Effect of collision angle on particle-particle adhesion of colliding particles through liquid droplet

In wet granulation processes, a particle adhesion mediated by a liquid bridge is one of the quite important phenomena. In an actual process, the liquid bridge shows dynamic motion due to continuous motion of the particles. Therefore, understanding of the particle adhesion phenomenon by a dynamic liquid bridge is essential to adequately and precisely control wet granulation processes. This study presents a direct numerical simulation of the particle–particle adhesion by a dynamic liquid bridge. Collision of a dry particle and a wet particle was simulated at various collision angles. In particular, translational and rotational motions of the particle at different collision angles were discussed through comparison with a conventional static liquid bridge force model. As a result, it was found that both translational and rotational motions were largely different between simulation results of the direct numerical simulation and static liquid bridge force model, especially at the tangential collision. To understand these results, we focused on the rotational behavior of the particle and deformation of the liquid bridge. It was concluded that the non-slip behavior of the liquid bridge on the particle surface is a key phenomenon for the particle-particle adhesion by the dynamic liquid bridge at the tangential collision.     

Investigation of the influence of impact velocity and liquid bridge volume on the maximum liquid bridge length

Several models exist to predict the capillary forces due to liquid bridges during static particle contacts. However, for dynamic impacts, there is still a lack of knowledge to accurately describe the geometry and rupture of liquid bridges. This is essential in order to calculate correctly the energy dissipation in numerical models. Therefore, the liquid bridge volume during the rebound phase of collision, the restitution coefficient, the rupture time and the maximum liquid bridge length were analyzed for a wide range of contact velocities from 0.0001 to 4.0 m?s^?1. To perform experiments at different velocities three experimental setups were developed. First, free-fall experiments with spherical particles colliding on a glass pane covered with a water layer were performed at different impact velocities from 0.3 to 1.5 m?s^?1 and water layer thicknesses. Secondly, a pneumatic setup was developed for investigating the maximum liquid bridge length at constant liquid bridge volume and contact velocities from 0.3 to 4.0 m?s^?1. A third setup was used to investigate the liquid bridge behavior during low velocities from 0.0001 to 0.04 m?s^?1. Based on the experimental results, a new model is presented to account for the significant influence of impact velocity on the maximum liquid bridge length.     

Experimental investigation of bubble and particle motion behaviors in a gas-solid fluidized bed with side wall liquid spray

Bubble and particle motion behaviors are investigated experimentally in a gas solid fluidized bed with liquid spray on the side wall. The particles used in the experiment are classified as Geldart B particles. The results reveal that when the fluid drag force is less than the liquid bridge force between particles, liquid distribute all over the bed. Bubble size increases as the increase of inter-particle force, then decreases owing to the increase of particle weight with increasing liquid flow rate. When the fluid drag force is greater than the liquid bridge force, liquid mainly distribute in the upper part of the bed. And it is difficult for the wet particles to form agglomerates. Bubble size decreases with increasing liquid flow rate due to the increasing of minimum fluidization velocity. Besides, the acoustic emission (AE) measurements illustrate that the liquid adhesion and evaporation on particles could enhance the particles motion intensity. Consequently, the bubble and particle behaviors change due to the variation in fluidized gas velocity and liquid flow rate should be seriously considered when attempting to successfully design and operate the side wall liquid spray gas solid fluidized bed.     

Experimental investigation of the coefficient of restitution of particles colliding with surfaces in air and water

The coefficient of restitution is a parameter used to describe the result of a collision between either two particles or a particle and a surface. The coefficient of restitution is a measure of the amount of kinetic energy dissipation during a collision. This work aimed to study the behavior of the coefficient of restitution based on the velocity of the impacting particle and the properties of the surface and/or particle involved in the collision. This goal was achieved by establishing an experimental system to measure the coefficient of restitution, conducting experiments, and determining dependence between parameters using analytical tools.To measure the coefficient of restitution correctly, based on a large data basis and wide ranges of properties and operating conditions, experiments were conducted on different surfaces and particulate materials with different collision angles and velocities. These experiments were conducted in different surroundings (air and liquid), which posed an important issue. For accurate prediction, after analyzing the results, a correlation was proposed to estimate the value of the coefficient of restitution depending on the mechanical properties of the particle and surface, angle and speed of the collision, and characteristics of the collision medium. Most of the tests for the wide range of properties and conditions were fit to the final correlation by ±30%.     

Selection function of particles under impact loads: The effect of collision angle

The current work investigates the effect of collision angle on the breakage of particles under impact loads. The experiments were performed using a homemade experimental system that accelerates the particles horizontally toward the target using compressed air. The design of the system allows the angle of the target and the air velocity, both adjustable to check different collision angles at different impact velocities; and the tested material that was blown to the target to be collectible for measuring the percentage of broken particles for the analysis. In this study, six different materials were tested by conducting experiments with different collision angles and impact velocities. As expected, the results showed that the collision angle affects the breakage of the particles. When the collision angle becomes acute, i.e., less than 90° (perpendicular collision with the target), it results in less breakage of the particles for all tested materials and at all tested velocities. Consequently, an empirical model got established. This model can predict the median impact velocity that causes half of the particle population to break, depending upon collision angle and particle size.     

Energy dissipation in collision of two balls covered by fine particles

A new fine particle impact damper (FPID) is composed of a spherical impactor and a small quantity of fine particles as damping agent. The model of energy dissipation in the collision between two balls covered by fine particles is necessary to investigate the mechanism and performance of FPID. In this study, a simplified model verified by FEA simulations is proposed to estimate the energy dissipation in collision between two balls covered by fine particles. In addition, the energy dissipation in the collision between two balls covered by fine particles is compared with that in the impact between two balls without fine particles, by means of theoretical predictions. FEA simulations are also carried out to discuss the effects of diameter ratio of particle to ball, particle material and particle amount on the energetic expression of the elastic–plastic loading (EPL) index (EPL_E). The results from the FEA simulations agree well with the estimations from the model proposed in this paper. It is concluded that the energy dissipation in the collision between two balls covered by fine particles can be predicted by classical collision models of two particles through the substitution of several parameters from balls; the plastic deformation of fine particles affixed on balls can exhaust much more energy than that of the two balls without particles, which is the reason for the good performance of FPID; the diameter ratio of particle to ball and the material of particles do not have significant effects on the EPL_E when the ratio is limited to the range of [1/200 – 1/10]. A correlation of the EPL_E and dimensionless initial relative velocity is also found for the collisions between two balls, which is independent not only of the particle size and material properties but also of the particles presence.     

Evolution of mesoscale structure in fluidized beds with non-spherical dry and wet particles

Fluidized beds with non-spherical dry and wet particles are widely used in industrial processes, and the mesoscale structure in the bed has an important influence. In this study, CFD-DEM simulations are performed to evaluate the flow behaviors and mesoscale structure in fluidized beds with non-spherical dry and wet particles. The accuracy of the model is validated by comparison with the results of the particle image velocimetry experiment. The force distributions at bubble boundaries are analyzed to explain the influence mechanism of different shapes of bubbles in non-spherical dry and wet particle systems. The factor analysis indicates the interaction of particle shape and viscous liquid on the translational and rotational kinetic energy of particles. When the bed height is low, as the particle aspect ratio increases, the bubble equivalent diameter gradually increases. In addition, as the liquid viscosity increases, the particle and bubble granular temperature gradually decrease, indicating the reduction of particle velocity fluctuate and the decrease of turbulent kinetic energy of bubble. These findings have guiding significance for the fluidization of non-spherical dry and wet particles and can be used to optimize related industrial processes.     

DEM simulations: mixing of dry and wet granular material with different contact angles

In solid mixing the raw materials typically differ at least in one material property, such as particle size, solid density and wetting properties, which in turn influence particle mobility. For example, smaller particles can percolate through the voids of larger ones under the influence of strain and gravity. This may produce fine particle accumulation at the bottom of the mixing vessel which results in undesired, inhomogeneous final products. When wet particles with different wetting properties need to be mixed, heteroagglomeration may occur as another segregation mechanism. We present a new capillary bridge force model to study segregation in moist cohesive mixing processes using DEM. New analytical equations of best fit are derived by solving the Young–Laplace equation and performing a regression analysis, in order to investigate discontinuous mixing processes of dry and moist materials with different particle sizes and different contact angles. Compared to a dry mixing process, mixing efficiency is improved by the addition of a small amount of liquid. While percolating segregation is reduced, heteroagglomerates occur in the wet mixing process.     

粒子非垂直入射对冷喷涂涂层形成的影响分析

当高速粒子喷涂复杂曲面部件时,绝大部分粒子与部件表面将呈一定角度侵切,非垂直入射粒子对涂层形成及特性将产生重要影响.采用有限元数值计算方法,研究冷喷涂材料改性过程中铜粒子与铜基体非垂直碰撞的变形行为.针对单个粒子以相同入射速度不同入射角度的碰撞条件,探讨粒子与基体的结合强度、侵彻深度以及绝热剪切失稳的发生条件.结果表明:有角度碰撞相对于理想垂直碰撞,冷喷涂沉积效果的情况是恶化的,随着入射角度的增大,粒子侵彻深度逐渐减少,粒子与基体的结合强度也逐渐减弱,甚至不会嵌入基体而发生脱离.发生绝热剪切失稳的条件是入射速度的法向分量大于碰撞过程的临界速度.     

Stress wave in monosized bead string with various water contents

Wet granular materials exhibit unique physical and mechanical properties, especially in relation to wave propagation, which is quite different from dry granular materials. In this paper, by introducing the capillary bridge force into the discrete element method, the stress wave in mono-sized bead string with various water content has been studied. First the vibration of two particles with liquid bridge has been analyzed. The presence of the liquid bridge force causes the kinetic response of the particles to exhibit completely different properties than that of the dry particles. The equilibrium position is affected by both the physical properties of the particles and the liquid bridge properties. Then the wave propagation behaviors in a mono-sized bead string have been analyzed. According to whether the liquid bridge volume has an effect on granular motion, the whole process can be divided into two stages. Stage I, particles are physically contacted with each other directly. The influence of liquid bridge force is independent of the bridge volume. Stage II, particles start to oscillate back and forth at their equilibrium positions, the influence of the liquid bridge force becomes related to the bridge volume. The kinetic energy dissipation first decreases and then increases. A U-shaped trend appears throughout the dissipation process. In our work, the mechanical properties of wet granular materials are studied from two levels: particle vibration and wave propagation, which will provide theoretical guidance for the application of granular materials in aqueous environment.     

Optimum design of agitator geometry for a dry stirred media mill by the discrete element method

Three different agitator geometries for a dry stirred media mill with a horizontal drum were studied experimentally and by DEM (discrete element method) simulation. Two optimized models, model A with stirring arms oriented in the same direction and model B with inclined stirring arms, achieved more rapid grinding with the lower adhesion of particles to the mill than the conventional stirring arms. Model A achieved the finest grinding with sharpest particle distribution.DEM simulation results suggested that rapid mixing, large collision energy, and a large number of collisions result in rapid grinding. DEM simulations of model A confirmed that the particle collision energy in this model was the highest of the models tested and resulted in the largest energy consumption and the largest temperature increase. In model B, DEM simulation results suggested that collision energy increased locally at the wall and resulted in a local temperature increase at the shaft. The high number of collisions in model B also resulted in rapid grinding but with a broad particle distribution. The decrease of the particle adhesion in models A and B was caused by a decrease in the collision energy between particles and the wall in the normal direction.     

Influence of interparticle forces on selective wet agglomeration

The influence of interparticle forces between primary particles, which include interaction force between dispersed particles in liquid calculated by DLVO theory and two kinds of forces caused by a liquid bridge of bridging liquid between particles, on selective wet agglomeration was investigated on the basis of the relationships between the results of separation efficiency obtained in author’s previous study and these interparticle forces. The first step of selective wet agglomeration is the collision between bridging liquid droplets and objective particles to be agglomerated. This collision is mainly influenced by the interparticle force calculated by DLVO theory. Incorporation of two objective particles, the second step in the agglomeration process, is influenced by liquid bridge force between objective particles. Growth to pellet-type agglomerates, the third step in the agglomeration process, is thought to be influenced mainly by aggregation force in the agglomerates by entry suction potential. The results of this study showed that selective wet agglomeration under the experimental conditions used in this study is influenced greatly by liquid bridge force and entry suction potential, which play major roles in the second step and third step, respectively, of the selective wet agglomeration process.     

Operating stability analysis of continuous gas–liquid–solid FBR under super-condensed mode

In the gas–liquid–solid fluidized bed reactor (FBR) under super-condensed mode, the injection of liquid causes the particle agglomeration that leads to a complicated and unstable fluidization system. In this work, a probabilistic stability model is developed on the basis of a three-particle collision theory to describe such mode. The criterion of the model is achieved by analyzing the particle interaction, relative velocity distribution, and energy transfer in particle collision. The model error mainly originates from by the simplification of the actual system. The developed model is applicable to the case that a droplet completely spreads on the particle surface, that is, the solid–liquid contact angle is less than 40°. We then systematically verify the current model by comparison with the experimental data from the literature. The developed model provides an application prospect in reactor design and scale-up.     

Experimental and numerical determination of the lubrication force between a spherical particle and a micro-structured surface

In many particulate processes suspensions need to be handled. Hydrodynamic forces in presence of a liquid as a surrounding continuum medium can significantly affect the particle collision behaviour. When particles approach a wall, lubrication force can become dominant with decreasing distance. This force was described analytically by different authors for a smooth flat wall. Roughness was found to be an important factor in this context, but the mechanisms are still not fully understood. In this work, the effects of topology on the lubrication force were studied using a regular prismatic micro-structured titanium surface produced by micro-milling. A nanoindentation setup was modified for the direct measurement of this force during the particle approach to polished and micro-structured surfaces in liquid. For a more detailed insight on the behaviour of the fluid in the decreasing gap between particle and surface microstructure, resolved computational fluid dynamics (CFD) simulations were performed using an overset mesh method. The comparison of simulation results with nanoindentation tests and analytical solution showed a good agreement. The effects of structure size and particle contact location at various approaching velocities on the lubrication force were investigated.     

Collision dynamics of wet particles: Comparison of literature models to new experiments

Collision dynamics of wet particles are often investigated in literature, since their knowledge is important for the design and modeling of granular process involving liquid layers or moisture. Several models were already reported predicting rebound behavior of wet particles. However, most of them are either developed for a viscous dominant regime, neglecting capillary effects all together, or capillary effects are strongly simplified. This work summarizes the various models and compares them to new experimental results for liquids at small and moderate viscosities, to check for applicability also for these materials. Several discrepancies between experiments at small liquid viscosities and models were found and reasons for these differences are discussed. Mainly, the negligence or simplification of capillary forces regarding energy dissipation during the collision leads to an overprediction of rebound velocities compared to the experiments reported in this work. Furthermore, selection of appropriate models for viscous forces during wet particle collisions has to be conducted with care.     

Segregation of cohesive granular materials during discharge from a rectangular hopper

Granular materials may readily segregate due to differences in particle properties such as size, shape, and density. Segregation is common in industrial processes involving granular materials and can occur even after a material has been uniformly blended. The specific objective of this work is to investigate via simulation the effect of particle cohesion due to liquid bridging on particle segregation. Specifically, a bi-disperse granular material flowing from a 3-D hopper is simulated using the discrete element method (DEM) for cohesive particles and the extent of discharge segregation is characterized over time. The cohesion between the particles is described by a pendular liquid bridge force model and the strength of the cohesive bond is characterized by the Bond number determined with respect to the smaller particle species. As the Bond number of the system increases, the extent of discharge segregation in the system decreases. A critical value of Bo = 1 is identified as the condition where the primary mechanism of segregation in the cohesionless hopper system, i.e. gravity-induced percolation, is essentially eliminated due to the liquid bridges between particles.     

Grazing exit electron probe microanalysis for surface and particle analysis

We developed a new method of grazing exit electron probe microanalysis (GE-EPMA) and applied it to analyze both Si surfaces and Mg-salt particles. In conventional EPMA, X-rays are detected at an exit (takeoff) angle of approximately 45°. Therefore, when particles collected on a sample carrier are analyzed by EPMA, the X-rays from both the particles and the carrier are detected, although we need only the X-rays emitted from the particle itself. In contrast to this, the X-rays are detected at grazing exit angles in GE-EPMA. The X-rays emitted from deep inside of the sample are not detected under grazing exit conditions, and only X-rays emitted from the surface and the particle are measured. It was found that surface-sensitive analysis of a Si wafer was possible with low background at grazing exit angles. The intensity ratio of O Kα to Si Kα increased near zero degrees, indicating that the Si wafer is covered with a native Si oxide. Moreover, Mg Kα X-rays from a Mg-salt particle, which was deposited on the Si wafer, were detected with a small Si Kα intensity at grazing exit angles of less than 0.5°. By decreasing the exit angle to less than zero, only the top of the particle was observed; therefore, GE-EPMA measurement would make it possible to investigate the surface layer of one particle.     

矿物颗粒形状对球磨机磨矿性能的影响

为了探究矿物颗粒形状对球磨机研磨作业的影响机制,运用离散单元法,采用球体和由球形颗粒凝聚而成的正四面体、平行六面体矿物颗粒模型,数值模拟球磨机的磨矿过程,分析矿物颗粒形状对运动形式、碰撞形式以及球磨机磨矿性能的影响。结果表明,矿物颗粒形状对球磨机磨矿性能的影响很大,相同条件下,球形矿粒碰撞能最大,正四面体矿粒次之,平行六面体矿粒最小。     

Effects of particle–particle collisions on sudden expansion gas-particle flows via a two-phase kinetic energy-particle temperature model

In the framework of the gas–particle two-fluid mode, an improved gas–particle two-phase kinetic energy incorporating into a particles collision model (k–k_p–θ) is proposed to study the sudden expansion gas–particle turbulent flows in a cylindrical pipe section. Anisotropy of gas–solid two-phase stress and the interaction between two-phase stresses are considered by means of a transport equation of two-phase fluctuation velocity correlation. Xu and Zhou [10] experimental data is used to quantitatively validate k–k_p–θ and k–k_p model for analysis the effects of particle–particle collision. Numerical predicted results show that time-averaged velocity, fluctuation velocity of gas and particle and correlation of two-phase fluctuation velocity considering particles collision are better than those of the without particle temperature model and they are in good agreement with experimental data. Larger particle concentration and particle temperature located at shear layer adjacent to wall surface and re-circulation region. Energy dissipation due to smaller scale particles collision contributes to homogeneous distribution of Reynolds stress and affects the particle transportation behavior together with particle inertia.     

A mixed contact model for an immersed collision between two solid surfaces

Experimental evidence shows that the presence of an ambient liquid can greatly modify the collision process between two solid surfaces. Interactions between the solid surfaces and the surrounding liquid result in energy dissipation at the particle level, which leads to solid-liquid mixture rheology deviating from dry granular flow behaviour. The present work investigates how the surrounding liquid modifies the impact and rebound of solid spheres. Existing collision models use elastohydrodynamic lubrication (EHL) theory to address the surface deformation under the developing lubrication pressure, thereby coupling the motion of the liquid and solid. With EHL theory, idealized smooth particles are made to rebound from a lubrication film. Modified EHL models, however, allow particles to rebound from mutual contacts of surface asperities, assuming negligible liquid effects. In this work, a new contact mechanism, 'mixed contact', is formulated, which considers the interplay between the asperities and the interstitial liquid as part of a hybrid rebound scheme. A recovery factor is further proposed to characterize the additional energy loss due to asperity-liquid interactions. The resulting collision model is evaluated through comparisons with experimental data, exhibiting a better performance than the existing models. In addition to the three non-dimensional numbers that result from the EHL analysis--the wet coefficient of restitution, the particle Stokes number and the elasticity parameter--a fourth parameter is introduced to correlate particle impact momentum to the EHL deformation impulse. This generalized collision model covers a wide range of impact conditions and could be employed in numerical codes to simulate the bulk motion of solid particles with non-negligible liquid effects.