Stochastic generation of particle structures with controlled degree of heterogeneity

The recently developed void expansion method (VEM) allows for an efficient generation of porous packings of spherical particles over a wide range of volume fractions. The method is based on a random placement of the structural particles under addition of much smaller “void-particles” whose radii are repeatedly increased during the void expansion. Thereby, they rearrange the structural particles until formation of a dense particle packing and introduce local heterogeneities in the structure. In this paper, microstructures with volume fractions between 0.4 and 0.6 produced by VEM are analyzed with respect to their degree of heterogeneity (DOH). In particular, the influence of the void- to structural particle number ratio, which constitutes a principal VEM-parameter, on the DOH is studied. The DOH is quantified using the pore size distribution, the Voronoi volume distribution and the density-fluctuation method in conjunction with fit functions or integral measures. This analysis has revealed that for volume fractions between 0.4 and 0.55 the void-particle number allows for a quasi-continuous adjustment of the DOH. Additionally, the DOH-range of VEM-generated microstructures with a volume fraction of 0.4 is compared to the range covered by microstructures generated using previous Brownian dynamics simulations, which represent the structure of coagulated colloidal suspensions. Both sets of microstructures cover similarly broad and overlapping DOH-ranges, which allows concluding that VEM is an efficient method to stochastically reproduce colloidal microstructures with varying DOH.     

Influence of different sources of microstructural heterogeneity on the degradation of asphalt mixtures

The response and degradation of the hot mix asphalt (HMA) materials used in pavement structures are affected by their inherent heterogeneity. The objective of this work is to study the impact of two different sources of HMA heterogeneity in the uncertainty of the mechanical moisture degradation of HMA. The first source of heterogeneity is the spatial variability of the properties of the bulk fine aggregate matrix (FAM) of the mixture, and the second is the location and shape of the coarse aggregate particles. The heterogeneity of the bulk FAM phase was modelled using a random field technique, while that of the coarse aggregates was accounted for by randomly generating realistic probable sets of aggregate particles. Thus, ‘computational replicates’ of HMA microstructures were generated and subjected to moisture diffusion and mechanical loading using a finite element approach. In the mechanical simulations, a non-linear viscoelastic moisture damage constitutive relationship based on continuum damage mechanics theory was selected to characterise the response of the bulk FAM phase. The results show that conducting computational simulations with realistic HMA microstructures that properly capture the heterogeneity of the material is useful to quantify the mean values and dispersion (i.e. uncertainty) associated with the response and degradation of the mixture. This information, which cannot be easily obtained in the field or in the laboratory due to the difficulty of acquiring a sufficient amount of data, is useful to conduct structural reliability analysis and to predict the life cycle behaviour of the material.     

3D inhomogeneous, misfitting second phase particles-equilibrium shapes and morphological development

A 3D simulation of equilibrium shapes of precipitates forming from diffusive phase transitions is presented. The concept of generalized forces is used to take elastic and interfacial energy into consideration when calculating the equilibrium morphologies. By using shape optimization techniques an efficient iterative scheme for finding equilibrium morphologies is presented. A first step towards simulating the temporal evolution of the microstructure is undertaken, by proposing a simple generalized evolution law. The numerical simulations underline the importance of elastic strain energy in the developing of certain microstructures, such as convex, concave, prolate and oblate cuboids. It is elaborated that particle size together with stiffness ratio between particle and matrix play an significant role.     

Dynamics of rotating paramagnetic particles simulated by lattice Boltzmann and particle dynamics methods

Novel biochemical sensors consisting of rotating chains of microscale paramagnetic particles have been proposed that would enable convenient, sensitive analyte detection. Predicting the dynamics of these particles is required to optimise their design. The results of lattice Boltzmann (LB) and particle dynamics (PD) simulations are reported, where the LB approach provides a verified solution of the complete Navier-Stokes equations, including the hydrodynamic interactions among the particles. On the other hand, the simpler PD approach neglects hydrodynamic interactions, and does not compute the fluid motion. It is shown that macroscopic properties, like the number of aggregated particles, depend only on the drag force and not on the total hydrodynamic force, making PD simulations yield reasonably accurate predictions. Relatively good agreement between the LB and PD simulations, and qualitative agreement with experimental data, are found for the number of aggregated particles as a function of the Mason number. The drag force on a rotating cylinder is significantly different from that on particle chains calculated from both simulations, demonstrating the different dynamics between the two cases. For microscopic quantities like the detailed force distributions on each particle, the complete Navier-Stokes solution, here represented by the LB simulation, is required.     

Heterogeneous and homogenized models for predicting the indentation response of particle reinforced metal matrix composites

In this study, three-dimensional heterogeneous and homogenized finite element models are used to predict the indentation response of particle reinforced metal matrix composites (PRMMCs). The matrix is assumed to have elasto-plastic behavior whereas the particles (uniform in size and spherical in shape) are assumed to be harder than the matrix, and possess linear elastic behavior. The particles (25 % by volume) are randomly distributed in the metal matrix. Two modeling approaches are used. In the first approach, the PRMMC is fully replaced by an equivalent homogenous material, and its material properties are obtained through homogenization using representative volume element approach under periodic boundary conditions. In second approach, a small cubical volume under the indenter is modeled as heterogeneous material with randomly distributed particles, whereas the remaining domain is assigned equivalent material properties obtained through homogenization. The elastic material properties obtained through simulations are found within Hashin–Shtrikman bounds. A suitable size cubical volume consisting of heterogeneities under the indenter is established by considering different cubical volumes so as to capture the actual indentation response. The simulations are also carried out for different particle sizes to establish a suitable particle size. These simulations show that the second modeling approach yields harder indentation response as compared to first modeling approach due to the local particle concentration under the indenter.     

Simulation of a confined polymer in solution using the dissipative particle dynamics method

The dynamics of a bead-and-spring polymer chain suspended in a sea of solvent particles are examined by dissipative particle dynamics (DPD) simulations. The solvent is treated as a structured medium, comprised of particles subject to both solvent-solvent and solvent-polymer interactions and to stochastic Brownian forces. Thus hydrodynamic interactions among the beads of the polymer evolve naturally from the dynamics of the solvent particles. DPD simulations are about two orders of magnitude faster than comparable molecular dynamics simulations. Here we report the results of an investigation into the effects of confining the dissolved polymer chain between two closely spaced parallel walls. Confinement changes the polymer configuration statistics and produces markedly different relaxation times for chain motion parallel and perpendicular to the surface. This effect may be partly responsible for the gap width-dependent theological properties observed in nanoscale rheometry.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

Computer simulations of realistic microstructures of coarse constituent particles in a hot-rolled aluminum alloy

Computer simulations of realistic microstructures of coarse constituent particles in hot-rolled 7075 Al-alloy plate are presented. These simulations incorporate realistic complex morphologies/shapes of the constituent particles as well as their spatially clustered non-uniform arrangements and partially anisotropic morphological orientations. The methodology permits simulations of sufficiently large microstructural windows that incorporate short-range (on the order of particle/feature size) as well as long-range (few hundred times the particle/feature size) microstructural heterogeneities and spatial patterns. Two-point correlation functions are used for microstructure representation. The two-point correlation functions of the simulated microstructures are closely matched with those of the corresponding real microstructures. The simulation parameters enable simulations of virtual microstructures of the alloy that cover a range of different volume fractions and average sizes of the constituent particles.     

Simulation of intense particle beams with regularly distributed Gaussian subbeams

Techniques for the simulation of intense particle beams are investigated with respect to the required number of simulation particles. It is shown that for nonchaotic systems it is advantageous if the particles initially are not distributed in a statistical manner but rather arranged in a regular pattern in phase space. This reduces the number of required simulation particles drastically. In the case of such an initially regular arrangement of particles the algorithm which assigns the charges of the particles to the computation mesh becomes of prime importance. The performances of different commonly used algorithms are investigated. The Gaussian assignment algorithm proved far superior to other more commonly used techniques, allowing simulations even at the theoretical limit of 1 particle per cell. Examples for very accurate simulations of beam dynamics with very few particles using an initially regular mesh of particles and Gaussian assignment are given.     

Particle modeling of dynamic fragmentation—II: Fracture in single- and multi-phase materials

The second paper of this series adopts particle modeling (PM) to simulation of dynamic fracture phenomena in homogeneous and heterogeneous materials, such as encountered in comminution and blasting processes in mining industry. As the basis for such simulations, we first develop a new method to prevent particles from topologically interpenetrating themselves within the material domain, when actual fracture does not actually take place. We then move to a number of application studies: (i) fragmentation of 2-D single- and multi-phase materials—including a simulation of a drop-weight test—and (ii) fragmentation of 3-D single-phase materials under either very rapid extension or compression. These investigations show patterns and trends of fragmentation of materials in function of their constitutive properties, their geometric shapes, and the loading conditions.     

Brownian dynamics study of polymer-stabilized nanoparticles

A Brownian dynamics simulation was carried out for a spherical nanoparticle with polymer chains tethered to its surface. These simulations are relevant to understanding the transport properties of polymer-stabilized nanoparticles in environmental and other applications. Hydrodynamic interactions (HI) were taken into account to properly describe the diffusion properties of a stabilized particle. HI are important in this context because of the close proximity of the surface-tethered polymer chains. HI were implemented using a method introduced by Fixman (1986 Macromolecules 19 1204), which uses a Chebyshev polynomial expansion to calculate the square root of the diffusion tensor. Simulation predictions were compared to published experimental data for the hydrodynamic radius of a silica particle stabilized by polystyrene tethered chains, and good agreement was achieved. A relationship that allows polymer-stabilized particles with arbitrary polymer-chain densities to be modelled is developed.     

Eulerian–Lagrangian method for three-dimensional simulation of fluidized bed coal gasification

A comprehensive three-dimensional numerical model has been developed to simulate the coal gasification in a fluidized bed gasifier. The methodology is based on the multiphase particle-in-cell (MP-PIC) model, which uses an Eulerian method for fluid phase and a discrete particle method for particle phase. Dense particulate flow, mass and heat transfer, homogeneous and heterogeneous chemistry between phases and within the fluid mixture are considered. The dynamics of the particle phase is calculated by solving a transport equation for the particle distribution function (PDF) f. Particle collisions and chemical reactions are solved on a grid cell with particle properties mapped from discrete particles to the grid. Solid mass consumed or produced in reactions changes the size of particles. Simulations were carried out in a coal gasifier with a height of 2.0 m and a diameter of 0.22 m at atmosphere. The calculated product gas compositions compare well with the experimental data. The formation of flow patterns, profiles of particle species and gas compositions, distributions of reaction rates and consumption of carbon mass were investigated under different operating conditions.     

Influence of particle elasticity in shear testers

Two dimensional simulations of non-cohesive granular matter in a biaxial shear tester are discussed. The effect of particle elasticity on the mechanical behavior is investigated using two complementary distinct element methods (DEM): Soft particle molecular dynamics simulations (Particle Flow Code, PFC) for elastic particles and contact dynamics simulations (CD) for the limit of perfectly rigid particles. As soon as the system dilates to form shear bands, it relaxes the elastic strains so that one finds the same stresses for rigid respectively elastic particles in steady state flow. The principal stresses in steady state flow are determined. They are proportional to each other, giving rise to an effective macroscopic friction coefficient which is about 10% smaller than the microscopic friction coefficient between the grains.     

Brownian dynamics simulations of rigid rod-like macromolecular particles flowing in bounded channels

Brownian dynamics simulations have been carried out of the joint probability distribution functions (PDF), P(ξ,θ), for macromolecular rod-like particles in the limit of infinite dilution in a solution under hydrodynamic linear flow. These PDF are calculated as a function of the orientations of the rod-like particles, θ and of the positions, ξ, of their centres of mass measured from a solid surface boundary. These simulations are developed in the neighbourhood of a solid surface boundary and in a confined space bounded by two such boundaries. They are constructed for a wide range of key quantities depicting the ratio of the hydrodynamic shear rate to the rotational Brownian diffusion coefficient. The notion of restitution is introduced to develop an algorithm for the consequences of the Brownian and hydrodynamic collisions of these macromolecules with impenetrable solid surface boundaries, which approach applies to a wide range of surfaces and macromolecules. The simulation results for the PDF distributions are given for typically low and high hydrodynamic flow conditions, and their properties are discussed. We show, for example, for low shear rates that a phenomenon which we call Brownian restitution enables the macromolecular rods to pass through a channel that is narrower than the rod length.     

A study on the prediction of the mechanical properties of nanoparticulate composites using the homogenization method with the effective interface concept

A sequential multi‐scale homogenization method combined with molecular dynamics (MD) simulation is developed for the mechanical characterization of nanoparticulate composites. In order to characterize the particle‐size effect of nanocomposites, the effective interface, which has been adopted in continuum micromechanics approaches, is considered as the characteristic phase. Owing to the existence of the interface and the size‐dependent elastic modulus that is observed from MD simulations, an analysis of the mechanical properties of nanocomposites with continuum micromechanics requires careful consideration of the particle‐concentration effect. Therefore, this study focuses on hierarchical information transfer from the molecular model to the continuum model through the homogenization method in lieu of an analytical micromechanics bridging method. Using the present multi‐scale homogenization method, the elastic properties of the effective interface are numerically evaluated and compared with the analytically obtained micromechanics solutions. In addition, the overall elastic modulus of nanocomposites is obtained from the present model and compared with the results of MD simulation, the micromechanics bridging model, and finite‐element analysis (FEA). Copyright © 2010 John Wiley & Sons, Ltd.     

Direct numerical simulation of particulate flows with heat transfer in a rotating cylindrical cavity

The purpose of this work was the direct numerical simulation of heat and fluid flow by granular mixing in a horizontal rotating kiln. To model particle behaviour and the heat and fluid flow in the drum, we solve the mass conservation, momentum and energy conservation equations directly on a fixed Eulerian grid for the whole domain including particles. At the same time the particle dynamics and their collisions are solved on a Lagrangian grid for each particle. To calculate the heat transfer inside the particles we use two models: the first is the direct solution of the energy conservation equation in the Lagrangian and Eulerian space, and the second is our so-called linear model that assumes homogeneous distribution of the temperature inside each particle. Numerical simulations showed that, if the thermal diffusivity of the gas phase significantly exceeds the same parameter of the particles, the linear model overpredicts the heating rate of the particles. The influence of the particle size and the angular velocity of the drum on the heating rates of particles is studied and discussed.     

Order formation of colloidal nanoparticles adsorbed on a substrate with friction

We examine the adsorption process and order formation of colloidal nanoparticles on a planar surface with friction. We perform Brownian dynamics simulations with a three-dimensional cell model in which the particle–particle and particle–substrate interactions are modeled on the DLVO theory, and examine the effects of the friction acting between the adsorbed particles and the substrate on the adsorbed structure formed on the substrate. The results obtained are as follows: when the friction is so strong that the adsorbed particles are stuck to the substrate, ordered structures never form, which seems to be quite natural. However, when the magnitude of the frictional force is moderate, an ordered structure can form even with low coverage because the frictional force aids order formation. This is because the friction counterbalances the particles’ Brownian motion, which would otherwise disturb the ordered structure. Furthermore, through a detailed examination of the distribution of the Brownian motion, it is demonstrated that an increase in the friction has a similar effect as a decrease in temperature.     

Rheological properties and structural correlations in particle-in-oil gels

Solid, hydrophobic matrices are used to increase the viscoelasticity of pharmaceutical products, cosmetics and foods. We have developed a method for transforming low viscosity oils into highly elastic solids. The solid is derived from an oil-in-water emulsion template where silanised fumed silica nanoparticles are attached to the droplet surfaces. Removing the water by freeze drying drives the template into a three dimensional network of particles in oil. The gels have oil contents as high as 98% due to the low concentration of particles required. We show that the gel elasticity is a power law function of the particle concentration, consistent with theoretical predictions. A key finding is that the gels can show strain thickening, an increase in elasticity under large applied strains. This is due to a sharp increase in the characteristic size of the gel microstructure above a critical particle concentration.     

Modeling transient absorption and thermal conductivity in a simple nanofluid

Molecular dynamics simulations are used to simulate the thermal properties of a model fluid containing nanoparticles (nanofluid). By modeling transient absorption experiments, we show that they provide a reliable determination of interfacial resistance between the particle and the fluid. The flexibility of molecular simulation allows us to consider separately the effect of confinement, particle mass, and Brownian motion on the thermal transfer between fluid and particle. Finally, we show that in the absence of collective effects, the heat conductivity of the nanofluid is well described by the classical Maxwell Garnet equation model.     

Behavior of a system of uniaxial ferroparticles in a rotating liquid matrix

Behavior of a system of single-domain ferromagnetic particles with easy-magnetization-axis-type magnetic anisotropy in a rotating fluid matrix is considered in a transverse magnetic field that is weak compared to the effective magnetic anisotropy field of a particle. The dynamics of a separate particle and orientational state of the system are considered with regard for Brownian rotational diffusion. It is found that a small deviation from the conventional rigid dipole model leads, at frequencies exceeding a certain critical value, to appearance of two attracting stationary states of the easiest magnetization axis that are situated in the plane perpendicular to the field and approach, with the growth of a particle, one or another direction of the matrix rotation axis. It is shown that this circumstance can radically change the behavior of a system of Brownian particles and, thus, magnetic and hydrodynamic properties of the ferrosuspension.