Influence of interparticle interactions on the kinetics of self-assembly and mechanical strength of nanoparticulate aggregates

Computer simulations based on Discrete Element Method have been performed in order to investigate the influence of interparticle interactions on the kinetics of self-assembly and the mechanical strength of nanoparticle aggregates.Three different systems have been considered.In the first system the interaction between particles has been simulated using the JKR (Johnson,Kendall and Roberts) contact theory,while in the second and third systems the interaction between particles has been simulated using van der Waals and electrostatic forces respectively.In order to compare the mechanical behaviour of the three systems,the magnitude of the maximum attractive force between particles has been kept the same in all cases.However,the relationship between force and separation distance differs from case to case and thus,the range of the interparticle force.The results clearly indicate that as the range of the interparticle force increases,the self-assembly process is faster and the work required to produce the mechanical failure of the assemblies increases by more than one order of magnitude.     

考虑颗粒转矩的接触网络诱发各向异性分析

颗粒材料的宏观力学行为与接触网络的组构各向异性密切相关, 根据接触点的滑动与否、转动与否和强弱力情况, 可以将颗粒间的接触系统分为不同的子接触网络. 一般而言, 不同的子接触网络在颗粒体系中的传力机制不同, 对宏观力学响应的贡献也有不同. 采用离散单元法(discrete element method, DEM)模拟了不同抗转动系数$\mu_r$下颗粒材料三轴剪切试验, 分析了剪切过程中不同子接触网络的组构张量的演变规律, 并探究了颗粒抗转动效应对子接触网络各向异性指标演变规律的影响. 研究发现: 剪切过程中转动、非转动接触的组构张量变化不是独立的, 受到颗粒间滑动与否的影响; 非滑动、强接触网络是颗粒间的主要传力结构, 非滑动接触网络的接触法向和法向接触力各向异性均随$\mu_r$的增大而增大, 其对宏观应力的贡献程度随$\mu_r$的增大而减小;强接触网络的接触法向各向异性随$\mu_r$的增大而增大, 但法向接触力各向异性随$\mu_r$的增大无明显变化, 强接触网络对宏观应力的贡献程度在不同$\mu_r$情况下均相同.      

Simulation and calibration of granules using the discrete element method

The discrete element method (DEM), developed by Cundall and Strack (1979) to solve geomechanical problems, is used to simulate the mechanical behavior of granules. According to the DEM, an individual granule can be modeled as a realistic mechanical system consisting of primary particles bonded by interaction forces.Granulometric properties of the model material, zeolite 4A, have been measured to determine their macro properties. To investigate the compression behavior, a compression test was performed using a strength tester on single granules between two pistons. A modeled granule consisting of more than 22,000 primary particles was generated. The micro properties of the modeled granule have been precisely set to allow its macro properties to be equivalent to the macro properties of zeolite 4A granules. To calibrate the mechanical properties, diametrical compression was simulated using two rigid walls stressed at a constant stressing velocity. The force–displacement curve of the modeled granule at compression has been calibrated by the experimental curve of zeolite 4A.     

Global and local large-deformation response of sub-micron,soft- and hard-particle filled polycarbonate

Since polymers play an increasingly important role in both structural and tribological applications, understanding their intrinsic mechanical response is key. Therefore in the last few decades much effort has been devoted into the development of constitutive models that capture the polymers' intrinsic mechanical response quantitatively. An example is the Eindhoven Glassy Polymer model. In practice most polymers are filled, e.g. with hard particles or fibers, with colorants, or with soft particles that serve as impact modifiers. To characterize the influence of type and amount of filler particles on the intrinsic mechanical response, we designed model systems of polycarbonate with different volume fractions of small, order 100 nm sized, either hard or soft particles, and tested them in lubricated uniaxial compression experiments. To reveal the local effects on interparticle level, three-dimensional representative volume elements (RVEs) were constructed. The matrix material is modeled with the EGP model and the fillers with their individual mechanical properties. It is first shown that (only) 32 particles are sufficient to capture the statistical variations in these systems. Comparing the simulated response of the RVEs with the experiments demonstrates that in the small strain regime the stress is under-predicted since the polymer matrix is modeled by using only one single relaxation time. The yield- and the large strain response is captured well for the soft-particle filled systems while, for the hard-particles at increased filler loadings, the predictions are less accurate. This is likely caused by polymer–filler interactions that result in accelerated physical aging of the polymer matrix close to the surfaces. Modifying the S_a-parameter, that captures the thermodynamic state of the polymer matrix, allows us to correctly predict the macroscopic response after yield. The simulations reveal that all rate-dependencies of the different filled systems originate from that of the polymer matrix. Finally, an onset is presented to predict local and global failure based on critical events on the microlevel, that are likely to cause the over-prediction in the large-strain response of the hard-particle filled systems.     

DRAG FORCE IN DENSE GAS—PARTICLE TWO—PHASE FLOW

Numerical simulations of flow over a stationary particle in a dense gas-particle two-phase flow have been carried out for small Reynolds numbers (less than 100). In order to study the influence of the particles interaction on the drag force, three particle arrangements have been tested: a single particle, two particles placed in the flow direction and many particles located regularly in the flow field. The Navier-Stokes equations are discretized in the three-dimensional space using finite volume method. For the first and second cases, the numerical results agree reasonably well with the data in literature. For the third case, i.e., the multiparticle case, the influence of the particle volume fraction and Reynolds numbers on the drag force has been investigated. The results show that the computational values of the drag ratio agree approximately with the published results at higher Reynolds numbers (from 34.2 to 68.4), but there is a large difference between them at small Reynolds numbers. The project supported by the Special Funds for Major State Basis Research Projects in China (G19990222).     

Using Mechanoluminescent Materials to Visualize Interparticle Contact Intensity in Granular Media

Mechanoluminescent materials have the property of emitting light when they are mechanically deformed. The paper deals with the potential use of these active substances to reveal interparticle contact force networks in granular media under mechanical loading. Preliminary uniaxial tensile tests were first performed on two types of longitudinal specimens for comparison purposes: pure epoxy resin and epoxy resin containing mechanoluminescent powders. Stress-strain curves showed that the powder acted as a reinforcement, but fractographic analysis by SEM revealed that debonding occurred between the epoxy matrix and powder grains during mechanical loading. Various two-dimensional cohesionless granular systems were then studied, using mechanoluminescent cylinders subjected to compression. Whereas uniaxial tensile tests featured homogeneous light emission, localized mechanoluminescence intensities were revealed in the contact zones between cylinders. The study shows that mechanoluminescent materials open perspectives for the identification of interparticle contact intensities in granular media.

     

Hydrodynamic interactions in quasi-two-dimensional colloidal suspensions

Dynamical correlations between colloidal particles, in a quasi-two-dimensional geometry, are measured by optical microscopy. The system consists of charged polystyrene spheres suspended in water and confined between two parallel plates. The long-range electrostatic interaction is screened and the interparticle direct interaction becomes an effective excluded volume interaction. Thus, the observed long-range correlations, between the motion of pairs of particles, are due to the solvent mediated hydrodynamic interactions. Such correlations are observed as a dependence in the interparticle distance of the diffusion coefficients for the normal modes, collective and relative, for which results are presented here for a range of particle concentrations.     

Interparticle force and torque on rigid spheroidal particles in acoustophoresis

The movement of the particles in acoustophoresis is driven by the acoustic radiation force acting on the particles. Particles with positive contrast factor tend to agglomerate once they are pushed by the primary force to the vicinity of the pressure node. The main driving force of this agglomeration is the interparticle force. In this study, the boundary element method is used to calculate the interparticle force and torque acting on a pair of spheroidal particles. The numerical results show that the interparticle force is dominant over the primary force when the spheroids are near the pressure nodal plane, similar to the case of two spheres. On contrary, the interparticle torque is insignificant compared to the primary torque, even when the spheroids are close to each other. The results also provide a preliminary study about how biological cells, which are mostly not spherical in shape, agglomerate and orient themselves in the vicinity of the pressure node.     

Superquadric DEM-SPH coupling method for interaction between non-spherical granular materials and fluids

The research on the coupling method of non-spherical granular materials and fluids aims to predict the particle–fluid interaction in this study. A coupling method based on superquadric elements is developed to describe the interaction between non-spherical solid particles and fluids. The discrete element method (DEM) and the smoothed particle hydrodynamics (SPH) are adopted to simulate granular materials and fluids. The repulsive force model is adopted to calculate the coupling force and then a contact detection method is established for the interaction between the superquadric element and the fluid particle. The contact detection method captures the shape of superquadric element and calculates the distance from the fluid particle to the surface of superquadric element. Simulation cases focusing on the coupling force model, energy transfer, and large-scale calculations have been implemented to verify the validity of the proposed coupling method. The coupling force model accurately represents the water entry process of a spherical solid particle, and reasonably reflects the difference of solid particles with different shapes. In the water entry process of multiple solid particles, the total energy of the water entry process of multiple solid particles tends to be stable. The collapse process of the partially submerged granular column is simulated and analyzed under different parameters. Therefore, this coupling method is suitable to simulate fluid–particle systems containing solid particles with multiple shapes.     

Sedimentation acceleration of remanent iron oxide by magnetic flocculation

Sedimentation based processes are widely used in industry to separate particles from a liquid phase. Since the advent of the ＂Nanoworld＂ the demand for effective separation technologies has rapidly risen, calling for the development of new separation concepts, one of which lies in hybrid separation using the superposition of a magnetic field for magnetic particles. Possible product portfolio of such separation consists of pigment production, nanomagnetics production for electronics and bio separation, A promising step in that direction is magnetic field enhanced cake filtration, which has by now progressed from batch to continuous ooeration. In sedimentation processes in a mass force field the settling behaviour of particles strongly depends on physico-chemical properties, concentration and size distribution of the particles. By adjusting the pH, the interparticle forces, in particular the electrostatic repulsion, can be manipulated. For remanent magnetic particles such as magnetite, pre-treatment in a magnetic field could lead to a change of interparticle interactions. By magnetizing the particles apart from van der Waals attraction and electrostatic repulsion, an additional potential is induced, the magnetic attraction, which could easily dominate the other potentials and result in agglomeration in the primary minimum. By sedimentation analysis, a wide spectrum of parameters like pH, magnetic field strength and concentration have been investigated. The results show a strong increase of sedimentation velocity by magnetic flocculation of the raw suspension. This leads to a rise in throughput due to the acceleration of sedimentation kinetics by imparting a non-chemical interaction to the physico-chemical properties in the feed stream of the separation apparatus.     

Effect of matrix viscoelasticity on the electrorheological properties of particle suspensions

We have investigated the electrorheological properties of dispersions of semi-conducting particles in oils and elastomers. We focused on how the dynamic mechanical properties measured under oscillatory shearing change with the viscosity of the oil or the elasticity of the elastomer. The dependence on electric field and strain amplitude were also investigated. We found that the largest increment of the mechanical properties under electric fields was obtained when using oils of low viscosity and elastomers of low elasticity. The strain amplitude which produced the largest variation with electric field was found to be 0.1% for the elastomer systems, but significantly larger (1%) for the oil systems. These results are interpreted in terms of a model based on the competition between the dipole–dipole electrostatic interaction (which acts to maintain neighbouring particles together) and the shearing force due to the deformation of the matrix (which acts to separate the particles). We find that there are parallels between the electrorheological behaviour of particles dispersed in elastomers and the behaviour of particles dispersed in oils. These results should find application in the selection of suitable matrix materials for electrorheological suspensions.     

Rheological characterization of bimodal colloidal dispersions

In order to investigate the effect of the particle size distribution on the rheological properties of concentrated colloidal dispersions both steady-state shear and oscillatory measurements have been performed on well-characterized bimodal dispersions of sterically stabilized PMMA particles. Replacing a minor amount of large particles by small ones in a concentrated dispersion, keeping the total effective volume fraction constant, decreases the viscosity quite drastically. On the other hand, replacing a small amount of small particles by big ones hardly effects the viscosity at all. This behavior can be attributed to the deformability of the stabilizing polymer layer. A procedure is proposed to calculate the limiting viscosities in a bimodal colloidal dispersion starting from the characteristics of the monodisperse systems. A good agreement has been obtained between the calculated values and the experimental results. The linear viscoelastic properties of the concentrated dispersions have been investigated by means of oscillatory measurements. The plateau values of the storage modulus for the bimodal dispersions decrease with an increasing fraction of the coarse particles. By substituting the bimodal dispersion by an equivalent monodisperse system the storage modulus can be superimposed on the values for the monodisperse suspensions when plotted as a function of the mean interparticle distance.     

Measurements of ultrafine particles from a gas-turbine burning biofuels

Measurements of ultrafine particles have been performed at the exhaust of a low emission microturbine for power generation. This device has been fuelled with liquid fuels, including a commercial diesel oil, a mixture of the diesel oil with a biodiesel and kerosene, and tested under different loads. Primarily attention has been focused on the measurements of the size distribution functions of the particles emitted from the system by using particle differential mobility analysis. A bimodal size distribution function of the particle emitted has been found in all the examined conditions. Burning diesel oil, the first mode of the size distribution function of the combustion-formed particles is centered at around 2–3 nm, whereas the second mode is centered at about 20–30 nm. The increase of the turbine load and the addition of 50% of biodiesel has not caused changes in the shape of size distribution of the particles. A slightly decrease of the amount of particle formed has been found. By using kerosene the amount of emitted particles increases of more than one order of magnitude. Also the shape of the size distribution function changes with the first mode shifted towards larger particles of the order of 8–10 nm but with a lower emission of larger 20–30 nm particles. Overall, in this conditions, the mass concentration of particles is increased respect to the diesel oil operation. Particle sizes measured with the diesel oil have been compared with the results on a diesel engine operated in the same power conditions and with the same fuel. Measurements have showed that the mean sizes of the formed particles do not change in the two combustion systems. However, diesel engine emits a number concentration of particles more than two orders of magnitude higher in the same conditions of power and with the same fuel. By running the engine in more premixed-like conditions, the size distribution function of the particles approaches that measured by burning kerosene in the microturbine indicating that the distribution function of the sizes of the emitted particles can be strongly affected by combustion conditions.     

On flow characteristics of liquid-solid mixed-phase nanofluid inside nanochannels

The atomic behavior of liquid-solid mixed-phase nanofluid flows inside nanochannels is investigated by a molecular dynamics simulation （MDS）. The results of visual observation and statistic analysis show that when the nanoparticles reach near each other, the strong interatomic force will make them attach together. This aggrega- tion continues until all nanoparticles make a continuous cluster. The effect of altering the external force magnitude causes changes in the agglomeration rate and system enthalpy. The density and velocity profiles are shown for two systems, i.e., argon （Ar）-copper （Cu） nanofluid and simple Ar fluid between two Cu walls. The results show that using nanopar- ticles changes the base fluid particles ordering along the nanochannel and increases the velocity. Moreover, using nanoparticles in simple fluids can increase the slip length and push the near-wall fluid particles into the main flow in the middle of the nanochannel.     

Modeling surface tension of a two‐dimensional droplet using smoothed particle hydrodynamics

Surface tension plays a significant role at the dynamic interface of free‐surface flows especially at the microscale in capillary‐dominated flows. A model for accurately predicting the formation of two‐dimensional viscous droplets in vacuum or gas of negligible density and viscosity resulting from axisymmetric oscillation due to surface tension is solved using smoothed particle hydrodynamics composed of the Navier‐Stokes system and appropriate interfacial conditions for the free‐surface boundaries. The evolution of the droplet and its free‐surface interface is tracked over time to investigate the effects of surface tension forces implemented using a modified continuous surface force method and is compared with those performed using interparticle interaction force. The dynamic viscous fluid and surface tension interactions are investigated via a controlled curvature model and test cases of nonsteady oscillating droplets; attention is focused here on droplet oscillation that is released from an initial static deformation. Accuracy of the results is attested by demonstrating that (i) the curvature of the droplet that is controlled; (ii) uniform distribution of fluid particles; (iii) clean asymmetric forces acting on the free surface; and (iv) nonsteady oscillating droplets compare well with analytical and published experiment findings. The advantage of the proposed continuous surface force method only requires the use of physical properties of the fluid, whereas the interparticle interaction force method is restricted by the requirement of tuning parameters.     

Structural stability and jamming of self-organized cluster conformations in dense granular materials

We examine emergent, self-organized particle cluster conformations in quasistatically deforming dense granular materials from the perspective of structural stability. A structural mechanics approach is employed, first, to devise a new stability measure for such conformations in equilibrium and, second, to use this measure to explore the evolving stability of jammed states of specific cluster conformations, i.e. particles forming force chains and minimal contact cycles. Knowledge gained on (a) the spatial and temporal evolution of stability of individual jammed conformations and (b) their relative stability levels, offer valuable clues on the rheology and, in particular, self-assembly of granular materials. This study is undertaken using data from assemblies of nonuniformly sized circular particles undergoing 2D deformation in two biaxial compression tests: a discrete element simulation of monotonic loading under constant confining pressure, and cyclic loading of a photoelastic disk assembly under constant volume. Our results suggest that the process of self-assembly in these systems is realized at multiple length scales, and that jammed force chains and minimal cycles form the basic building blocks of this process. In particular, 3-cycles are stabilizing agents that act as granular trusses to the load-bearing force chain columns. This co-evolutionary synergy between force chains and 3-cycles proved common to the different materials under different loading conditions. Indeed, the remarkable similarities in the evolution of stability, prevalence and persistence of minimal cycles and force chains in these systems suggest that these structures and their co-evolution together form a generic feature of dense granular systems under quasistatic loading.     

颗粒物质中的多尺度问题

颗粒物质是大量离散的固体颗粒相互作用而组成的复杂体系. 依据颗粒排布的稀疏程度, 体系可分为颗粒气体、颗粒流体和颗粒固体,它们有不同本质的动量传递和能量耗散机制. 后两者属于密集颗粒物质体系,内部形成了颗粒$\to $力链$ \to$体系的多尺度结 构,并涉及多个特征时间尺度,是典型的多尺度体系. 合理分割体系结构层 次、正确理解不同层次的物理过程、并确定它们之间的关联是密集颗粒物质研究的核心任务. 本文依次分析了密集颗粒物质的内在物理图像、多尺度结构层次和特征时间等,并介绍了多 尺度研究框架.     

Interaction force and residual stress models for volume-averaged momentum equation for flow laden with particles of comparable diameter to computational grid width

An interaction model considering the local stress on a particle surface is developed based on a volume averaging technique. With a scope to apply to turbulence modulation caused by particles of diameter comparable to the Kolmogorov length scale, grid width for resolving vortical structures outside the boundary layer of the particles is set to be close to the particle diameter. The interaction force in the volume-averaged momentum equation is modelled based on analytical solutions of two fundamental flows. For the uniform flow case, the nonlinear effect of the first-order term in a series expansion with respect to the particle Reynolds number is found to be essential for the anisotropic Eulerian distribution of the interaction force. For the shear flow case, the anisotropic distribution of the interaction force is also essential, and it is modelled based on the Stokes’s solution. Considering that the length scale of the averaging volume is determined to be comparable to the grid width and the particle diameter, the residual stress, which originates from the volume averaging of the nonlinear term in the momentum equation, is also modelled based on an undisturbed linear shear flow. According to the test simulation using the interaction force and residual stress models of the fundamental flows, the anisotropic interaction force model essentially improves the representation of the flow field and the mechanical work, and the effect of the residual stress is found to be reasonably reproduced by the present model.     

Analysis of the movement behaviour of soil between subsoilers based on the discrete element method

The identification of the movement behaviour of soil in the area under the combined effect of two subsoilers (i.e., the area between two subsoilers) is one of the key issues in determining a reasonable inter-subsoiling shovel distance. The present study established a working model of subsoiling using the discrete element method (DEM). Based on this model and an indoor soil-bin experiment, the present study focused on investigating the micro-movement and macro-disturbed behaviour of soil in the area under the combined effect of two subsoilers. The results show the following. (1) The range of transverse and longitudinal disturbance of soil decreased with increasing distance between the soil and subsoiler. The range of disturbance of the soil in the shallow layer was the widest, followed by the range of disturbance of the soil in the middle layer and the range of disturbance of the soil in the deep layer. The simulated and experimental values of the mean displacement of the soil in the shallow layer (tracer blocks with a side length of 10 mm) were 34.81 mm and 34.55 mm, respectively (error: 0.75%). (2) The force on the soil particles in the deep layer was the greatest, followed by the force on the soil particles in the middle layer and the force on the soil particles in the shallow layer. The force on and the velocity of movement of the soil particles at different locations decreased with increasing distance between the soil and subsoiler. (3) The discrete element simulation could accurately simulate the disturbance process of the soil subjected to subsoiling. The sectional profiles of the disturbed soil obtained from the simulation and experiment were consistent with each other. The relative error between the simulated and experimental values of the soil looseness and the soil disturbance coefficient was 14.45% and 12.06%, respectively. Based on the DEM combined with an indoor soil-bin experiment, the present study determined the movement behaviour of the soil in the area under the combined effect of two subsoilers. The results of the present study can facilitate in-depth investigations of the subsoiling shovel–soil interaction and provide a basis for making decisions to optimise subsoiler arrangements.