Grain boundary curvature and grain growth kinetics with particle pinning

Second-phase particles are used extensively in design of polycrystalline materials to control the grain size. According to Zener’s theory, a distribution of particles creates a pinning pressure on a moving grain boundary. As a result, a limiting grain size is observed, but the effect of pinning on the detail of grain growth kinetics is less known. The influence of the particles on the microstructure occurs in multiple length scales, established by particle radius and the grain size. In this article, we use a meso-scale phase-field model that simulates grain growth in the presence of a uniform pinning pressure. The curvature of the grain boundary network is measured to determine the driving pressure of grain growth in 2D and 3D systems. It was observed that the grain growth continues, even under conditions where the average driving pressure is smaller than the pinning pressure. The limiting grain size is reached when the maximum of driving pressure distribution in the structure is equal to the pinning pressure. This results in a limiting grain size, larger than the one predicted by conventional models, and further analysis shows consistency with experimental observations. A physical model is proposed for the kinetics of grain growth using parameters based on the curvature analysis of the grain boundaries. This model can describe the simulated grain growth kinetics.     

Grain boundary pinning in two-phase materials

The calculation of the Zener stress involves two parts (1) the determination of the force between a particle and a grain boundary, and the shape of the resulting dimple on the grain boundary and (2) the statistical problem of summing the forces over the boundary. Calculations of the forces from spherical, needle-shaped and plate shaped particles are used to estimate the Zener stress by means of a point obstacle model and statistical dimple model. The results are compared with experimental determinations of stable grain sizes, with a computer simulation growth and with experimental measurements of retarded primary recrystallisation. When the particles are non-spherical or inhomogeneously distributed the Zener stress is anisotropic; this effect has been observed experimentally.     

Pinning effect of different shape second-phase particles on grain growth in polycrystalline: numerical and analytical investigations

The pinning effect of different shape second-phase particles on the grain growth in polycrystalline structures is numerical simulated by the phase-field method. Simulation results indicate that the average grain size is highly dependent on the shape and distribution of the second-phase particles, and the shape effect of particles on grain growth restraining is enhanced with increasing numbers of particles. In order to discuss the relation between the constraint grain growth and the second-phase particles, pinning forces induced by different shape particles are theoretically calculated via the Zener pinning theory. The calculated pining forces indicate that the maximum pinning force is highly dependent on the contact mode between grains and particles, and the distance between particles has a significantly influence on the pinning forces. Therefore, controlling the shape and distributions of second-phase particles in polycrystalline metals or ceramics might be an efficient way to achieve materials with specified microstructures.     

Rigid and differential plasma crystal rotation induced by magnetic fields

Observations show that plasma crystals, suspended in the sheath of a radio-frequency discharge, rotate under the influence of a vertical magnetic field. Depending on the discharge conditions, two different cases are observed: a rigid-body rotation (all the particles move with a constant angular velocity) and sheared rotation (the angular velocity of particles has a radial distribution). When the discharge voltage is increased sufficiently, the particles may even reverse their direction of motion. A simple analytical model is used to explain qualitatively the mechanism of the observed particle motion and its dependence on the confining potential and discharge conditions. The model takes into account electrostatic, ion drag, neutral drag, and effective interparticle interaction forces. For the special case of rigid-body rotation, the confining potential is reconstructed. Using data for the radial dependence of particle rotation velocity, the shear stresses are estimated. The critical shear stress at which shear-induced melting occurs is used to roughly estimate the shear elastic modulus of the plasma crystal. The latter is also used to estimate the viscosity contribution due to elasticity in the plasma liquid. Further development is suggested in order to quantitatively implement these ideas.     

Grain Boundary Kinetics in Oxide Ceramics with the Cubic Fluorite Crystal Structure and its Derivatives

Kinetics of grain boundaries in oxides with the cubic fluorite structure and its derivatives has been investigated using fine grain ceramics that are fully dense. Grain growth measurements in these materials have provided information on grain boundary diffusivity over a diffusion distance of the order of the initial grain size. With the addition of solute cations, grain boundary mobility can be varied over many orders of magnitude, often with very different activation energies. This is caused by the variation of defect population and the defect-solute association. Definitive evidence for solute drag has also been observed in some cases, but solute drag can not be confirmed as a general mechanism in solid solutions. Lastly, while grain boundary at low temperature may continue to serve as a fast diffusion path, it may not be able to migrate because of additional pinning mechanisms such as those exerted by grain boundary nodal points or lines. This means that sintering without grain growth is possible, opening up an avenue for obtaining ultrafine ceramics by pressureless sintering.     

Impact of trailing wake drag on the statistical properties and dynamics of finite-sized particle in turbulence

We study by means of an Eulerian-Lagrangian model the statistical properties of velocity and acceleration of a neutrally-buoyant finite-sized particle in a turbulent flow statistically homogeneous and isotropic. The particle equation of motion, besides added mass and steady Stokes drag, keeps into account the unsteady Stokes drag force-known as Basset-Boussinesq history force-and the non-Stokesian drag based on Schiller-Naumann parametrization, together with the finite-size Faxén corrections. We focus on the case of flow at low Taylor-Reynolds number, Re_λ?31, for which fully resolved numerical data which can be taken as a reference are available [Homann H., Bec J. Finite-size effects in the dynamics of neutrally buoyant particles in turbulent flow. J Fluid Mech 651 (2010) 81-91]. Remarkably, we show that while drag forces have always minor effects on the acceleration statistics, their role is important on the velocity behavior. We propose also that the scaling relations for the particle velocity variance as a function of its size, which have been first detected in fully resolved simulations, does not originate from inertial-scale properties of the background turbulent flow but it is likely to arise from the non-Stokesian component of the drag produced by the wake behind the particle. Furthermore, by means of comparison with fully resolved simulations, we show that the Faxén correction to the added mass has a dominant role in the particle acceleration statistics even for particles whose size attains the integral scale.     

Poroelastic modeling of seismic boundary conditions across a fracture

Permeability of a fracture can affect how the fracture interacts with seismic waves. To examine this effect, a simple mathematical model that describes the poroelastic nature of wave-fracture interaction is useful. In this paper, a set of boundary conditions is presented which relate wave-induced particle velocity (or displacement) and stress including fluid pressure across a compliant, fluid-bearing fracture. These conditions are derived by modeling a fracture as a thin porous layer with increased compliance and finite permeability. Assuming a small layer thickness, the boundary conditions can be derived by integrating the governing equations of poroelastic wave propagation. A finite jump in the stress and velocity across a fracture is expressed as a function of the stress and velocity at the boundaries. Further simplification for a thin fracture yields a set of characteristic parameters that control the seismic response of single fractures with a wide range of mechanical and hydraulic properties. These boundary conditions have potential applications in simplifying numerical models such as finite-difference and finite-element methods to compute seismic wave scattering off nonplanar (e.g., curved and intersecting) fractures.     

Effect of thermal fluctuations on the coarsening dynamics of 2D hexagonal system

The dynamics of ordering in a 2D hexagonal system was investigated through the Cahn-Hilliard-Cook model. At low thermal noise amplitudes, pinning forces acting on grain boundaries dominate the dynamics and the coarsening evolves logarithmically in time. As noise amplitude increases, fluctuations becomes large enough to unlock dislocations located along grain boundaries and the grain boundary motion is driven by curvature. The grain boundary relaxation leads to a grain structure with Lifshitz's configurations. In this case the dynamic is also logarithmic as a consequence of the pinning of triple points.     

Deformation-induced changes in single-phase Al-0.1Mg alloy

Al-0.1wt.%Mg has been chosen to explore the effects of deformation on the microstructure of nominally single-phase materials. For these materials, the rate of static grain growth is much higher compared to that of Zener pinned systems and dual-phase alloys, where growth is hindered due to the pinning force exerted by second-phase particles on grain boundaries. Therefore, deformation-induced microstructural changes in single-phase alloys occur without any restricting pinning pressure. This paper illustrates the complex effect of deformation on the microstructural changes mainly associated with dynamic recovery. The process affects the initial microstructure due to an intensive substructure development. Dynamic recrystallisation, associated with the formation of new grains, is considered to be a transient phenomenon that quantitatively influences the mean grain size formed during straining. This work also aims to estimate the stored energy of the deformed regions and texture components to explore their contribution to the migration of high-angle grain boundaries.     

On the vortex formation at the moving front of lightweight granular particles

The formation of vortices at a moving front of lightweight granular particles is investigated experimentally. The particles used in this study are made of polystyrene foam with three different diameters of nearly uniform size. Pairs of vortices are found to emerge at the moving front at regular intervals, thereby forming a wavy pattern. Once the vortices are produced, the flow velocity tends to increase. A simple analysis suggests the existence of a velocity boundary layer at the moving front, whose thickness increases with increasing particle diameter. The frontal radius of each vortex pair is about the size of this boundary layer; when the radius exceeds this size, the front tends to bifurcate into a train of vortices with the size of the boundary layer. The formation of twin vortices leads to a reduction in the air drag force exerted on the system, and thereby the system attains a higher flow velocity, i.e., a higher conversion rate of gravitational potential energy to the kinetic energy of the particle motion. The higher conversion rate of potential energy thus feeds back to the development of the vortex motion, resulting in the twin vortex formation.     

基于拟颗粒的气固两相曳力模型研究

为了研究气固两相流动大涡模拟中合适的曳力计算模型,本文引入拟颗粒和拟颗粒表面能的概念,通过拟颗粒表面能与外界输入能量之间的平衡关系来确定拟颗粒的粒径。根据拟颗粒粒径,得到运算量较小且考虑颗粒团聚效应的曳力计算模型。应用本文的曳力计算模型对二维竖直槽道内稠密气固两相流动进行了大涡模拟,结果表明颗粒的浓度分布具有上稀下浓,壁面附近浓中心稀及颗粒聚集等特点。这与实验结果在定性上是一致的。对气相和颗粒相的瞬时速度场进行了分析,发现气相和颗粒相速度场分布的非对称性是形成颗粒浓度分布壁面附近浓中心稀的重要原因之一。     

Simulations of Bingham plastic flows with the multiple-relaxation-time lattice Boltzmann model

Fresh cement mortar is a type of workable paste,which can be well approximated as a Bingham plastic and whose flow behavior is of major concern in engineering.In this paper,Papanastasiou’s model for Bingham fluids is solved by using the multiplerelaxation-time lattice Boltzmann model(MRT-LB).Analysis of the stress growth exponent m in Bingham fluid flow simulations shows that Papanastasiou’s model provides a good approximation of realistic Bingham plastics for values of m108.For lower values of m,Papanastasiou’s model is valid for fluids between Bingham and Newtonian fluids.The MRT-LB model is validated by two benchmark problems:2D steady Poiseuille flows and lid-driven cavity flows.Comparing the numerical results of the velocity distributions with corresponding analytical solutions shows that the MRT-LB model is appropriate for studying Bingham fluids while also providing better numerical stability.We further apply the MRT-LB model to simulate flow through a sudden expansion channel and the flow surrounding a round particle.Besides the rich flow structures obtained in this work,the dynamics fluid force on the round particle is calculated.Results show that both the Reynolds number Re and the Bingham number Bn afect the drag coefcients CD,and a drag coefcient with Re and Bn being taken into account is proposed.The relationship of Bn and the ratio of unyielded zone thickness to particle diameter is also analyzed.Finally,the Bingham fluid flowing around a set of randomly dispersed particles is simulated to obtain the apparent viscosity and velocity fields.These results help simulation of fresh concrete flowing in porous media.     

Triple Junction Mobility: A Molecular Dynamics Study

We present a molecular dynamics simulation study of the migration of individual grain boundary triple junctions. The simulation cell was designed to achieve steady state migration. Observations of the triple junction angle and grain boundary profiles confirm that steady state was achieved. The static, equilibrium grain boundary triple junction angles and the dynamic triple junction angles were measured as a function of grain size and grain boundary misorientation. In most cases, the static and dynamic triple junction angles are nearly identical, while substantial deviations were observed for low boundary misorientations. The intrinsic, steady-state triple junction mobilities were extracted from measurements of the rate of change of grain boundary area in simulations with and without triple junctions. The triple junction velocity is found to be inversely proportional to the grain size width. The normalized triple junction mobility exhibits strong variations with boundary misorientation, with strong minima at misorientations corresponding to orientations corresponding to low values of . The triple junctions create substantial drag on grain boundary migration at these low mobility misorientations.     

Directional Mode-Locking of Dynamics of Two-Dimensional Superparamagnetic Colloidal System in a Periodic Pinning Array

Using Langevin simulations,we study numerically the directional mode-locking of the dynamics of twodimensional superparamagnetic colloidal system in a periodic pinning array.When the colloidal particles are initially commensurate with the pinning sites,there appear mode-locking steps in the average velocity of colloidal particles along certain directions of the external driving force.With an increase in the pinning strength,the width of the step increases linearly but the velocity at the step decreases parabolically.     

A conservative scheme for the relativistic Vlasov–Maxwell system

A new scheme for numerical integration of the 1D2V relativistic Vlasov–Maxwell system is proposed. Assuming that all particles in a cell of the phase space move with the same velocity as that of the particle located at the center of the cell at the beginning of each time step, we successfully integrate the system with no artificial loss of particles. Furthermore, splitting the equations into advection and interaction parts, the method conserves the sum of the kinetic energy of particles and the electromagnetic energy. Three test problems, the gyration of particles, the Weibel instability, and the wakefield acceleration, are solved by using our scheme. We confirm that our scheme can reproduce analytical results of the problems. Though we deal with the 1D2V relativistic Vlasov–Maxwell system, our method can be applied to the 2D3V and 3D3V cases.     

Two-dimensional lattice-Boltzmann simulations of single phase flow in a pseudo two-dimensional micromodel

We compare two-dimensional and three dimensional lattice-Boltzmann (LB) simulations of fluid flow in a pseudo-2D micromodel used in experimental work. We show that 2D LB simulations can be used to compute the average velocity field in 3D systems in which the third dimension is small compared with the other two dimensions, and where the velocity component along the third dimension is zero. Correct results are obtained provided a viscous drag force, representing the effect of the third dimension, is used in the 2D model. The use of 2D simulations allows to significantly reduce the computational cost of the calculations, and hence to increase the size and resolution of the systems that can be studied using the LB method.     

Analysis of the forces acting on the saltating particles in the coupled wind-sand-electricity fields

Based on the theoretical model describing the saltation of sand particles in the coupled wind-sand-electricity fields, the numerical simulations of the forces acting on saltating particles, such as the aerodynamic drag force, Magnus effect, Saffman force and electrostatic force, are analyzed in comparison to the gravity force of the particles in the steady windblown sand movement. Furthermore, the laws of the above forces vary with the friction velocity, the diameter of the sand particle, the initial angular velocity and the lift-off velocity are discussed. Supported by the National Natural Science Foundation of China (Grant Nos. 10772075 and 10772074), the Key Project of the National Natural Science Foundation of China (Grant No.10532040), and the Program for New Century Excellent Talents in University (Grant No. NCET-04-0979)     

Binding of Resonant Dielectric Particles to Metal Surfaces Using Plasmons

Forces between dielectric particles induced by optical fields can bind them into new systems, varying from optical molecules to large aggregates. Here it is shown that surface plasmons can bind resonant dielectric particles to the waveguiding surfaces resulting in stable levitation of the particles by the optical forces alone. At the same time, the particles can be propelled efficiently along the surface. The predictions follow from solving the 3D electromagnetic problem of plasmon scattering on a dielectric microsphere near the metal surface. To tackle the problem, an accurate and fast hybrid approach is developed: the fields are expanded into 2D angular components which are calculated using finite-difference time-domain simulations. The rigorous numerical results are also explained qualitatively using an analytically solvable model in which a resonant magnetic dipole illuminated by a plasmon interacts with the surface. The particle binding to surfaces is a remarkable outcome of the strong optical interaction at nanoscale and it may offer new configurations for particle manipulations by guided waves, especially in chip-scale structures.