and 12 h to long-term stage. In the first and second stages, the fractal dimensions of gel and capillary water increase linearly with hydration time, while the fractal dimension of surface water decreases linearly. The boundary is a sudden change of fractal dimensions after about 4–6 h of hydration. The third stage starts after about 12 h of hydration, at which time the fractal dimensions begin to converge to fixed values. Besides, this study reveals the mathematical relationship between fractal dimension (Df) and particle size distribution modulus (q), which is conducive to achieve the full-cycle regulation of LW/B-CC.

Investigation on the rock-breaking performance of specially-shaped PDC cutter under confining pressure conditions

Cutter shape has a significant influence on the rock-breaking performance of drill bit. Compared with conventional Polycrystalline Diamond Compact (PDC) cutter, the emergence of specially-shaped PDC cutters (SSPCs) with different geometric shapes is of great benefit to solve the problems of low rate of penetration (ROP) and rock-breaking efficiency in deep hard and hot dry rock formations. However, the high confining pressure and high in-situ stress (HCHS) have a significant influence on the rock-breaking performance of PDC cutter which cannot be ignored. Given that the above facts, this paper selects five kinds of PDC cutters with different cutter shapes, and implements a series of cutting experiments of granite under confining pressure conditions (CPCs) and atmospheric pressure condition (APC) using a true triaxial rock cutting device. The influence of cutter profile on the rock-breaking performance of PDC cutter was studied from the perspective of cutting force, mechanical specific energy (MSE), cuttings, coarseness index (CI) and fractal dimension. The results show that the rock breaking under CPC is more difficult than that under APC, resulting in the increased cutting force and MSE. Moreover, the cuttings obtained under CPC are smaller in size and the cutting grooves are smoother. Cutter shape has a great influence on the rock-breaking efficiency of PDC cutter, the rock-breaking efficiency of axe-shaped cutter is higher, while that of stinger cutter is lower. Moreover, PDC cutters with different shapes have different sensitivities to confining pressure, and stinger cutter has the lowest sensitivity to confining pressure, in other words, confining pressure has little influence on the rock breaking process of stinger cutter. What is more, the distribution of cuttings is characterized by the fractal dimension and particle size distribution parameter from the perspective of cuttings morphology and size respectively, and they present completely opposite changing trends. The obtained results are of great significance to the optimization of cutter profile, the design of bit cutter arrangement and the drilling of deep formation.

Fragmentation energy calculation model of coal crushed by impact load

ABSTRACT Rock fragmentation is a common physical and mechanical phenomenon that exists in a variety of ranges from the mining and processing. Communication is an important operation in coal processing whereby the coal block coming from coalmines is crushed into fragmentations with reduced size, which accounts for 80% of the electricity consumption of mineral processing circuits. Fragmentation energy, which is related to the coal particle size distribution, is an essential parameter for improving the efficiency of shearer, road-header, and crusher. Coal particles are generally simplified into fine or near spherical shapes for analytical and numerical simulation purposes. This research aims to establish the fragmentation energy calculation model for coal fragmentations with coarse and wide size distribution based on the analysis of size distribution and energy-size relationships of coal particles. It has been demonstrated by the results that the fragmentation energy of impact load crushed coal can be determined based on Rittinger’s theory with fractal or RR model particle size distribution.

Measurement and Analysis of Brake and Tyre Particle Emissions from Automotive Series Components for High-Load Driving Tests on a Wheel and Suspension Test Bed

A current challenge in realising clean road transport is non-exhaust emissions. Important advances regarding measurement systems, including well-defined characterisation techniques, as well as regulation, will be made in the next few years. In this work, we present the detailed results of particle emission analyses, consisting of aerosol (size distribution, particle number (PN), and mass (PM)) and electron microscopy (EM) measurements, under different load conditions on a test bed for a wheel suspension and brakes. Standard tyres and brakes from serial production were tested with a high-load driving cycle, while particle measurements were conducted by gravimetric measurements and with a TSI SMPS, a TSI APS, and a GRIMM OPS. Furthermore, samples were analysed by electron microscopy. A bimodal particle size distribution (PSD) was obtained with an SMPS, with peaks at 20 nm and around 400 nm. The results of an EM analysis of >1400 single particles from the electrostatic sampler match the PSD results. The EM analysis also showed ultrafine particles, mainly containing O, Fe, Si, Ba, Mg, and S, and also fractal particles with high-C fractions. Our results suggest, in agreement with the previously published literature, that particulate emissions are related to the brake disc temperature and occur in significant amounts above a threshold temperature.

Effect of Heating Emissions on the Fractal Size Distribution of Atmospheric Particle Concentrations

Excessive particle concentrations during heating periods, which greatly affect people’s physical and mental health and their normal lives, continue to be a concern. It is more practical to understand and analyze the relationship between the fractal dimension and particle size concentration distribution of atmospheric particulate matter before and after adjusting heating energy consumption types. The data discussed and analyzed in this paper were collected by monitoring stations and measured from 2016 to 2018 in Xi’an. The data include fractal dimension and particle size concentration changes in the atmospheric particulate matter before and after adjusting the heating energy consumption types. The results indicate that adjusting the heating energy consumption types has a significant impact on particulate matter. The average concentration of PM2.5 decreased by 26.4 μg/m3. The average concentration of PM10 decreased by 31.8 μg/m3. At the same time, the different particle sizes showed a downward trend. The particles ranging from 0.265 to 0.475 μm demonstrated the maximum decrease, which was 8.80%. The heating period in Xi’an mainly involves particles ranging from 0 to 0.475 μm. The fractal dimensions of the atmospheric particulate matter before and after adjusting the heating energy consumption types were 4.809 and 3.397, respectively. After adjusting the heating energy consumption types, the fractal dimension decreased by 1.412. At that time, the proportions of particle sizes that were less than 1.0 μm, 2.0 μm, and 2.5 μm decreased by 1.467%, 0.604%, and 0.424%, respectively. This paper provides new methods and a reference value for the distribution and effective control of atmospheric particulate matter by adjusting heating energy consumption types.

Enhancing K-Nearest Neighbors Algorithm in Wireless Sensor Networks through Stochastic Fractal Search and Particle Swarm Optimization

The utilization of wireless sensor networks (WSNs) holds significant importance in diverse data collection applications. Efficient operation of computers, especially in predictive tasks, is imperative for obtaining accurate results within WSNs. This research introduces an innovative approach employing Stochastic Fractal Search-Particle Swarm Optimization (SFS-PSO) to enhance the performance of the K-Nearest Neighbors (KNN) algorithm. The proposed methodology initiates with the establishment of a particle population, dynamically adjusting their positions and velocities and integrating a diffusion process. Through an iterative process of incremental adjustments and evaluations, the algorithm fine-tunes its parameters, resulting in a refined KNN regression model. The enhanced model exhibits substantial improvements, as indicated by the notable reduction in root mean square error (RMSE) and mean absolute error (MAE), accompanied by a strengthened correlation between variables. The favorable outcomes underscore the efficacy of the SFS-PSO optimization technique in augmenting the KNN algorithm's performance within wireless sensor networks. In simpler terms, the application of SFS-PSO in conjunction with KNN leads to a significant decrease in RMSE, reaching a value as low as 0.00894, demonstrating the notable effectiveness of this optimization approach in refining the predictive capabilities of the KNN algorithm in the context of WSNs.

Aerosols are not spherical cows: using discrete dipole approximation to model the properties of fractal particles

ABSTRACT The optical properties of particulate-matter aerosols, within the context of exoplanet and brown dwarf atmospheres, are compared using three different models: Mie theory, modified mean field (MMF) theory, and discrete dipole approximation (DDA). Previous results have demonstrated that fractal haze particles (MMF and DDA) absorb much less long-wavelength radiation than their spherical counterparts (Mie), however it is shown here that the opposite can also be true if a more varying refractive index profile is used. Additionally, it is demonstrated that absorption/scattering cross-sections, and the asymmetry parameter, are underestimated if Mie theory is used. Although DDA can be used to obtain more accurate results, it is known to be much more computationally intensive; to avoid this, the use of low-resolution aerosol models is explored, which could dramatically speed up the process of obtaining accurate computations of optical cross-sections within a certain parameter space. The validity of DDA is probed for wavelengths of interest for observations of aerosols within exoplanet and brown dwarf atmospheres ($0.2-15~\mu$m). Finally, novel code is presented to compare the results of Mie, MMF, and DDA theories (coral: Comparison Of Radiative AnaLyses), as well as to increase and decrease the resolution of DDA shape files accordingly (spherify). Both codes can be applied to a range of other interesting astrophysical environments in addition to exoplanet atmospheres, for example dust grains within protoplanetary discs.

DEM study on role of fines in mobility of dry granular flows considering particle size-shape correlation

Many field observations show that the shape characteristic of particles constituting natural or industrial loose deposits is often size-correlated, that is, either more regular or irregular for larger particles than fines, depending on the particle formation process. Motivated by this, the role of fines in mobility of gravity-driven dry granular flows has been explored numerically through the collapse of granular columns with fractal particle size distributions. A series of granular columns with different combinations of initial aspect ratio, fractal dimension and particle size-elongation correlation (i.e., positively, negatively correlated and uncorrelated cases) are prepared by the discrete element method to conduct column collapse simulations. Among which, a general framework for generating size-shape correlated particles has been proposed using the Fourier-based particle morphology characterization method. Results show that fines may enhance or hardly influence the mobility of dry granular flows, hinging on the actual particle size-shape correlation. Specifically, for the particle size-elongation uncorrelated and negatively correlated cases, the mobility of dry granular flows is almost independent of the fine content, while it increases with the fine content for the size-elongation positively correlated case. The underlying mechanisms are also explored to unravel the observed flow mobility differences from perspectives of the flow characteristic and energy dissipation.

Single‐Scattering Properties of Encapsulated Fractal Black Carbon Particles Computed Using the Invariant Imbedding T‐Matrix Method and Deep Learning Approaches

AbstractEfficient and accurate computation of the single‐scattering properties of black carbon (BC) aerosols is fundamental in various fields, including remote sensing and climate simulations. In this study, we developed a composite model of fractal aggregates of BC encapsulated with hygroscopic aerosols to represent the ambient BC. We used the invariant imbedding T‐matrix method to compute the optical properties of fully and partially encapsulated BC aerosols. In this new model, the traditional assumption of unoverlapped surfaces in the super‐position T‐matrix method is unnecessary. After extensive simulations, we established a database of single‐scattering properties, including the extinction efficiency, the single‐scattering albedo, the asymmetry factor and six phase matrix elements. Moreover, we obtained deep neural networks (DNNs) from this database using a deep learning method. These DNN models provide a universal interface for predicting the optical properties of ambient BC aerosols. Specifically, through a modified architecture of the DNN, we trained two models based on the database to predict three integrated optical properties (extinction efficiency, single‐scattering albedo, and asymmetry factor) and six phase matrix elements. We performed statistical assessments based on the true values in the database and the predicted values from the DNNs, demonstrating that the DNNs accurately predicted all single‐scattering properties. Therefore, the developed DNN models can be conveniently implemented in aerosol optical parameterization for remote sensing studies and atmospheric models.

Study on the relationship between fractal dimension and particle fragmentation for marine coral sand under impact load

As a subsoil for many offshore structures, marine coral sand can encounter various impact loads, resulting in particle fragmentation. The "fractal theory" is an excellent method to quantify particle fragmentation. However, the relationship between the fractal dimension and relative breakage as well as its influencing factors are somewhat limited for coral sand under impact loads. Therefore, this paper systematically investigates the fractal behavior of a classic type of coral sand in the South China Sea through a series of impact load experiments. The experiment results show that the gradation curve of the coral sand under impact loading exhibits evident fractal characteristics after fragmentation, with the fractal dimension increasing with increasing fragmentation. And the ultimate fractal dimension is independent of the particle size and uniformity coefficient. Therefore, taking the ultimate fractal dimension as an ultimate state of particle fragmentation, a relative breakage index based on the relationship between the original, current, and ultimate fractal dimensions is proposed. These results can support more efficient and accurate predictions of particle fragmentation, thus promoting the safer design and construction of offshore engineering in coral sand.

In situ characterization of particle formation in spray flame synthesis using wide-angle light scattering

Wide-angle light scattering (WALS) was used for in situ measurements of droplet and nanoparticle size distributions during the synthesis of titania and iron oxide particles from liquid precursor solutions in the standardized SpraySyn burner for spray flame synthesis. Titania was synthesized from titanium tetraisopropoxide (TTIP) and iron oxide from iron(III) nitrate nonahydrate (INN) using ethanol (EtOH) as solvent. Scattering images were taken at heights up to 120 mm above the burner surface and classified into droplet and particle scattering. Droplet size distributions were derived from a sequential analysis of scattering data containing the oscillating Mie pattern, the lognormal size distribution parameters for spherical and fractal particle fractions from a multivariate approach on averaged particle scattering data. The results show that the precursor addition leads to altered evaporation behavior and even droplet disruption probably induced by puffing or micro-explosions compared to pure EtOH. In the case of TTIP (a hygroscopic alkoxide), the synthesis of a large fraction of spheres was observed, while the nitrate INN leads to the formation of mostly fractal aggregates.

Study on the Movement of Pulverized Coal Particles in Fractal Fracture Network.

Coalbed methane (CBM) exploitation is a complex multiphase flow process. With the development of CBM extraction technology, it is recognized that the migration of reservoir fluid in the fracture network is affected by the matrix fracture structure, fracture width, and pulverized coal particles plugging, therefore the fluid-particle coupling problem has received increasing attention. In this paper, six groups of fracture models with different fractal dimensions are established using the Weierstrass-Mandelbrot function, and the fluid-particle coupling phenomena in fractures with different roughness and aperture are simulated using an immersed boundary-lattice Boltzmann method (IB-LBM), by comparing the numerical simulation results with the theoretical analysis, it is proved that the IB-LBM numerical method has high accuracy and effectiveness. The effects of fractal dimension, particle size, and particle concentration on the plugging effect were investigated. The results show that the plugging effect on the fracture is enhanced with the increase of the pulverized coal particles content. When the concentration and size of pulverized coal particles are the same, the migration path of pulverized coal particles in complex fractures is more tortuous and more likely to be plugged. It may lead to a shift in the main seepage network of the fracture and the formation of new seepage channels. The research in this paper provides a data basis for the formation and plugging pattern of pulverized coal particles in coal seam fractures, which can provide a basis for the control of pulverized coal particles concentration in CBM drainage.

Evaluation of particle release during cleaning of coated surfaces with pulsed Nd:YAG laser

The released particles during laser-based surface ablation of an epoxy resin coating were investigated for their number, size, mass and chemical composition. The laser used was a pulsed Nd:YAG laser with a maximum average power of 91 W. During the experiments, the applied laser power was investigated as a varying parameter. With the highest power, a maximum particle count of 4.3*108 particles/cm³ was measured, which corresponds to a mass of approximately 55 mg/m³. With decreasing laser power, the particle loading of the aerosol decreases. The particle sizes are bimodal distributed between 10 nm and approximately 3 μm. The first peak is at 34 nm and the second peak is at 630 nm. In terms of number, the nanoparticles dominate the distribution. During the analysis of the particles, fractal and spherical particles were determined, whereby the fractal particles are mainly in the nanometre range and the spherical particles mostly in the μm range. The chemical analysis of the particles showed that they consist of carbon and hydrogen.