Effect Of Inter-particle Collisions Research Articles

Behavior of Gas–Solid Two-Phase Flow in a Backward Facing Step - Effect of Interparticle Collisions

Abstract This article presents a computational investigation of the dilute gas–solid flow's loss coefficient and reattachment length in a horizontally placed backward-facing step. The article's primary objective is to study the effect of the interparticle collision and three significant parameters, namely, inlet solid-phase volume fraction (αs=0.002, 0.005), particle size (dp = 70 μm and 200 μm), and solid-particle density (ρs = 1500 kg/m3 and 3000 kg/m3). The numerical procedure uses the Eulerian–Eulerian approach in conjunction with the Kinetic theory of Granular flow and the four-way coupling approach. The outcomes show that the loss coefficient and the reattachment length increase as the interparticle collision intensifies with the system. Moreover, these parameters show higher values with small particle sizes and higher solid-phase volume fractions. The reattachment length is higher with less dense solid particles and higher with heavier solid particles.

Effect of sediment particles on the velocity profile of sediment–water mixtures in open-channel flow

The presence of sediment particles in open-channel flow has an important effect on turbulence; thus, an empirical, turbulent eddy viscosity formula was established for application in the limit for low concentrations. The current study establishes a theoretical relation for the mixture viscosity based on the two-phase mixture model. The percentage contribution of the three mechanisms of mixture viscosity, namely, fluid turbulence (FT), particle turbulence (PT), and inter-particle collisions (IPCs), was calculated under different conditions. The study results indicate that the contribution of FT is dominant, whereas those of PT and IPCs are not significant when the particle inertia (PI) is small, suggesting that the movement of sediment-laden flows is mainly controlled by the fluid properties. The effects of PT and IPCs increase with increases in sediment concentration and PI. Specifically, the effect of collisions among particles generally becomes dominant near the bed surface. A good agreement between the calculated velocity profile of the mixture and available experimental data for large particle sizes and high concentrations proves that the proposed relation for mixture viscosity is more reasonable than the previous empirical relation owing to the consideration of the effects of PT and IPCs, and, thus, can be applied to both dilute and dense suspensions.

Flow regimes within horizontal particle-laden pipe flows

This study presents numerical simulations for particle-laden gas–solid flows in horizontal circular pipes to identify the key flow regimes as a function of the main dimensionless parameters. A Euler–Lagrangian approach is employed, using direct numerical simulations (DNS) coupled with a Lagrangian particle tracking (LPT) method, to consider the drag, gravitational and lift forces on particles, as well as the effect of inter-particle collisions. The influence of the Stokes number (Sk), mass loading ratio (Φm) and Froude number (Fr) on critical flow regimes is assessed to identify conditions under which gravity bias becomes either negligible or dominant with regard to fluid characteristics and particle statistics. Three different regimes of the flow behaviour are identified, depending on the combination of these dimensionless parameters. These flow regimes are described and their dependence on these three parameters (Sk, Φm and Fr) is reported, including the significance of gravity in generating a bias on distributions of the flow statistics.

Dissipation measures in weakly collisional plasmas

ABSTRACT The physical foundations of the dissipation of energy and the associated heating in weakly collisional plasmas are poorly understood. Here, we compare and contrast several measures that have been used to characterize energy dissipation and kinetic-scale conversion in plasmas by means of a suite of kinetic numerical simulations describing both magnetic reconnection and decaying plasma turbulence. We adopt three different numerical codes that can also include interparticle collisions: the fully kinetic particle-in-cell vpic, the fully kinetic continuum Gkeyll, and the Eulerian Hybrid Vlasov–Maxwell (HVM) code. We differentiate between (i) four energy-based parameters, whose definition is related to energy transfer in a fluid description of a plasma, and (ii) four distribution function-based parameters, requiring knowledge of the particle velocity distribution function. There is an overall agreement between the dissipation measures obtained in the PIC and continuum reconnection simulations, with slight differences due to the presence/absence of secondary islands in the two simulations. There are also many qualitative similarities between the signatures in the reconnection simulations and the self-consistent current sheets that form in turbulence, although the latter exhibits significant variations compared to the reconnection results. All the parameters confirm that dissipation occurs close to regions of intense magnetic stresses, thus exhibiting local correlation. The distribution function-based measures show a broader width compared to energy-based proxies, suggesting that energy transfer is co-localized at coherent structures, but can affect the particle distribution function in wider regions. The effect of interparticle collisions on these parameters is finally discussed.

Solid–liquid two-phase flow and erosion calculation of butterfly valves at small opening based on DEM method

Purpose The study aims to decrease the effect of solid particles on a butterfly valve, which will cause seal failure and leakage, providing a reference for anti-wear design. Design/methodology/approach In this paper, computational fluid dynamics discrete element method (CFD-DEM) simulation was conducted to study the solid–liquid two-phase flow characteristics and erosion characteristics of a butterfly valve with a different opening. Findings Abrasion at 10% opening is affected by high-speed jets in upper and lower parts of the pipeline, where the erosion is intense. The impact of the jet on the upper part of 20% opening begins to weaken. With the top backflow vortex disappearing, the effect of lower jet is enhanced. Meanwhile, the bottom backflow vortex phenomenon is obvious, and the abrasion position moves downward. At 30% opening, the velocity is further weakened, and the circulation effect of lower flow channel is more obvious than that of the upper one. Originality/value It is the first time to use DEM to investigate the two-phase flow and erosion characteristics at a small opening of a butterfly valve, considering the effect of inter-particle collision. Therefore, this study carries on the thorough analysis and discussion. At the same opening degree, with increasing of the particle size, the abrasion of valve frontal surface increases when the size is less than 150 µm and decreases when it is greater than 150 µm. For the valve backflow surface, this boundary value becomes 200 µm. Peer review The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2020-0264/

Quantification of preferential concentration of colliding particles in a homogeneous isotropic turbulent flow

This paper addresses the effect of inter-particle collisions on the segregation of non-settling inertial particles in homogeneous isotropic turbulence. For this purpose, direct numerical simulations of particles in statistically steady homogeneous isotropic turbulence have been performed by the lattice Boltzmann method considering inter-particle collisions. The preferential concentration of suspended particles is quantified using several clustering measures: segregation parameter, correlation dimension, radial distribution function, Voronoï diagrams and the topological tool of Minkowski functionals. Effects of particle inertia, inter-particle collisions and increasing volume fraction in the aforementioned measures are discussed. The obtained results show that collisions between particles have a remarkable influence on the formation of clusters. In particular, under locally dilute conditions, increasing particle volume fraction implies a moderate clustering intensification, but for locally dense conditions an increase of the mean inter-particle distance inside clusters can be envisaged as a consequence of the re-dispersing effect of inter-particle collisions.

Issue Highlights

The Canadian Journal of Chemical EngineeringVolume 97, Issue 2 p. 423-423 Issue HighlightsFree Access Issue Highlights First published: 11 January 2019 https://doi.org/10.1002/cjce.23265AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat 442 CFD in Chemical Engineering: Process Design Symposium at the 10th World Congress of Chemical Engineering (WCCE10) José Roberto Nunhez, Jos J. Derksen and Vivek V. Ranade This special section of the Canadian Journal of Chemical Engineering presents 16 selected papers of the “CFD in Chemical Engineering: Process Design” symposium as part of the 10th World Congress of Chemical Engineering (WCCE10) held in Barcelona, Spain on October 1–5, 2017. The symposium had about 100 presenters showing a diversity of applications as well as modelling approaches. The papers will provide the reader a flavour of the high quality of the research presented and the organizers hope this special section will stimulate further work on this very important area from an industrial as well as from a scientific point of view.1 511 Influence of Inter-Particle Collisions and Agglomeration on Cyclone Performance and Collection Efficiency Oscar Lino Sgrott Júnior and Martin Sommerfeld For further improving the understanding of particle separation in gas cyclones, numerical calculations based on the coupled Euler/Lagrange approach were conducted using Open-FOAM. Since the flow in cyclones is highly anisotropic, the gas flow field was simulated based on LES in combination with a dynamic sub-grid-scale turbulence model. The effect of inter-particle collision and agglomeration on the performance of a cyclone was analyzed in a hypothetical study considering a high efficiency Stairmand cyclone. The present study shows that inter-particle collisions and agglomeration affect the grade efficiency and particle concentration distribution prediction and, therefore, should not be neglected.2 523 Mixing in an Agitated Tubular Reactor Jos J. Derksen A novel type of continuous mixer consisting of an oscillating tube with a freely moving mixing element inside has been analyzed computationally through direct and large-eddy simulation. Next to fluid flow we solve passive scalar transport so that we can determine mixing times as a function of process conditions as well as design parameters. A key finding is that the mixing element should have sufficient inertia so that it strongly agitates the fluid passing through the tube and achieves fast mixing.3 586 Nusselt Number Correlation for a Jacketed Stirred Tank using Computational Fluid Dynamics Silvia Araujo Daza, Ronald Jaimes Prada, José R. Nunhez and Guilherme J. Castilho In this article, computational fluid dynamics (CFD) has been used as an alternative to obtain a Nusselt number correlation for a jacketed stirred tank equipped with a six-blade Rushton impeller. The correlation did not use any experimental data, only data from the CFD simulations. The applied CFD methodology conirms that it is possible to obtain Nusselt correlations from a CFD model for different conigurations of stirred tanks, saving money and time in comparison with experimental studies. The numerical correlation obtained from the simulated model agrees well with published experimental data providing a reliable representation of the heat transfer inside the tank4 References 1 J. R. Nunhez, J. J. Derksen, V. V. Ranade, Can. J. Chem. Eng. 2019, 97, 422 2 O. Sgrott Júnior, M. Sommerfeld, Can. J. Chem. Eng. 2019, 97, 511. 3 J. J. Derksen, Can. J. Chem. Eng. 2019, 97, 523. 4 S. Araujo, R. J. Prada, J. R. Nunhez, G. J. Castilho, Can. J. Chem. Eng. 2019, 97, 586. Volume97, Issue2February 2019Pages 423-423 ReferencesRelatedInformation

Model for particle behavior in debris bed

In analyzing the safety of core disruptive accidents in Sodium-cooled Fast Reactors (SFRs), it is important to evaluate whether the decay heat of debris bed can be removed. The decay heat removability changes depending on the shape of debris bed, which would be deformed by coolant vapor with time. In the present paper, a new model was developed to analyze debris bed behavior with SIMMER, which is a safety analysis code for SFRs. In the new model, the effects of inter-particle collisions and contacts are modeled as inter-particle interaction. Test simulation results show the roles of physical properties in the new model on the dense particle behavior. Assessment results of proposed model based on model experiments indicate that the new model is capable of describing the transient of the shape of the particle bed in the liquid driven by the gas phase. Considering the fact that the process of leveling behavior in model experiments is common for the debris bed in SFRs, the new model can be employed as an analysis tool for debris bed behavior.

Direct Numerical Study on Effect of Interparticle Collision in Particle-Laden Turbulence

Particle-laden turbulent flow is widely seen in the natural world and industrial applications, and thus studies on multiphase flows with particles are of great significance for improving the efficiency of industrial processes and environment protection. In the present study, the Euler–Lagrange direct numerical simulation based on the point-source-in-cell model was employed to calculate the dilute particle-laden flow in a vertical channel. The turbulence flowfield was obtained by directly solving the Navier–Stokes equation. The particle’s motion was described by the Basset–Boussinesq–Oseen equation, and the shear lift force and Magnus lift force were also included in the particle equation of motion. The main purpose was focused on the effect of interparticle collision, which was detected by using a deterministic method. It was found through investigation that interparticle collision has a significant effect on the particle-laden flow even when the particle’s volume fraction is very small [about ]. Interparticle collision increases the near-wall particle velocity. The near-wall particle accumulation is decreased because interparticle collision can not only promote the particle migration from the near-wall region to the channel center but also change interphase forces. It was also found that interparticle collision has little effect on the mean velocity profile and the turbulence intensity of the gas phase. In addition, interparticle collision enhances the fluctuating intensities of particles in the wall-normal direction and spanwise direction. In the streamwise direction, the fluctuating intensity of particles is enhanced in the very-near-wall region and the channel center, while it is reduced in other regions by interparticle collision.

Particle Dispersion Simulation in Turbulent Flow Due to Particle-Particle and Particle-Wall Collisions

AbstractSimulation of the 3-D, fully developed turbulent channel flows laden with various mass loading ratios of particles is made using an Eulerian-Lagrangian approach in which the carrier-fluid flow field is solved with a low-Reynolds-number k-ε turbulence model while the deterministic Lagrangian method together with binary-collision hard-sphere model is applied for the solution of particle motion. Effects of inter-particle collisions and particle-wall collisions under different extents of wall roughness on particle dispersion are addressed in the study. A cost-effective searching algorithm of collision pair among particles is developed. It is found that the effects of inter-particle collisions on particle dispersion cannot be negligible when the ratio of the mean free time of particle to the mean particle relaxation time of particle is less or equal to O(10). In addition, the wall roughness extent plays an important role in the simulation of particle-wall collisions particularly for cases with small mass loading ratios.

Numerical investigation of mass loading effects on elbow erosion

Wear due to particles is often the key factor for pipeline failure. In this work, the effects of different sand particle concentrations on the erosion of an elbow pipe are investigated numerically. In order to assess the quality of the numerical predictions of the erosion rate, experimental data were first used to validate the erosion and restitution models at low concentration. The input parameters for the empirical erosion correlation were obtained from accurate CFD models for the gas–solid flow within the bend. One, two and four-way couplings were evaluated at different mass loadings. In general, it was found that even at low to moderate mass loadings, the effects of inter-particle collisions on the penetration ratio cannot be neglected. Another important finding is that the maximum penetration ratio gradually diminishes as the mass loading increases. As counterintuitive as it may appear, this phenomenon has actually been observed in experiments and is named cushioning effect. Based on the analysis of the simulation results, it can be concluded that a layer of particles builds up adjacent to the elbow wall, protecting it from direct particle collisions. Conversely, the inter-particle collisions damp the particle impact to the surface, therefore reducing the penetration peak.

Numerical study of particle behavior in laminar axisymmetric opposed-jet flows

The particle behavior in laminar axisymmetric opposed-jet flows is investigated numerically using a high order finite difference method and Lagrangian particle tracking. The deterministic hard-sphere collision model is used to deal with the inter-particle collisions, and the feedback of the particles on the carrier phase is neglected in the present work. In the scope of particle volume fractions and particle Stokes numbers studied, the particle collision rates in the impinging zone can agree with the prediction of cylinder formula (Saffman & Turner, 1956). The results found that inter-particle collisions have significant influence on particle distribution, velocities and residence time. When particle volume fraction at nozzle outlet is smaller than O(10−4), inter-particle collisions make little difference on the particle concentration profile, which is primarily decided by the maximum penetration distance (MPD) of a particular particle. Particle will prefer to concentrate at the location of MPD when the MPD is within the flow domain, otherwise particles will evenly distribute along the axis of two nozzles. When particle volume fraction is higher than O(10−3), the effect of inter-particle collisions become significant, which can impede particles reaching the MPD so that particles will prefer to concentrate at the impinging plane. Inter-particle collisions can restrain the penetration process of particles, and shorten the particle residence time at the same time. Due to massive collisions, particle mean velocity profile has the similar shape with the profile of gas velocity in the impinging zone, and slip velocity between particles and gas will be decreased.

Computations of Particle-Laden Turbulent Jet Flows Based on Eulerian Model

Numerical simulations using an Eulerian two-fluid model were performed for spatially developing, two-dimensional, axisymmetric jets issued from a 30-mm-diameter circular nozzle. The nozzle was simulated separately for various flow conditions to get fully developed velocity profiles at its exit. The effect of interparticle collisions in the nozzle gives rise to solids pressure and viscosity, which are modeled using kinetic theory of granular flows (KTGF). The particle sizes are in the range of 30 μm to 2 mm, and the particle loading is varied from 1 to 5. The fully developed velocity profiles are expressed by power law, U=Uc(1-(r/R))N. The exponent, N, is found to be 0.14 for gas phase, irrespective of particle sizes and particulate loadings. However, the solid-phase velocity varies significantly with the particle diameter. For particle sizes up to 200 μm, the exponent is 0.12. The center line velocity (Uc) of the solid phase decreases and, hence, the slip velocity increases as the particle size increases. For 1 mm and 2 mm size particles, the exponent is found to be 0.08 and 0.05, respectively. The developed velocity profiles of both the phases are used as the inlet velocities for the jet simulation. The modulations on the flow structures and turbulent characteristics of gas flow due to the solid particles with different particle sizes and loadings are investigated. The jet spreading and the decay of the centerline mean velocity are computed for all particle sizes and loadings considered under the present study. Additions of solid particles to the gas flow significantly modulate the gas turbulence in the nozzle as well as the jet flows. Fine particles suppress the turbulence, whereas coarse particles enhance it.

Characterisation of pneumatic conveying systems using the Euler/Lagrange approach

Abstract This paper deals with the transport of solid particles in pneumatic conveying systems, namely a 5 m horizontal pipe, a 90° bend and 5 m a vertical pipe. The pipe diameter is 150 mm in all cases and the average conveying velocity is 27 m/s. Three-dimensional stationary numerical computations were performed by the Euler/Lagrange approach in connection with the k–e turbulence model accounting for full two-way coupling. Particle transport is calculated by considering all the relevant forces (including drag, gravity and transverse lift forces) and dispersion due to turbulence. Particle–wall collisions and wall roughness are modelled according to Sommerfeld and Huber [1] and inter-particle collisions are described by the stochastic modelling approach of Sommerfeld [2] . The objective of the present contribution is to demonstrate the capability of this computational approach for accurately predicting more complex pneumatic conveying systems where the transported powder has a rather wide size distribution. In particular the effect of inter-particle collisions will be demonstrated. As known from many single-phase studies a secondary flow is developing along the pipe bend. Since in the present study rather small glass powder is considered (i.e. 15 μm D p [3] for validation in both, a long horizontal pipe (mass loading ratio η = 0.7) and the vertical pipe of the pipe system (mass loading ratio η = 0.3). The agreement between the predictions and the experimental results was found to be very good for both situations. Consequently, such numerical computations can largely support the understanding of the influence of the relevant elementary transport effects on the pneumatic conveying characteristics. Moreover, a detailed analysis of the segregation phenomena occurring in the bend and the influence of the particle phase on the flow structure can be performed by the calculations, which is hardly possible by an experiment. With the validation on the numerical computations by experiments, it is now possible to apply the computations for designing pneumatic conveying systems and predicting relevant integral parameters as for example the pressure drop. The calculated pressure drop for the pipe system yielded an excellent agreement with empirical correlations.

Interaction of a planar shock wave with a dense particle curtain: Modeling and experiments

The interaction of a planar shock wave with a dense particle curtain is investigated through modeling and experiments. The physics in the interaction between a shock wave with a dense gas-particle mixture is markedly differently from that with a dilute mixture. Following the passage of the shock wave, the dense particle curtain expands rapidly as it propagates downstream and pressures equilibrate throughout the flow field. In the simulations, the particles are viewed as point-particles and are traced in a Lagrangian framework. A physics-based model is then developed to account for interphase coupling. Compared to the standard drag law, four major improvements are made in the present interphase coupling model to take into account: (1) unsteady force contributions to particle force; (2) effect of compressibility on hydrodynamic forces; (3) effect of particle volume fraction on hydrodynamic forces; (4) effect of inter-particle collision. The complex behavior of the dense particle curtain is due to the interplay between two-way coupling, finite particle inertia, and unsteady forces. Incorporation of these effects through significant modeling improvements is essential for the simulation results to agree well with the experimental data. As a result of the large pressure gradient inside the particle curtain, the unsteady forces remain significant for a long time compared to the quasi-steady force and greatly influence the particle curtain motion.

Simulating coarse particle conveying by a set of Eulerian, Lagrangian and hybrid particle models

This paper considers the behaviour of mono-disperse coarse glass particles in a pneumatic conveying experiment which consists of a curved and straight rectangular duct. Thus, the flow situation comprises the formation of a particle strand in the curved section as well as its dispersion in the subsequent straight horizontal channel. Thereby, from a physical point of view the effects of inter-particle collisions, particle rotation and wall roughness are of crucial importance. Based on this experimental setup six numerical models for the granular phase are applied in order to picture these physical phenomena. While the first set of three models – the (a) Lagrangian Discrete Phase (DP) model, the (b) Discrete Element Method (DEM) and the (c) ‘standard’ Eulerian-granular (EUgran) model – is readily available in commercial codes the remaining three models represent in-house developments. As a first modification the standard DP model is enhanced by sub-models accounting for inter-particle collisions, wall roughness and particle rotation in order to get an (d) enhanced Discrete Phase (DP+) model. Next, two combinations between the Eulerian and Lagrangian models, the (e) Dense Discrete Phase Model (DDPM), and a (f) Eulerian based hybrid model (EUgran+) are presented and discussed. Thus, all in all six numerical models are evaluated by qualitatively checking the main flow pattern, subsequently by a quantitative validation of dedicated profiles of particle velocity and concentration and finally, by qualitatively comparing the computational effort of each numerical model. While all ‘out of the box’ models fail in predicting even basic flow patterns the remaining enhanced models agree well with the experimental results. Nevertheless, their required computational effort is significantly different.

NUMERICAL SIMULATION OF UPRISING TURBULENT FLOW BY 2D RANS FOR FLUIDIZED-BED CONDITIONS

2D RANS (Reynolds Average Navier Stokes) equations are used for numerical modeling of uprising particulate (gas-solid particle) turbulent flow in conditions of fluidized beds. The two-fluid model approach was used in giving numerical simulations. The flow domain is a round pipe with diameter of 1 m and height of 6 m (a real industrial object). The flow of mean velocity 4 m/s carries solid particles (material density 2000 kg/m; sizes of 0.3, 1 and 1.5 mm) with mass flow ratio 10 kg/kg. The mathematical model pertains to gravitational and viscous drag forces, Magnus and Saffman lift forces, effects of inter-particle collisions as well as particle interaction with the wall, effect of turbulence modulation (turbulence enhancement) at particles’ presence. The fluidized-bed conditions consider that flow conditions were set for high-temperature flow, density of the carrier fluid 0.329 kg/m, and kinematic viscosity 1.55·10 m/s. The results are presented in the form of distribution of axial and radial velocity components of gaseous and solid phases, particle mass concentration and kinetic turbulent energy along the flow height at the flow exit (highest downstream position) and in the middle cross-section (intermediate position) in order to observe development of particulate flow. As shown by the results, the 2D RANS model qualitatively and quantitatively describes the real-time distribution of flow in a real flow domain, i.e. the model covers reasonable physical phenomena occurring in fluidized-bed conditions.

Transport and deposition of colliding particles in turbulent channel flows

The purpose of this paper is twofold: (i) to present statistical models that describe particle–turbulence interactions as well as particle–particle collisions and (ii) to gain a better understanding of the effect of inter-particle collisions on transport, deposition, and preferential concentration of heavy particles in turbulent channel flows. The models presented are based on a kinetic equation for the probability density function of the particle velocity distribution in anisotropic turbulent flow. The model predictions compare reasonable well with numerical simulations and properly reproduce the crucial trends of computations.

Thermal forces on planetary ring particles: application to the main system of Saturn

Context. The motion of small particles in planetary rings is affected in the long-term by radiation forces. While the Poynting-Robertson effect has been extensively discussed and applied to the dynamics of micron-sized ring particles, studies of thermal self-acceleration of particles are only in their infancy. Aims. We extend the pioneering work of Rubincam (2006, Icarus 184, 532) by a more thorough analytical formulation of both planetary and solar thermal forces on ring particles. Methods. Within a sparse disk model we analytically compute both seasonal and diurnal variants of the thermal forces and we demonstrate that the diurnal effect components vanish for a sample of rapidly rotating particles with randomly oriented spin axes. For sufficiently slowly rotating ring particles, though, these diurnal components might significantly modify the expected planetocentric secular drift rates of their orbits. We also take into account the orbital effects of Poynting-Robertson drag that begin to dominate the thermal forces for particles with sizes <5 mm. Our formulation of the Poynting-Robertson drag is the first to account properly for the influence of the planetary shadow. Results. We critically review the previous suggestion that Saturn's A and B ring boundaries might correlate with radiative null-torque orbits of small particles. Using the best estimates of optical and thermal parameters of Saturn's ring particles, we show that the millimetre to several centimetre size particles mostly drift inward to the planet with a characteristic radial speed ν r ∼ 3 × 10 -6 cm/s, corresponding to drift across the whole main ring system in ∼(1-5) x 10 8 years if the effects of inter-particle collisions are neglected. The radial speed is comparable to, or even larger than, the effective radial drift rate of small particles due to redistribution of collisional ejecta from micrometeoroid impacts. Therefore, radiation forces may be important for estimating the evolution timescales of Saturn's rings as derived from the ballistic transport theory. We propose that, in addition to collisional coagulation, radiation forces may efficiently remove centimetre-sized particles and thus help explain the observed paucity of these particles in Saturn's rings. A population of particles with spin axes aligned with normal to the disk plane, if it exists, would experience a net outward drift provided their rotation rate is larger than their orbital frequency.

Prediction of flow behavior of micro-particles in risers in the presence of van der Waals forces

Flow behavior of gas and micro-particles in riser is predicted within the framework of the classical Euler–Lagrange approach. The Newtonian equation of motion considering the effect of van der Waals forces is solved for each simulated particle in the system. Particle collisional dynamics is modeled by means of the direct simulation Monte Carlo (DSMC) method. The influence of van der Waals forces on the particle collisions is investigated. The effect of interparticle collisions on the particle concentration and velocity distributions is presented. These numerical results allow one to understand the effect of the considered parameters on the flow behavior of micro-particles agglomerations.