Particle Interaction Forces Research Articles

SYMPLER: SYMbolic ParticLE simulatoR with grid-computing interface

We present the main design concepts of the object-oriented particle dynamics code SYMPLER. With this freely available software, simulations can be performed ranging from microscopic classical molecular dynamics up to the Lagrangian particle-based discretisation of macroscopic continuum mechanics equations. We show how the runtime definition of arbitrary degrees of freedom and of arbitrary equations of motion allows for modular and symbolic computation with high flexibility. Arbitrary symbolic expressions for inter-particle forces can be defined as well as fluxes of arbitrarily many additional scalar, vectorial or tensorial degrees of freedom. The integration in a high performance grid computing environment makes huge geographically distributed computational resources accessible to the software by an easy-to-use interface. Program summaryProgram title: SYMPLERCatalogue identifier: AERQ_v1_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AERQ_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 221255No. of bytes in distributed program, including test data, etc.: 1805954Distribution format: tar.gzProgramming language: C++.Computer: Any system operatable with Linux.Operating system: Linux, MacOS.Has the code been vectorised or parallelised?: Experimental OpenMP parallelisation for usually up to 8 cores, the grid-version can use hundreds of cores.RAM: tens of MB to several GB, depending on problem.Classification: 7.7, 12, 16.1, 16.3, 16.13, 23.External routines: GSL, libxml2; optional: libsdl, OpenMP, libjama, libtnt, libsuperluNature of problem:A unified flexible and modular simulation tool allowing for the investigation of structural, thermodynamic, and dynamical properties of fluids and solids from microscopic over mesoscopic up to macroscopic time and length scales with suitable particle based simulation methods such as molecular dynamics, dissipative particle dynamics or smoothed particle hydrodynamics. The user should be enabled to freely define his own physical models without the need for recoding or code extensions.Solution method:SYMPLER provides flexibility to the user by 1.a modular object oriented structure that is passed to the user level and allows easy switching among different integration algorithms, particle interaction forces, boundary conditions, etc.2.an arbitrary number of particle-species for the simulation of complex multi-component systems3.an arbitrary number of additional user-defined degrees of freedom per particle-species4.symbolic definition of runtime-compiled mathematical expressions for particle interactions5.import of CAD-geometries6.a flexible choice of available computational cores through a grid-computing interface, amongst others.Restrictions:Classical deterministic and stochastic Newtonian dynamics.Unusual features:Symbolic runtime-compiled user-defined expressions.Additional comments:The current version and all future updates to the code are also found at http://sympler.org.Running time:Some benchmarks are given in the paper. The running time is problem dependent and ranges from seconds to days.

Particle Interaction Forces Induce Soil Particle Transport during Rainfall

Soil particle transport causes serious environmental problems, and particle interaction forces will be the controlling force for soil transport during rainfall. However, few reports can be found in literature concerning the quantitative evaluation of particle interaction forces on soil particle transport. In this study, purple soil was adopted to study soil particle transport under different force strength conditions of particle interaction during rainfall simulation with precipitation intensity of 150 mm h–1 for 110 min. We first analyzed soil particle interaction forces quantitatively under different KNO3 and Ca(NO3)2 concentrations (0.0001, 0.001, 0.005, 0.01, 0.05, 0.1, and 1 mol L–1) which adjusted surface potential of soil particle from –323 to –50 mV. The results indicated that the net Derjaguin–Landau–Verwey–Overbeek (DLVO) force could not solely cause soil particle transport during rainfall. The hydration repulsive force, which was much stronger than the DLVO force, played a crucial role in soil particle transport. During rainfall, soil particle in aggregate was separated to a distance of 1.5 to 2 nm by the strong hydration repulsive force (swelling process). Then aggregate was thoroughly broken by the electrostatic repulsive force. The hydration repulsive force dominated aggregate swelling, and the electrostatic force determined the transport intensity. We found that, at surface potentials lower than –100 mV, soil transport did not occur even precipitation intensity reaching 150 mm h–1; and –200 mV of surface potential was the critical potential for soil particle transport. We conclude that the surface hydration force and electrostatic repulsive force were the controlling force for soil particle transport during rainfall.

Transition of axial segregation patterns in a long rotating drum

Axial segregation of a bidisperse mixture of particles in a long rotating drum is studied using the discrete element method. Simulation results show that particle interaction is responsible for axial segregation, the patterns of which are influenced by the end wall effect. Axial segregation patterns transform under competing influences of the end walls and the particle interaction forces. The two influential factors vary with various rotational speeds and end wall friction levels. The result is the transition of different axial segregation patterns: two large-particle bands at both ends, two small-particle bands at both ends, or a random segregation pattern where either a large-particle band or small-particle band may appear at either end.

Stabilization of concentration waves in fluidized beds of magnetic particles

Abstract In this work, a linear stability analysis is carried out to evaluate the behavior of concentration waves in polarized fluidized beds. The magnetic effects are taken into account by the addition of a magnetic stress tensor on the particulate phase stress tensor. A non-linear model is proposed for the fluid–particle interaction force, so that the inertial effects arising from the wakes behind the particles are incorporated. We see that the alignment of the magnetic particles with the magnetic field stabilizes the fluidized bed flow and the efficiency of this stabilization is maximum when the field lines are parallel to the fluidization direction. The results are in qualitative agreement with experiments. The interaction of the magnetized particles with an external magnetic field produce a stronger stabilization of linear instabilities in fluidized beds than the one induced by particle pressure, associated with velocity fluctuations and collision of the particles, and by the interaction of the wakes of the particles, associated with the inertia of the flow. All three effects act in the sense of stabilizing fluidized beds against concentration waves.

Experimental evaluation of the particle size dependence of the dislocation–particle interaction force in TiC-precipitation-strengthened steel

The particle size dependence of the interaction force per TiC particle was experimentally evaluated from the amount of particle strengthening and the particle spacing. The amount of pure particle strengthening by TiC precipitates was successfully estimated from ferritic model steels with significantly low dislocation density and homogeneously dispersed fine precipitates. The interaction force indicated that very fine TiC particles are effective and that an equivalent volume diameter of 2–3 nm is the most potent for particle strengthening.

Computational Fluid Dynamic Simulation Based Cluster Structures-Dependent Drag Coefficient Model in Dual Circulating Fluidized Beds of Chemical Looping Combustion

A computational fluid dynamic (CFD) model for the dual circulating fluidized beds of chemical looping combustion technology has been developed. A continuum two-fluid model is used to describe both the gas and solid phases. Detailed submodels to account for fluid–particle and particle–particle interaction forces were incorporated. The gas–solids drag coefficient is predicted by means of the cluster structures-dependent (CSD) drag coefficient model. Flow behavior of gas and particles in the air reactor (AR) and fuel reactor (FR) is predicted. The solid circulation rate increases with the increase of solids inventory of the AR and FR. When the loop seal is connected to dual circulating fluidized beds of AR and FR, the fluidizing state of AR and FR is found to be affected by hydrodynamics in the loop seals.

CFD simulation of a chemical-looping fuel reactor utilizing solid fuel

A computational fluid dynamic (CFD) study has been carried out for the fuel reactor for a new type of combustion technology called chemical-looping combustion (CLC). CLC involves combustion of fuels by heterogeneous chemical reactions with an oxygen carrier, usually a granular metal oxide, exchanged between two reactors. There have been extensive experimental studies on CLC, however CFD simulations of this concept are quite limited. In the present paper we have developed a CFD model for the fuel reactor of a chemical-looping combustor described in the literature, which utilized a Fe-based carrier (ilmenite) and coal. An Eulerian multiphase continuum model was used to describe both the gas and solid phases, with detailed sub-models to account for fluid–particle and particle–particle interaction forces. Global reaction models of fuel and carrier chemistry were utilized. The transient results obtained from the simulations were compared with detailed experimental time-varying outlet species concentrations ( Leion et al., 2008) and provided a reasonable match with the reported experimental data.

Simulation of the layer inversion phenomenon in binary liquid--fluidized beds by DEM–CFD with a drag law for polydisperse systems

Liquid-fluidized beds of particular binary mixtures exhibit the layer inversion phenomenon, a peculiar result of the mechanical equilibrium developing in such multiphase systems. Because of the crucial role of the hydrodynamic interaction, these are ideal test cases for assessing fluid-particle models in multi-particle CFD simulations. In the present work the layer inversion phenomenon is reproduced via Discrete Element Method (DEM) simulations, in which the drag force model for polydisperse systems described in Cello et al. (2010) is used. The simulations serve primarily to assess the suitability of the DEM–CFD approach and particularly the validity of the above drag model, although the results available may also prove very useful to investigate the prevailing mechanisms. To analyze a sufficiently broad variety of cases, involving different solid species, size ratios and operating conditions, three systems selected amongst the published literature are considered. The comparison of simulation and experimental observation is carried out in terms of overall bed and mixed layer interface heights, voidage and component distributions along bed height and time evolution of the species centers of mass. Simulations with liquid velocities below, above and at the critical inversion conditions are carried out. Additionally, simulations using a drag force model traditionally used for monodisperse beds are reported for comparison. The results not only demonstrate the importance of correctly accounting for the local size distribution in the bed, but also prove the validity of the overall computational approach. The predictions of the simulations are in good to excellent agreement with experiments, depending on the system considered, both in terms of critical velocity and, most notably, expansion of the individual components in the bed. The analysis of the hydrodynamics in the bed allows to investigate the local particle flow field, highlighting the presence of a steady irregular motion of the solids in apparently chaotic vortices continuously forming and disappearing, which is thought to be the mechanism responsible for mixing. The fluid–particle interaction forces exhibit a constant profile along bed height, even in the presence of a strongly non-uniform concentration profile.

Thermodiffusion of rigid particles in pure liquids

Thermodiffusion of particles suspended in a pure liquid is a thorny problem which has not yet received a solution admitted by all the different communities interested in. We approach the subject with macroscopic tools exclusively, hydrodynamics and irreversible thermodynamics. These tools have proved their relevance for molecular mixtures and the Soret effect, and we here extend them to suspensions of particles with supra-molecular size. In particular, we obtain the momentum balance of the particulate phase from which are deduced all the physical phenomena inducing a migration of the particles relative to the carrier fluid. Focussing on thermodiffusion, we show that the osmotic pressure is irrelevant and that thermodiffusion cannot have but two distinct origins : the temperature dependence of the stress associated with the distorted particle microstructure and a fluid–particle interaction force involving the temperature gradient. For deformable particles, it is well known that the origin of the fluid–particle temperature gradient force is the temperature dependence of the surface tension. For rigid particles, we suggest it stems from the temperature dependence of the small density jump, the carrier liquid displays close to the particle’s surface.

Computational fluid dynamic simulations of chemical looping fuel reactors utilizing gaseous fuels

A computational fluid dynamic (CFD) model for the fuel reactor of chemical looping combustion technology has been developed, with special focus on accurately representing the heterogeneous chemical reactions. A continuum two-fluid model was used to describe both the gas and solid phases. Detailed sub-models to account for fluid–particle and particle–particle interaction forces were also incorporated. Two experimental cases were analyzed in this study (Son and Kim, 2006; Mattison et al., 2001). Simulations were carried out to test the capability of the CFD model to capture changes in outlet gas concentrations with changes in number of parameters such as superficial velocity, metal oxide concentration, reactor temperature, etc. For the experiments of Mattisson et al. (2001), detailed time varying outlet concentration values were compared, and it was found that CFD simulations provided a reasonable match with this data.

Geometric aspects of particle segregation

Size segregation is a natural occurrence both in everyday life and in industrial processes. Understanding and research of the phenomenon has overwhelmingly been from a mechanistic point of view. This paper demonstrates through simulations that segregation can also be explained and trends predicted geometrically. The algorithm used in this study contains three simple elements: random walks combined with a rebounding probability to encourage particles to settle, plus the non-overlap constraint. It is implemented digitally in a regular lattice grid, to make it easy to deal with arbitrary shapes. It does not explicitly consider any particle interaction forces, and it does not include any rules specifically designed to promote or suppress segregation. Yet particle movement, which occurs within a digitized cubic grid, leads to shaking-induced segregation comparable to that observed in physical tests. The paper details the comparison of shaking-induced particle segregation between a series of computer based simulations and those of physical experiments undertaken in the laboratory. A range of mixtures, comprising nonspherical, arbitrary shaped/sized particles are investigated, having been packed into pseudo-two-dimensional containers. The simulation results suggest that segregation can be adequately explained, from a geometrical point of view, as a result of the relative motion between particles of different sizes and shapes. The geometrical algorithm thus provides a fast and qualitative prediction as to how likely segregation is to occur for any given mixture of arbitrary shapes.

CFD–DEM study of the effect of particle density distribution on the multiphase flow and performance of dense medium cyclone

A mathematical model is developed to study the coal-medium flow in a dense medium cyclone (DMC) of 1000 mm body diameter. In the model, the motion of coal particles is obtained using the Discrete Element Method (DEM) facilitated with the concept of “parcel–particle” while the flow of medium as a liquid-magnetite mixture Computational Fluid Dynamics (CFD) based on the local averaged Navier–Stokes equations. In addition the Reynolds Stress Model (RSM) is adopted to describe the anisotropic turbulence, the Volume of Fluid (VOF) model is used to describe the air-core position and multiphase mixture model used to estimate the flow of fine magnetite particles. The simulated medium and coal flows allow estimates to be made of pressure drop, efflux stream medium densities and partition curves for coal particles of different sizes and densities. These estimates are compared favourably with industrial scale measurements of a 1000 mm DMC operating under similar conditions. On this base, the effect of particle density distribution that represents the major difference between two major coal type, i.e., coking coal and thermal coal, is studied. The results are analysed in terms of medium flow pattern, particle flow pattern, partition performance and particle–fluid, particle–wall and particle–particle interaction forces.

CFD simulations of expanding/contracting homogeneous fluidized beds and their transition to bubbling

This work presents a new Eulerian–Eulerian fluid dynamic model for monodisperse suspensions of solid particles fluidized by Newtonian incompressible fluids. The closure relationships for the fluid–particle interaction force distinguish the proposed equations of motion. The force consists of buoyancy, local fluid acceleration, drag and elastic forces. The closures of Mazzei and Lettieri [2007. A drag force closure for uniformly-dispersed fluidized suspensions. Chemical Engineering Science 62, 6142] based on the Richardson and Zaki [1954. Sedimentation and fluidization: part I. Transactions of the Institution of Chemical Engineers 32, 35] empirical correlation, and Mazzei et al. [2006. A revised mono-dimensional particle bed model for fluidized beds. Chemical Engineering Science 61, 1958], generalized for multidimensional applications, model the drag and elastic forces, respectively. For the first time these relations are solved in a computational fluid dynamic code. To test the drag force closure, we evaluate the steady-state expansion profiles of liquid-fluidized systems computationally, and compare them with those obtained using the closures of Wen and Yu [1966. Mechanics of fluidization. Chemical Engineering Progress Symposium Series 62, 100] and Ergun [1952. Fluid flow through packed columns. Chemical Engineering Progress 48, 89] and with experimental data. We successively analyze the behavior of uniform systems subjected to sudden changes in fluid flux, and compare the computational results with the theoretical predictions of the mechanistic one-dimensional model of Gibilaro et al. [1984. A simple mechanistic description of the unsteady-state expansion of liquid-fluidized beds. Chemical Engineering Science 39, 607]. To conclude the work, we investigate the stability of homogeneous gas-fluidized suspensions and the transition from the particulate to the aggregative state. Analytical and computational results (obtained by linear stability analysis and by integration of the equations of motion, respectively) are compared with experimental findings. The dynamics predicted are described and discussed; considerations on the meaning of fluid dynamic stability are debated.

Sedimentation of concentrated monodisperse colloidal suspensions: Role of collective particle interaction forces

The sedimentation velocities and concentration profiles of low-charge, monodisperse hydroxylate latex particle suspensions were investigated experimentally as a function of the particle concentration to study the effects of the collective particle interactions on suspension stability. We used the Kossel diffraction technique to measure the particle concentration profile and sedimentation rate. We conducted the sedimentation experiments using three different particle sizes. Collective hydrodynamic interactions dominate the particle–particle interactions at particle concentrations up to 6.5 vol%. However, at higher particle concentrations, additional collective particle–particle interactions resulting from the self-depletion attraction cause particle aggregation inside the suspension. The collective particle–particle interaction forces play a much more important role when relatively small particles (500 nm in diameter or less) are used. We developed a theoretical model based on the statistical particle dynamics simulation method to examine the role of the collective particle interactions in concentrated suspensions in the colloidal microstructure formation and sedimentation rates. The theoretical results agree with the experimentally-measured values of the settling velocities and concentration profiles.

Control of particle cluster dispersion using responsive polymeric additives

The dispersion behavior of clusters of hydrophilic and hydrophobic silica treated with a thermoresponsive polymer has been investigated. The influence of the thermoresponsive interfacial chemistry was assessed by performing dispersion studies in poly(dimethylsiloxane) (PDMS) at 25 and 68 °C for agglomerates of powders incorporating poly( N-isopropyl acrylamide) (PNIPAM), a thermoresponsive polymer, and water. While the dispersion of clusters of hydrophilic silica was found to be temperature independent, dispersion of hydrophobic silica exhibited a temperature dependency. The response of the polymer upon temperature variation brings about modifications in the interparticle interactions of the PNIPAM-treated powders thus leading to changes in the cluster cohesivity. The dependence of the cluster cohesivity on temperature was evidenced through changes in the dispersion mechanism and kinetics of the treated silica clusters at both tested temperatures. In addition, optical microscopy of silica suspensions with and without PNIPAM at 25 and 60 °C, illustrated the effect of the polymer presence and configuration on the particle–particle interaction forces. While micrographs of the particles at 25 °C show less evidence of particle aggregation, the micrographs at 60 °C illustrate an increase in aggregation suggesting an enhancement in the attractive forces between particles.

Stability analysis and CFD validation of a new fluid–particle interaction force for mono-component gas–solid fluidized beds

A new closure relationship for the fluid–particle interaction force has been developed for the CFD modelling of gas fluidized beds. As a first step in verifying the applicability of the new closure, the mono-dimensional version of the equations of change for the fluid and solid phases has been examined analytically. Here, linear stability analysis theory has been applied to the continuity and momentum equations in the face of small fluctuations in the voidage or particle velocity. The effort leads to the development of a new stability criterion for homogenous gas fluidized beds with better predictive capability than the Foscolo and Gibilaro [P. Foscolo, L. Gibilaro, A fully predictive criterion for the transition between particulate and aggregate fluidisation, Chem. Eng. Sci. 39 (1984) 1667–1675.] criterion. This was attributed to the better predictive ability of the dynamic wave velocity developed in this work and which is expressed as a function of the local concentration of the particles. CFD validation of the drag force closure equation is also carried out. Here predictions of bed height and bed voidage obtained from the CFD simulation of a Geldart [D. Geldart, Types of gas fluidization, Powder Technol. 7 (1973) 285.] Group A material FCC catalyst (70 μm) were used to validate the model. Results from simulations showed a very good agreement with predictions from the Richardson–Zaki [J. Richardson, W. Zaki, Sedimentation and fluidization, Trans. Inst. Chem. Eng. 32 (1954) 35.] equation. In the final part of the paper, CFD simulations of three Group B industrial powders are presented comparing the model predictions obtained for the case where the solid stress tensor is at first neglected and subsequently included in the model via the standard granular kinetic theory, results revealed that the collisional stresses do not dominate the macroscopic fluid bed predictions for bubbling dense gas–solid systems.

Molecular Simulation Study of Vapor-Liquid Equilibrium of Morse Fluids

The Morse potential energy function (PEF) is considered regarding the characterization of interaction forces of particles with tuning parameters. Phase coexistence of Morse fluids is predicted for different steepness and range of the PEF parameters using the grand-canonical transition matrix Monte Carlo (GC-TMMC) method, with quantification of the parameter S, which is the product of a constant with a unit of reciprocal length and the equilibrium distance between two molecules. We found that a lower limit of S exists bounded by infinite critical temperature. The critical properties of the vapor-liquid equilibrium curves are estimated using a rectilinear diameter method and a scaling law approach. A Clausius-Clayperon type relation of S and critical temperature is derived in this work. Vapor-liquid surface tension of Morse fluids by finite size scaling and GC-TMMC is also reported. Surface tensions are found to be higher at lower S.

CFD modeling of binary‐fluidized suspensions and investigation of role of particle–particle drag on mixing and segregation

AbstractA model is presented for the prediction of the fluid dynamic behaviour of binary suspensions of solid particles fluidized by Newtonian fluids. The equations of motion for the fluid and solid phases are derived by extending the averaged two‐fluid equations of change for identical spheres in Newtonian fluids developed by Anderson and Jackson and Jackson. A new closure relationship for the fluid–particle interaction force is employed and a new numerical algorithm is developed to control the solid compaction in each particle phase. The article also presents a comparison between three different equations of closure for the particle–particle drag implemented within the model. Predictions of the fluidization behavior obtained by the proposed model are validated against experimental results in terms of solid mixing and segregation, bed expansion and bubble dynamics. Two‐dimensional CFD simulations are performed in a bed of rectangular geometry using ballotini with particle sizes of 200 and 350 μm. © 2007 American Institute of Chemical Engineers AIChE J, 2007

Exact expressions for colloidal plane–particle interaction forces and energies withapplications to atomic force microscopy

We begin by deriving a general useful theoretical relationship between the plane–particleinteraction forces in solution, and the corresponding plane–plane interaction energies. Thisis the main result of the paper. It provides a simple tool to obtain closed-formparticle–plane forces from knowledge of plane–plane interaction energies. To illustrate thesimplicity of use of this general formalism, we apply it to find particle–plane interactionswithin the Derjaguin–Landau–Verwey–Overbeek (DLVO) framework. Specifically,we obtain analytical expressions for forces and interaction energies in the vander Waals and the electrical double layer cases. The van der Waals expression iscalculated here for benchmarking purposes and is compared with well-establishedexpressions from Hamaker theory. The interactions for the electric double layersituation are computed in two cases: the linear superposition approximation andthe constant surface potential. In both cases, our closed-form expressions werecompared with existent numerical results. We also use the main result of thispaper to generate an analytical force-separation expression based on atomic forcemicroscope experiments for a tip and surface immersed in an aqueous solution, andcompare it with the corresponding numerical results. Finally, based on our mainresult, we generalize the Derjaguin approximation by calculating the next order ofapproximation, thus obtaining a formula valuable for colloidal interaction estimations.

Manipulation of particles using dielectrophoresis

A numerical scheme based on the distributed Lagrange multiplier method (DLM) is used to study the motion of particles of electrorheological suspensions subjected to non-uniform electric fields. At small Reynolds number, the time taken by the particles to collect at the minimums or maximums of the electric field is primarily determined by a parameter defined to be the ratio of the dielectrophoretic and viscous forces. Simulations show that in non-uniform electric fields the collection time is also influenced by a parameter defined by the ratio of the electrostatic particle–particle interaction and dielectrophoretic forces. The collection time decreases as this parameter decreases because when this parameter is less than one, particles move to the regions of high or low electric field regions individually. However, when this parameter is greater than one, particles regroup into chains which then move toward the electric field maximums or minimums without breaking. It is also shown that when the real part of the Clausius–Mosotti factor ( β) is negative the positions of the local minimums of the electric field, and thus also the locations where particles collect, can be modified by changing the electric potential boundary conditions.