PROBABILISTIC THREE-DIMENSIONAL MODEL FOR SLOW SHEARING PARTICULATE FLOW: DRY FRICTION

A probabilistic model for the slow shearing motion of spherical particles dominated by dry inter-particle frictional forces is proposed. The particles can move by sliding, rolling, solid body rotation and jumping following the criterion of minimum energy dissipation. The continuous deformation of particle assembly is regarded as a Markov process in discrete time and continuous space. The components of the contact angle between two neighboring particles are taken as the primary random variables. The coefficients of the probabilistic governing equation are determined from the rate of energy dissipation and micromechanical analysis of particle motion. The inter-particle sliding and rolling friction laws are input data. The constitutive relationships, apparent viscosity and internal friction angle of the particulate material as a whole are obtained by integration. The validity of the proposed model is verified by comparing the model predictions to analytical solutions and available experimental results.     

垂直管道中塞状流的模拟

运用简化的硬球模型模拟垂直管道中的塞状流. 固相行为通过跟踪离散颗粒的运动轨迹处理,气相运动由局部平均的Navier–Stokes方程处理,气固两相间的耦合作用服从牛顿第三定律. 每个颗粒的运动过程被分解为颗粒间相互碰撞的过程及流体对其悬浮的过程. 该模型定性地模拟了垂直管道中的塞状流,即在细而长的管道中,颗粒形成沿管道运动的塞状物,且塞状物的运动速度独立于塞状物的长度,但随着气体速度的增加而增加.     

Direct numerical simulation of a three-dimensional particle laden plane mixing layer considering inter-particle collisions

To investigate the behavior of inter-particle collision and its effects on multiphase flow, the direct numerical simulation of a three-dimensional gas–solid two-phase plane mixing layer is conducted. The flow is assumed to be temporally evolving and incompressible. The particle trajectories are traced by the one-way or two-way coupled Lagrangian method separately. The deterministic hard-sphere model is used to describe the inter-particle collision. Calculations are performed for a particle Stokes numbers of 3. The results show that the preferential concentration phenomenon of particles is found after the beginning of the rolling up of the large-scale vortex structures due to the influence of the vortex. It is also found that the inter-particle collision occurs frequently in the local regions with higher particle concentration of the flow field. The evolution of inter-particle collision can be divided into 3 stages under the influence of the growth of the vortex and the particle dispersion. The results under the two-way coupling show that the particle distribution is more uniform. The modifications of the mixed fluid thickness, the Reynolds stresses, and the mean stream-wise velocity of two phases due to inter-particle collision are quantitatively investigated.     

Eulerian-Lagrangian simulation of aeolian sand transport

A numerical investigation of aeolian sand transport is performed with an Eulerian-Lagrangian model. In this model, the gas phase is described by the volume-averaged Navier-Stokes equations of two-phase flow. The particle motion is obtained by solving Newton's second law of motion taking into account the inter-particle collisions, where a soft sphere model is used to describe inter-particle collisions. The dynamic process of aeolian sand transport is simulated. The simulation results show that the variation of mean horizontal velocity of the particles with height can be expressed by a logarithmical function or a power function at h > 0.02 m, and the power function can be described below 0.02 m. The sand mass flux decreases exponentially with height for h > 0.02 m, but there is a deviation from the exponential decay due to the creep grains in the near-bed region. It is also shown that the inter-particle collisions play an important role in sand saltation. Therefore the present numerical model is capable of being applied to the study of windblown sand movement.     

Simulation of Colloidal Particle Packing for Photonic Bandgap Crystals

We study the packing history and packing structures of photonic bandgap crystals consisting of mono-sized SiO₂ particles. Simulations with combined actions of Brownian motion, inter-particle interactions, and imposed external fields are considered. Numerical tactics to support modeling of Brownian particle agglomerations and consolidation and drying processing are developed. Our results suggest that the desired close-packed patterns on the surface are propagated from those at the bottom layer during consolidation. The driving forces for this pattern formation and growth are the coupling between inter-particle interactions and constraints from imposed external fields.     

气固流化床中细长颗粒数量浓度分布的数值研究

细长颗粒的循环流化在工业生产中具有非常广泛的应用背景,如生物质秸秆在循环流化床中的燃烧、烟丝在循环流化床中的干燥或加湿等。由于细长颗粒具有六自由度,因此,其运动姿态比球形颗粒复杂,其在流化床内的流化特性也不同于球形颗粒。细长颗粒的数量浓度分布是细长颗粒流化特性的重要特征之一。根据直接模拟Monte Carlo(DSMC)方法的基本思想及刚体动力学原理,建立了考虑细长颗粒间相互碰撞的三维细长颗粒流化运动数学模型,并采用此模型对某一实际流化床内的气固两相流场进行了模拟研究。在实验提升管内,所有物料中小长径比的细长颗粒最先由提升管的近壁处到达提升管出口。细长颗粒在流化过程中有明显的迁移和絮团现象。在流化状态下,细长颗粒的数量浓度分布基本不随入口风速发生变化。     

Towards understanding particle rigid-body motion during solid-state sintering

A quantitative understanding of particle rigid body (RB) motion that inherently accompanies grain boundary (GB) diffusion is highly desirable to understand and control the dynamic interplay between coarsening and densification during solid state sintering. By computer simulation using a multi-phase-field approach, we analyze systematically the roles played by each of these processes at different stages of the shrinkage of the internal pore in a three-particle green body as a function of particle size as well as thermodynamic and kinetic factors of interfaces. We demonstrate that particle RB translation promotes both neck growth, and pore rounding and shrinkage. Moreover, the forces acting at GBs and pulling neighboring particles towards one another dynamically evolve as particles fuse. In contrast, particle RB rotation has no contribution to pore shrinkage. The translational force acting on an individual particle varies with not only its size, but also the number and sizes of its neighboring particles.     

Quantitative measurement of particle segregation mechanisms

Pharmaceutical, food, chemical, mining, and energy industries routinely handle and process materials with different particle sizes. Often the different size materials represent different chemical components. Pharmaceutical mixtures are typically mixtures of fine, active, with relatively coarse, incipient ingredients. Food industry mixtures combine particles with very different sizes and shapes. There is a great tendency for these dissimilar materials to separate during processing and handling. The cause of this separation depends on the size and shape of the particles in the mixture. If the fines are less than one-third the size of coarse particles and free flowing, they may percolate through the coarse matrix of particles resulting in sifting segregation. If the particle shapes are different, then the internal friction angles of individual components may be different, resulting in angle of repose segregation. Preventing segregation of a given material mixture depends on the cause of the segregation. If angle of repose segregation is the predominate mechanism, then segregation mitigation can be accomplished by limiting pile formation. However, if sifting segregation is the predominate mechanism, then limiting pile formation may not limit the segregation if the process equipment is subject to significant inter-particle motion or shear. This paper presents a method of measuring the magnitude of sifting segregation occurring in bulk material. It also includes data that relates bulk material strength to separation tendency. This relationship shows an inverse functionality between the yield strength of the material and the bulk segregation. Finally, the work presented in this paper compares segregation due to sifting and repose angle mechanisms to provide a means of differentiating between these mechanisms.     

Zur Bewegung feiner Partikeln,die in turbulent strömenden Medien suspendiert sind

Motion of fine grained particles, suspended in turbulent flow . This article considers the motion of particles, suspended in turbulent flow. If the particles are sufficiently small to respond to turbulence, their motion includes stochastic components. Concerning processes like air classification or separation of fine powders the stochastic contribution – characterized by the conception of a particle diffusivity – the particle motion exhibits a detrimental influence. Sharpness of cut and separation efficiency are reduced. The paper aims to present the state of the art in particle diffusion. First, theoretical investigations are reported, attention being focused on the equation of motion of the particle which is the link between the motion of the fluid and the motion of the particle. Then, experimental results are reviewed. The following tendencies can be seen: Particles which response to turbulence of fluid flow show increasing diffusivity with increasing inertia. Field forces like gravity or electrical field forces exhibit a damping effect on diffusivity.     

Spontaneous inter-particle percolation: A kinematic simulation study

Spontaneous inter-particle percolation is a mechanism of particle segregation which arises when a particle falls through the voids among large particles due to gravity or other applied force, the size difference being such that this can occur without the need for applying strain. It is a phenomenon arising in some packed bed processing operations and in some dispersers for particles. Here the mechanism is modelled by computer simulation. The model uses particle sizes, a coefficient of restitution and also, to cater for less elastic materials, a coefficient of friction. This yields percolation velocities quantitatively consistent with prior laboratory studies, showing the correct dependence on coefficient of restitution and particle size. The simulation clarifies the dependence of radial dispersion on packing height. The radial distributions are well described only at higher coefficients of restitution, pointing to the need for a better means of describing collisions between percolating and packed particles.     

Air-suspension coating in the food industry: Part II — micro-level process approach

A review of air-suspension particle coating concluded that, in order to speed product and process development, a phenomenological approach is necessary to develop generic guidelines for the selection of coating materials and process variables. This paper identifies 10 fundamental phenomena (micro-level processes) that occur during an air-suspension particle coating process: particle motion, atomisation, droplet-particle collision, droplet impact and adherence, droplet impact and spreading, infiltration, drying, film formation, layering and inter-particle agglomeration. Their relevance to the coating objectives is discussed and from these four are identified as key micro-level processes: drying, droplet impact and spreading, and stickiness which encompasses the two key micro-level processes of droplet impact and adherence and inter-particle agglomeration. It is believed that significant advances in particle coating research can be made through examination of these key micro-level processes.     

稀疏两相射流中颗粒碰撞的数值研究

为了研究稀疏气固两相流动中颗粒间的碰撞行为及其对颗粒扩散的影响,对三维两相湍流射流进行了直接数值模拟。其中对流场控制方程的求解采用有限容积法和分步投影算法,对颗粒的跟踪采用拉格朗日方法,对颗粒间的碰撞采用硬球模型模拟。结果发现,在流场中局部浓度较高的区域颗粒碰撞频繁发生;受局部富集效应和湍流输运作用两方面的影响,颗粒的平均碰撞次数并不是随着Stokes数的增加呈现简单的线性增加,而是在Stokes数为0.1附近存在一个极值;考虑颗粒间的碰撞作用以后,颗粒的分布更加均匀,沿横向和展向的扩散也都有所增加。     

Experimental study on collision rates of inertial particles in particulate flows under the effect of gravity

To investigate the inter-particle collision frequency, the present experiment conducts two streams of particulate flow converging into a main flow in a junction. Each stream of particulate flow consists of inertial steel particles of 1 and 2 mm diameter, respectively. Particles glide down inside two branches of slanting glass rectangular ducting. We use a high-speed camera to record the trajectory of particle and a PTV technique for data processing. The correlation between the inter-particle collision frequency, particulate concentration, effective diameter and mean fluctuation velocity of inertial particles is explored experimentally. The effect of inter-particle collision frequency under the effect of gravity force is considered and analyzed. Due to the high inertia of steel particles, the turbulent effect of gas-phase is eliminated. A significant difference between the characteristics of the gravitational particulate flow and the homogeneous isotropic flow is found. The physical interpretation for it and the statistical correlation with inter-particle collision frequency are discussed. The results support the analogy of kinetic theory for inertial particles in gas-solid flow provided the gravity effect is excluded.     

Stochastic modeling of particle motion along a sliding conveyor

The sliding conveyor consists of a plane surface, known as the track, along which particles are induced to move by vibrating the bed sinusoidal with respect to time. The forces on the particle include gravity, bed reaction force and friction. Because friction coefficients are inherently variable, particle motion along the bed is erratic and unpredictable. A deterministic model of particle motion (where friction is considered to be known and invariant) is selected and its output validated by experiment. Two probabilistic solution techniques are developed and applied to the deterministic model, in order to account for the randomness that is present. The two methods consider particle displacement to be represented by discrete time and continuous time random processes, respectively, and permits analytical solutions for mean and variance in displacement versus time to be found. These are compared with experimental measurements of particle motion. Ultimately this analysis can be employed to calculate residence‐time distributions for such items of process equipment. © 2009 American Institute of Chemical Engineers AIChE J, 2010     

Incipient motion of individual particles in horizontal particle-fluid systems: B. Theoretical analysis

This paper presents a theoretical analysis of the force and moment balance during incipient motion of a single particle. The analysis showed that large particles start their motion by rolling for spherical particles and by sliding for non-spherical particles. It also showed that fine spherical or near spherical powders start their motion by rolling. The theoretical analysis shown that the incipient motion velocity of individual particles for all fluid, system and particle properties might be presented as power relationships between the Reynolds and Archimedes numbers.     

Collision rate of small particles in a homogeneous and isotropic turbulence

A theoretical equation is derived for the collision rate of aerosol particles in a homogeneous and isotropic turbulent system. This equation takes into account the relative velocity between fluid and particles. The calculated results indicate that the relative velocity between fluid and particles is the main factor in the turbulent coagulation (agglomeration, coalescence) of unequally sized particles in an air flow. This hold true, even when the particle sizes are less than 1 micron. For particles of equal radii the coagulation coefficient reaches its minimum value, because the effect of motion relative to the fluid now becomes zero and only the spatial variation of turbulent motion remains to cause collisions between the particles. For particles following a fluid motion completely, as in a water stream, the equation for the collision rate reduces to the Saffman and Turner equation.     

Effect of particle shape and size on the shrinkage of stainless steel compacts

The effects of particle size and shape on the shrinkage of commercial 316 L stainless steel compacts are evaluated. Emphasis is placed on the effect of changes in surface area and the anisotropy in inter-particle contacts brought about by the irregular powders. The effects of fine particle addition on this anisotropy and surface area are presented and plained. An empirical relationship is derived which can be used to predict changes in the axial, radial and volume shrinkage when spherical particles are substituted into a commercial blend. The effect of spherical particle substitution on the shrinkage ratio is also discussed. It is shown how the combined effects of fine particle additions and substitutions of spherical particles for irregular particles can be used to produce a compact which exhibits a shrinkage ratio (radial to axial shrinkage) of unity.     

Diffusiophoresis of a colloidal sphere in nonelectrolyte gradients parallel to one or two plane walls

The quasisteady diffusiophoretic motion of a spherical particle in a fluid solution of a nonionic solute located between two infinite parallel plane walls is studied theoretically in the absence of fluid inertia and solute convection. The imposed solute concentration gradient is constant and parallel to the two plane walls, which may be either impermeable to the solute molecules or prescribed with the far-field concentration distribution. The particle-solute interaction layer at the particle surface is assumed to be thin relative to the particle radius and to the particle-wall gap widths, but the polarization effect of the diffuse solute in the thin interfacial layer caused by the strong adsorption of the solute is incorporated. The presence of the neighboring walls causes two basic effects on the particle velocity: first, the local solute concentration gradient on the particle surface is enhanced or reduced by the walls, thereby speeding up or slowing down the particle; secondly, the walls increase viscous retardation of the moving particle. To solve the continuity and momentum equations, the general solutions are constructed from the fundamental solutions in both the rectangular and the spherical coordinate systems. The boundary conditions are enforced first at the plane walls by the Fourier transforms and then on the particle surface by a collocation technique. Numerical results for the diffusiophoretic velocity of the particle relative to that under identical conditions in an unbounded fluid solution are presented for various values of the relaxation parameter of the particle as well as the relative separation distances between the particle and the two plates. For the special case of diffusiophoretic motions of a spherical particle parallel to a single plate and on the central plane of a slit, the collocation results agree well with the approximate analytical solutions obtained by using a method of reflections. The presence of the lateral walls can reduce or enhance the particle velocity, depending on the surface properties of the particle, the relative particle-wall separation distances, and the solutal boundary condition at the walls. In general, the boundary effect on diffusiophoresis is quite complicated and relatively weak in comparison with that on sedimentation.     

Probabilistic analysis of transport-reaction processes over catalytic particles: Theory and experimental testing

We developed a probabilistic theory of transport-reaction processes over various types of configurations of catalytic particles, particularly for a single particle. The theory describes a single pulse-response experiment which is similar to the single pulse temporal analysis of products (TAP) experiment. The analysis is based on the general theory of Brownian motion with “killing” and the Feynman-Kac formula. Different diffusion-reaction problems, particularly the problem “diffusion-very fast reaction” (infinite rate reaction), have been analyzed. In the latter case, the probability for a reactant to be converted equals a purely geometric characteristic, namely, the probability for a reactant molecule to hit at least one catalyst particle in a configuration of particles. Solving a boundary value problem, the probability of conversion can be found as a function of the apparent kinetic parameter. Based on experimental data on exit flow and conversion this parameter can be extracted. Experimental data in studies of CO oxidation over a single particle of Pt catalyst show a qualitative agreement with data from computational experiments based on the developed probabilistic theory. For two-particle catalyst configurations, it was found computationally a non-trivial dependence of the reactant conversion on some geometric characteristics, especially the distance between particles. A distance was found for which conversion is highest.