Mixed Particles Research Articles

Multiphase Reactions between Organic Peroxides and Sulfur Dioxide in Internally Mixed Inorganic and Organic Particles: Key Roles of Particle Phase Separation and Acidity.

Organic peroxides (POs) are ubiquitous in the atmosphere and particularly reactive toward dissolved sulfur dioxide (SO2), yet the reaction kinetics between POs and SO2, especially in complex inorganic-organic mixed particles, remain poorly constrained. Here, we report the first investigation of the multiphase reactions between SO2 and POs in monoterpene-derived secondary organic aerosol internally mixed with different inorganic salts (ammonium sulfate, ammonium bisulfate, or sodium nitrate). We find that when the particles are phase-separated, the PO-S(IV) reactivity is consistent with that measured in pure SOA and depends markedly on the water content in the organic shell. However, when the organic and inorganic phases are miscible, the PO-S(IV) reactivity varies substantially among different aerosol systems, mainly driven by their distinct acidities (not by ionic strength). The second-order PO-S(IV) rate constant decreases monotonically from 5 × 105 to 75 M-1 s-1 in the pH range of 0.1-5.6. Both proton catalysis and general acid catalysis contribute to S(IV) oxidation, with their corresponding third-order rate constants determined to be (6.4 ± 0.7) × 106 and (6.9 ± 4.6) × 104 M-2 s-1 at pH 2-6, respectively. The measured kinetics imply that the PO-S(IV) reaction in aerosol is an important sulfate formation pathway, with the reaction kinetics dominated by general acid catalysis at pH > 3 under typical continental atmospheric conditions.

Impact of soy protein dispersibility on the structural and sensory properties of fat-free ice cream

Soy protein can be an effective fat replacer in ice cream due to its contribution to the viscosity and foaming ability. In this study, we investigated the individual effect of soy protein particle size and mix viscosity on the physical, rheological, tribological and sensory properties of fat-free ice cream. Particle size was varied by homogenization and subsequent separation of the dispersible and non-dispersible fractions. Three series of ice cream mixes were made in which (i) particle size and viscosity were varied, (ii) particle size was varied with a constant viscosity, and (iii) the ratio between the dispersible and non-dispersible protein fractions, particle size and viscosity were varied. The results showed that dispersible protein particles (0.25 μm) led to lower hardness and higher scoopability as their presence was related to increased overrun and reduced non-air thickness between the air cells. In comparison, large non-dispersible particles (3.8–145 μm) enhanced the melting resistance and stability of ice cream by forming a network in the serum phase. Therefore, the size of the protein particles determined their functionality in ice cream. Based on sensory evaluation, samples with a protein particle size of approximately 4 μm showed a relatively denser texture, a lower melting rate and better lubrication behavior (lower friction), as well as a sensory profile similar to that of full-fat ice cream. This study indicates that both textural and sensory properties of fat-free ice cream can be improved by manipulating the size of plant proteins and mix viscosity.

Radiation driven-dust hydrodynamics in late-phase AGB stars

The interplay of stellar luminosity variations and dust hydrodynamics in Asymptotic Giant Branch (AGB) stars and the consequences for dust survival and mass loss remain elusive. In this work, we broadly investigate the role of dust and radiation hydrodynamics in forming dust and gas structures, heterogeneous clumps observable in AGB remnants and planetary nebulae (PNe). Of interest in this study are the spatial perturbations driven by instabilities in the space that the mass travels through. These spatial perturbations in the dust and gas field may be responsible for forming larger clumps, such as cometary knots, seen in the PNe phase. Previous studies have considered similar physics in dust-driven winds at shorter lengths and time scales, using either 1D simulations or 2D simulations with a single mixed particle–gas fluid. Here we present an Eulerian–Lagrangian method for studying this problem at larger length and time scales. Simulations are performed in 2D, solving the Euler equations with source terms resulting from the particle phase, represented by free Lagrangian points. Radiation coupling was implemented for the particle phase, modeling radiation heating and acceleration of the particles and subsequent coupling to the gas phase through non-continuum heat and momentum transfer models. Spatial perturbations of the dust and radiation fields were found to drive the formation of small dust mass clumps that survive to late times, though these remain below the size of those observed in many PNe.

Effect of the gradation of binary mixed particle materials on compressive strength and permeability

The gradation of binary mixed particulate materials has a considerable impact on their compressive strength and permeability. To investigate the effect of various gradations on compressive strength and permeability. Uniaxial compression tests and permeability tests were conducted, and simulation-based three-dimensional discrete element numerical models of five distinct binary mixed particulate materials with varying levels were developed. From the standpoint of mesoscopic contact force composition, the effect of coal gangue particle content (ωc) on the strength formation mechanism of binary mixed particle materials was studied. The results indicate that the compressive strength of binary mixed particles increases rapidly with increasing ωc, but the increase is not evident when ωc > 40 %. Moreover, the permeability increases as ωc increases under the same conditions. The grading of recommendation 2# (ωc = 40 %, ωb = 60 %) is optimal. Simulation yields a prescribed grade that is consistent with the test.

Discrete element method study of parameter optimization and particle mixing behaviour in a soil mixer

Soil mixing is an emerging research in the field of construction resource recovery. In this study, the mixing behaviour of soil particles in a mixer is numerically simulated by the discrete element method (DEM). A four-factor, three-level orthogonal experiment is designed to optimize the mixer design by selecting the fly-cutter speed, spindle speed, number of blades and fly-cutter diameter, using Lacey mixing index and power consumption as evaluation indicators. Then, the impact of soil cohesion and type on the mixing behaviour is investigated. The results show that the optimal parameter combination of this experiment is 280 rpm fly-cutter speed, 40 rpm spindle speed, 4 blades and 250 mm fly-cutter diameter. This optimal combination reaches a comparatively uniform state mix in 5.9 s with an average power consumption of 704.11 W. In addition, the wear and tear of the mixer increases as soil cohesion increases, while the mixing quality of materials declines, resulting in a “shaft hugging” phenomenon. The mixing efficiency varies greatly among different soil types, but the radial and tangential velocities have a similar law. This work can provide some guidance for the optimization design of a mixer and study of soil mixing.

Predictive modeling of mixing time for super-ellipsoid particles in a four-bladed mixer: A DEM-based approach

Numerical simulations of super-ellipsoid particles in a four-bladed mixer using the discrete element method is presented. The effect of number of particles, blade rake angle and impeller rotation speed, on the performance of the mixer was examined. Mixing mechanism and flow pattern of particles were studied through velocity profiles, particle trajectories and granular temperature. It was found that the spherical particles mix faster than the prolate and the oblate particles. In case of using acute blade rake angles, the mixing is slower than obtuse angle. It was found that the granular temperature is higher in the vicinity of the wall for all particle shapes. The spherical particles have the highest granular temperature than the prolate and the oblate particles, which have same granular temperatures. To predict the mixing time, regression models were employed. The voting regressor model was shown to be successful at predicting the mixing time.

A study on light extinction model and inversion of mixed particle system based on Monte Carlo method

The extinction characteristics of mixed particles, which are composed of various types of particles, appear to be more complex. To statistically analyze photon destinations and investigate the extinction characteristics of mixed particles by tracing all underlying events in detail, a Monte Carlo method-based extinction model has been developed. Meanwhile, an extinction spectrum measurement system was designed. A series of experiments for both single-type particle and mixed-particle systems were performed. Afterwards, global optimization algorithms are introduced to perform simultaneous inversion of sizes of mixed particles and mixing ratio based on the experimental spectrum. The inversion results show that the error for any single parameter is <2%. Performing a simultaneous inversion for particle sizes and mixing ratios leads to an increase in the relative error, but it does not exceed 9%. It indicates that the model could simultaneously invert the mixing ratio and handle particle systems with two different sizes.

Interactions enhance dispersion in fluctuating channels via emergent flows

Understanding particle motion in narrow channels can guide progress in numerous applications, from filtration to vascular transport. Thermal or active fluctuations of fluid-filled channel walls can slow down or increase the dispersion of tracer particles via entropic trapping in the wall bulges or hydrodynamic flows induced by wall fluctuations, respectively. Previous studies concentrated primarily on the case of a single Brownian tracer. Here, we address what happens when there is a large ensemble of interacting Brownian tracers – a common situation in applications. Introducing repulsive interactions between tracer particles, while ignoring the presence of a background fluid, leads to an effective flow field. This flow field enhances tracer dispersion, a phenomenon reminiscent of that seen for single tracers in incompressible background fluid. We characterise the dispersion by the long-time diffusion coefficient of tracers numerically and analytically with a mean-field density functional analysis. We find a surprising effect where an increased particle density enhances the diffusion coefficient, challenging the notion that crowding effects tend to reduce diffusion. Here, inter-particle interactions push particles closer to the fluctuating channel walls. Interactions between the fluctuating wall and the now-nearby particles then drive particle mixing. Our mechanism is sufficiently general that we expect it to apply to various systems. In addition, our perturbation theory quantifies dispersion in generic advection–diffusion systems.

Effects of volatility, viscosity, and non-ideality on particle–particle mixing timescales of secondary organic aerosols

Effects of volatility, viscosity, and non-ideality on particle–particle mixing timescales of secondary organic aerosols

Numerical study on the elucidation of powder mixing mechanism in a container blender

Numerical simulations by the discrete element method (DEM) and DEM-computational fluid dynamics (CFD) have greatly facilitated the investigation of mixing kinetics in various particle mixing systems, including the common container blender. Recently, airflow within the container blender has been found to remarkably improve the mixing efficiency of fine particles. Nevertheless, a wide range of particle sizes has not been examined regarding the airflow effect. Thus, to comprehensively understand the particle size dependence of the airflow impact on powder mixing, this study aims to investigate the relationship of various particle diameters and powder mixing in an industrial container blender. An advanced mathematical-statistical method, named proper orthogonal decomposition-analysis of variance (POD-ANOVA), is used to clarify the complex mixing mechanisms. Numerical results show that airflow has different impacts on the mixing efficiency determined by the particle size range. The mixing of coarse particles with diameters above 1.000 mm is not significantly influenced by airflow, whereas medium-sized particles, ranging from 0.5000 to 1.000 mm, display reduced mixing efficiency as particle size decreases. Conversely, for small particles (0.2000–0.5000 mm), the mixing efficiency improves when decreasing the particle size. The underlying variations of powder mixing mechanisms have been well elucidated, and the convection mixing mechanism is found to be crucial in determining the mixing efficiency via POD-ANOVA analysis. Consequently, this work provides critical insights into the airflow effect during powder mixing, which has been verified to be highly dependent on particle size and is dominated by the convection mechanism.

Study on the Function of Conveying, Kneading Block and Reversing Elements on the Mixing Efficiency and Dispersion Effect inside the Barrel of an Extruder with Numerical Simulation.

In order to better understand the extrusion process mechanism of plant protein inside a barrel, the parameter changes and flow characteristics of fluids under conveying, kneading block and reversing elements were investigated with numerical simulation. The results showed that the shear rate increased obviously with the increase in pitch; the shear rate value of the reversing element was larger, while that of the kneading block was the opposite. The screw combinations of conveying, kneading blocks and reversing elements all have a certain degree of mixing effect on the particles, and the reduction in pitch can effectively increase the mixing effect of the particles. The conveying element can provide a relatively constant acceleration for the particles, due to the pumping capability and pressure buildup as the pitch increases. The kneading block and the reversing element can increase the leakage flow between the discs and backflow, resulting in an extension of the residence time distribution that facilitates fluid interaction in the barrel and improves the dispersion of the particles. The restraint by the reversing element on the particles is obviously weaker than that of the kneading block and shows a higher particle mixing degree. Overall, the influence of different elements on the flow condition, mixing degree and residence time is significantly different, which improves the process controllability and provides references for potential applications to meet multiple demands.

Analysis of ex-vessel debris bed formation of multi-material and multiphase composition based on coupled system of MELCOR2 and THERMOS–JBREAK/MSPREAD

THERMOS is being developed to analyze the multidimensional process by which molten debris released from the lower head of the reactor pressure vessel forms a non-uniform debris bed. THERMOS consists of four modules, JBREAK, DPCOOL, MSPREAD and REMELT. To evaluate a wide range of ex-vessel debris bed formation, the authors have developed the coupled system composed of the integrated severe accident (SA) analysis code MELCOR2, THERMOS-JBREAK and THERMOS-MSPREAD. JBREAK simulates the molten jet release and impingement on the cavity floor using the separated flow model consisting of the molten jet and particle debris. MSPREAD simulates the melt spread as the multi-layered structure composed of the partially solidified molten debris, the upper and lower crusts growing on both sides using the shallow water equation.The conversion algorithm of the multi-material and multiphase composition of the released molten jet calculated by MELCOR2, which is based on lumped parameters, to the composition suitable for THERMOS, which is based on distributed parameters, is recognized to be critical to the success of this system and has been implemented as the Python script MELTHER. This conversion also includes the contribution of suspended particles embedded in the molten jet to the viscosity of partially solidified molten debris. As the JBREAK–MSPREAD interface, the method of overlapping the mesh systems of the two codes was implemented to solve the multidimensional flow equations in the near impinging region. Filtration of the molten debris inside the particle layer at the jet-impinging point was modeled using the particle debris deposition and molten debris filtration models.This coupled system was applied to a station blackout scenario in a typical BWR3 Mark-I plant, where approximately 14 tons of mixed molten and particle debris were released from the lower head and impinged on the pedestal floor. The calculation space was set to handle molten jet falling, impingement on the floor, and spreading from the pedestal to the outside dry well region. Complex anisotropic melt spreading was analyzed on the dry pedestal floor with two sumps covered with thin lids and a low weir at the bottom of the slit made in the cylindrical wall separating the pedestal floor and outer dry well regions.A series of sensitivity analyses were performed varying a combination of the initial suspended particle fraction and melt filtration inside the particle layer. Deceleration of the molten debris flow is significant due to the melt-particle bed frictional force and therefore the timing of molten debris running over the sump lids is faster when there is no particle layer. In this case, a large circulating flow is generated on the pedestal floor, and this flow promotes cooling and increases the viscosity. Influences of the initial suspended particle fraction on the melt viscosity become more pronounced in the peripheral region, and spreading behaviors are more susceptible to protrusions on the pedestal floor.

Scalable manufacturing of the Al-based master composites containing TiB2 and TiC particles and their modification effect on the hot cracking of rapidly solidified Al alloys

This work proposed a scalable manufacturing method for preparing the Al-based master composites containing micrometer-TiB2 and nanometer-TiC particles through molten salt reaction combined with vibration assisted dispersion. The modification effect of the Al-based master composites on the hot cracking and microstructure of 6000 and 7000 series Al alloys with high crack sensitivity during rapid solidification is initially investigated. The results show that the addition of the mixed particles could significantly refine the grains, effectively suppress the hot cracks, and improve the mechanical properties of rapidly solidified Al alloys. Meanwhile, the modification effect of the mixed particles is better than those of the single-phased micrometer-TiB2 particles or nanometer-TiC particles. This scalable and low-cost manufacturing process provides a practical way for preparation of metal matrix composites with low concentration of particles, and proposed a new path to solve the hot cracking problems in the rapid solidification areas such as additive manufacturing.

Microwave absorption, physicochemical, elemental mapping, and high-frequency perspectives of the Co, Cu, Zn doped Ni-Ce absorbers for Ku band frequency

The excellent absorbing ability, low weight, and thin size are the key challenges for addressing the electromagnetic issues in military systems and stealth missile technology. Recently, we increased the absorption features of the Co, Cu, and Zn-doped Ni spinel ferrites to improve the absorption performance of the absorbers in a high-frequency regime. The two-step process was employed to synthesize Co, Cu, and Zn substituted Ni-Ce nano ferrites with a nominal composition of Ni0.5×0.3Ce0.2Fe2O4 (X = Co, Cu, Zn). Various tools for the characterizations, such as XRD, FESEM, FTIR, TG/DTA, XPS, VSM, and VNA, investigated these synthesized nanocrystalline ferrites from structural, spectral, thermal, morphological, elemental, magnetic, dielectric, and absorption points of view. XRD results revealed the existence of cubic phase structure in Ni-Ce ferrites. The crystallite size was enhanced from 43 to 54 nm. FTIR spectra showed the existence of tetrahedral and octahedral bands of the Co, Cu, and Zn doped circular-shaped Ni-Ce ferrites. FESEM images revealed the mixed particles of polygonal, circular shaped Co, Cu and Zn doped Ni-Ce ferrite sample. Electron mapping analysis reveals the presence of Ni, Ce, Co, Zn, Cu, Fe, and O elements. VSM analysis was used to calculate the magnetization and other parameters of the samples. Co-doped NiCe absorber depicted RL of -46.8 dB for 2.9 mm thickness at 16 GHz, whereas the Cu-doped NiCe absorber depicted RL of -43.5 dB for 2.8 mm at 14.9 GHz. In addition, Zn doped NiCe absorber shows RL of -51.5 dB is perceived for 2.8 mm thickness at 17.6 GHz, respectively. The Zn-doped NiCe absorber is an excellent absorber for Ku band absorption applications. The prepared absorbers could be used for EMI shielding materials in the next-generation absorbing devices for multipurpose applications.

Research on the Preparation Process of SBS-Modified Asphalt Using Early Shearing Instead of High-Speed Shearing of Modifier

To investigate the effect of pre-shredding as a replacement for high-speed shearing in the preparation process of SBS-modified asphalt, the particle size and mixing time of pre-shredded SBS modifier were studied. Laser confocal microscopy was used to observe the morphological changes and dispersion state of the SBS modifier during the mixing process, and process parameters were determined through rheological performance tests. FTIR tests were conducted on the original asphalt and PAV-aged modified asphalt to assess the impact of the pre-shredding process on the chemical composition and aging resistance of the modified asphalt. The specific conclusions were as follows. During the preparation process of the SBS modifier using low-speed mixing, the morphological changes of the SBS modifier can be summarized as follows: It cycles through edge networking, mesh fiberization, and filamentous granulation, and eventually presents a granular atomization form after multiple cycles. It is recommended that the mixing time be maintained between 30 and 60 min, which results in the microstructure of the modified asphalt consisting of filamentous and point-like combinations. This asphalt exhibited excellent performance in high-temperature rut resistance, fatigue resistance, and low-temperature crack resistance. When the mixing time was too long, the SBS modifier formed small granules in an atomized state, which weakened the strength of the mesh structure and led to a decrease in overall performance. It is recommended that the SBS be shredded into particles sized between 18 and 30 mesh or 30 and 100 mesh. SBS-modified asphalt with SBS particles sized between 18 and 30 mesh exhibited greater hardness in the mesh structure, resulting in better high-temperature rut resistance. SBS-modified asphalt with SBS particles sized between 30 and 100 mesh had better extensibility in the mesh structure, leading to superior performance in medium-temperature fatigue resistance and low-temperature crack resistance. Compared to the conventional process, the pre-shredding process for preparing SBS-modified asphalt improved aging resistance by 10% to 13%. Additionally, SBS-modified asphalt prepared using the pre-shredding process saved 1 to 3 h of processing time compared to the traditional preparation method, reducing energy consumption. Furthermore, the asphalt produced through the new process exhibited better performance, reducing road wear and saving maintenance costs.

Numerical Simulation of Geotechnical Isolation of Building Subjected to Earthquake Using Rubber Sand Mixtures

The use of recycled rubber in various civil engineering applications has seen a considerable rise in recent years. The rubber-soil mixture can exhibit a higher energy absorption capacity than soil alone, which would reduce the energy applied to structures, the stresses, and shocks they undergo. Base isolation is the process of isolating the base of a structure to limit the effects of earthquakes, so that the seismic forces applied to the base of the bedrock cannot move with the same intensity towards the super structure.In this work, the beneficial effects of rubber mixtures (RSM) in mitigating earthquakes when these mixtures are inserted as layers in the soil profile are highlighted; the approach is based on a method of using worn tires for seismic protection applications for infrastructures subjected to seismic loads. It involves mixing particles from used tires with soil materials and placing the mixtures under the foundation of the building as geotechnical insulation systems for vibration absorption.The foundation of a four-storey building is implanted in a soil profile in which a layer of rubber-sand mixture (RSM) has been inserted; to perform the role of seismic isolation when subjected to seismic excitation.The investigation is focused on the variation in the thickness of the layer on the one hand (between 1m and 4m), and on the other hand on the position of this layer in the soil mass (top, middle and bottom of the profile).The peaks of horizontal accelerations recorded at the base and top of the structure show that the sand-rubber mixture has adequate and promising potential for their application as seismic isolation materials for low-rise buildings. Moreover, the thickness of the layer and its location are two very determining parameters in the improvement of the performances of these RSM mixtures, especially in terms of reduction of the acceleration peak recorded.

Traveling Salesman Problem Solving Based on Hybrid Particle Swarm Optimization Algorithm

Genetic algorithms all the methods used to solve the Traveling Agent (TSP) problem, the use of genetic algorithms on TSP problems is more common than other methods, and it is also possible to achieve global search and obtain the best values. Compared with the traditional genetic algorithm, the particle swarm algorithm is not only easy to be applied, but also can be widely used because of the function of rapid search, but at the same time, the shortcomings of the traditional standard particle swarm algorithm are more prominent, and it is easy to fall into the situation of optimal solution of local problems. So first of all, we use the classical TSP algorithm to propose a mixed particle swarm algorithm, which solves the TSP problem by using the selection, crossover, variation and other operators of the traditional genetic algorithm, and through the conclusion of the solution, it can be shown that the method not only greatly improves the search function of the traditional standard particle swarm, but also greatly improves the convergence speed while obtaining the approximate optimal solution.

Cloud condensation nuclei activity of internally mixed particle populations at a remote marine free troposphere site in the North Atlantic Ocean

This study reports results from research conducted at the Observatory of Mount Pico (OMP), 2225 m above mean sea level on Pico Island in the Azores archipelago in June and July 2017. We investigated the chemical composition, mixing state, and cloud condensation nuclei (CCN) activities of long-range transported free tropospheric (FT) particles. FLEXible PARTicle Lagrangian particle dispersion model (FLEXPART) simulations reveal that most air masses that arrived at the OMP during the sampling period originated in North America and were highly aged (average plume age > 10 days). We probed size-resolved chemical composition, mixing state, and hygroscopicity parameter (κ) of individual particles using computer-controlled scanning electron microscopy with an energy-dispersive X-ray spectrometer (CCSEM-EDX). Based on the estimated individual particle mass from elemental composition, we calculated the mixing state index, χ. During our study, FT particle populations were internally mixed (χ of samples are between 53 % and 87 %), owing to the long atmospheric aging time. We used data from a miniature Cloud Condensation Nucleus Counter (miniCCNC) to derive the hygroscopicity parameter, κCCNC. Combining κCCNC and FLEXPART, we found that air masses recirculated above the North Atlantic Ocean with lower mean altitude had higher κCCNC due to the higher contribution of sea salt particles. We used CCSEM-EDX and phase state measurements to predict single-particle κ (κCCSEM-EDX) values, which overlap with the lower range of κCCNC measured below 0.15 % SS. Therefore, CCSEM-EDX measurements can be useful in predicting the lower bound of κ, which can be used in climate models to predict CCN activities, especially in remote locations where online CCN measurements are unavailable.

Dynamic impact tests and temperature rise induced damage constitutive model of ice-rich frozen sandy soil

In this study, a soil-ice particle mixing method was used to prepare ice-rich frozen sandy soil specimens. Subsequently, the mechanical behaviors of ice-rich frozen sandy soil with a wide range of total moisture contents (15%–150%) were studied at three negative temperatures (−5, −10, and −15 °C) under the impact pressures from 0.2 MPa to 0.4 MPa. The melting of ice particles caused by the rise in temperature of frozen soil specimens was identified as temperature damage. Moreover, damage mechanism of ice-rich sandy frozen soil specimen during failure process was considered as the combined action of crack propagation and temperature rise. The analysis of the relationship between temperature rise value and dynamic strain was then calculated based on the heat conduction theory. Additionally, the phase transition equilibrium between unfrozen water and effective ice was used to determine the variation in ice volume content as the temperature rises, and the temperature damage variable was defined according to the reduction of dynamic elasticity modulus of ice-rich frozen sandy soil. Lastly, the compound damage variable was deduced and considered in the damage constitutive model. Accordingly, the theoretical and test data were compared to determine the model parameters. The results of the curve comparison indicate that the proposed model is feasible and suitable to be applied to predict the dynamic mechanics of ice-rich frozen sandy soil.

Study of mixing characteristics of boiler slag in hexagonal cold slag tube

The slag cooler is an important auxiliary machine of the boiler. Taking the high-temperature ash particles in the hexagonal slag cooling tube as the research object, based on the EDEM discrete element method, a particle-particle contact model is established, and the mixing index and difference function are used as the mixing evaluation index, in-depth analysis of the impact of different filling rates on the mixing of high-temperature ash particles. The results show that as the filling rate decreases, the time for ash particles to reach stable mixing becomes shorter, and the time for particles to reach stable mixing under different filling rates is 22 seconds, 28 seconds, and 34 seconds, respectively. The smaller the filling rate, the smaller the fluctuation range of the difference function R and S values, therefore, the better the mixing effect of the particles in the material bed.