Initial Particle Distribution Research Articles

Diffusion-controlled formation and collapse of a d-dimensional A-particle island in the B-particle sea.

We consider diffusion-controlled evolution of a d-dimensional A-particle island in the B-particle sea at propagation of the sharp reaction front A+B→0 at equal species diffusivities. The A-particle island is formed by a localized (point) A-source with a strength λ that acts for a finite time T. We reveal the conditions under which the island collapse time t_{c} becomes much longer than the injection period T (long-living island) and demonstrate that regardless of d the evolution of the long-living island radius r_{f}(t) is described by the universal law ζ_{f}=r_{f}/r_{f}^{M}=sqrt[eτ|lnτ|], where τ=t/t_{c} and r_{f}^{M} is the maximal island expansion radius at the front turning point t_{M}=t_{c}/e. We find that in the long-living island regime the ratio t_{c}/T changes with the increase of the injection period T by the law ∝(λ^{2}T^{2-d})^{1/d}, i.e., increases with the increase of T in the one-dimensional (1D) case, does not change with the increase of T in the 2D case and decreases with the increase of T in the 3D case. We derive the scaling laws for particles death in the long-living island and determine the limits of their applicability. We demonstrate also that these laws describe asymptotically the evolution of the d-dimensional spherical island with a uniform initial particle distribution generalizing the results obtained earlier for the quasi-one-dimensional geometry. As striking results, we present a systematic analysis of the front relative width evolution for fluctuation, logarithmically modified, and mean-field regimes, and we demonstrate that in a wide range of parameters the front remains sharp up to a narrow vicinity of the collapse point.

A New Particle Generation Method for Arbitrary 2D Geometries in SPH Modeling

For smoothed particle hydrodynamics (SPH), homogeneous particle distribution is important to ensure the computational accuracy and stability, but it is hard to achieve this for complex geometries. In this paper, a new particle generation method is developed to generate particles for arbitrary 2D geometries. In the method, the geometry required for generating particles is orthogonally partitioned into a series of sub-domains. Among the resultant sub-domains, the most ones having standard area are directly converted into particles. The others are iteratively meshed into elements with nearly standard area and particles are placed according to these elements. The present method is implemented based on Abaqus. Examples of particle generation are given to compare various particle generation methods. It is found that the present method shows advantages over some existing methods in the approximation of geometric boundary as well as the regularity and homogeneity of particle distribution. Several physical problems are adopted to examine the influence of initial particle distribution on SPH solution. The calculated results show that particle distributions generated by the present method can lead to better accuracy and stability than those created by some existing methods.

Finite slice analysis (FINA)-A general reconstruction method for velocity mapped and time-sliced ion imaging.

Since the advent of ion imaging, one of the key issues in the field has been creating methods to reconstruct the initial 3D distribution of particles from its 2D projection. This has led to the development of a number of different numerical methods and fitting techniques to solve this fundamental issue in imaging. In recent years, slice-imaging methods have been developed that permit direct recording of the 3D distribution, i.e., a thin slice of the recoiling fragment distribution. However, in practice, most slice imaging experiments achieve a velocity slice width of around 10%-25% around the center of the distribution. This still carries significant out-of-plane elements that can blur the spectrum, lose fine resolution, and underestimate the contribution from slow recoiling products. To overcome these limitations, we developed a new numerical method to remove these out-of-plane elements from a sliced image. The finite sliced analysis method models the off-axis elements of the 3D particle distribution through the use of radial basis functions. Once applied, the method reconstructs the underlying central slice of the 3D particle distribution. The approach may be applied to arbitrarily sliced or unsliced data and has the further advantage that it neither requires nor enforces full cylindrical symmetry of the data. We demonstrate this reconstruction approach with a broad range of synthetic and experimental data that, at the same time, allows us to examine the impact of finite slicing on the recovered distributions in detail.

Tribological Properties and Microstructure of the Metal-Polymer Composite thin Layer Deposited on a Copper Plate by Electrocontact Sintering

Abstract The properties of the electrocontact sintered metal-polymer composite materials are strongly determined by the heat flow taking place during sintering, which, in turn, is influenced by the amount and initial distribution of the polymer particles in the metal matrix. In case of the metal-polymer powder mixture in the form of a thin layer deposited on the bulk metal substrate, the influence of the latter is also taken into consideration. Thus, the model simulating the heating and sintering of the thin layer made of metal-polymer powder mixture on a metal plate is proposed. Based on mathematical calculations relating to the model describing the thermal state of the system, it is shown how heat flow fields are formed within the layer, depending on the polymer content and its distribution. These theoretical simulations seem to be useful in optimising the production of the antifriction metal-polymer layer on a bulk copper substrate by electrocontact sintering. The results of the tribological experiments and microstructural observations are in a good agreement with the theoretical model.

Three-Dimensional Interaction of a Large Number of Dense DEP Particles on a Plane Perpendicular to an AC Electrical Field

The interaction of dielectrophoresis (DEP) particles in an electric field has been observed in many experiments, known as the “particle chains phenomenon”. However, the study in 3D models (spherical particles) is rarely reported due to its complexity and significant computational cost. In this paper, we employed the iterative dipole moment (IDM) method to study the 3D interaction of a large number of dense DEP particles randomly distributed on a plane perpendicular to a uniform alternating current (AC) electric field in a bounded or unbounded space. The numerical results indicated that the particles cannot move out of the initial plane. The similar particles (either all positive or all negative DEP particles) always repelled each other, and did not form a chain. The dissimilar particles (a mixture of positive and negative DEP particles) always attracted each other, and formed particle chains consisting of alternately arranged positive and negative DEP particles. The particle chain patterns can be randomly multitudinous depending on the initial particle distribution, the electric properties of particles/fluid, the particle sizes and the number of particles. It is also found that the particle chain patterns can be effectively manipulated via tuning the frequency of the AC field and an almost uniform distribution of particles in a bounded plane chip can be achieved when all of the particles are similar, which may have potential applications in the particle manipulation of microfluidics.

Interaction of atomized colloid with an ac electric field in a dielectric barrier discharge reactor used for deposition of nanocomposite coatings

Nanocomposite thin films can be obtained by polymerization of a colloidal solution in a dielectric barrier discharge (DBD) at atmospheric pressure. In such a process, the dispersion of nanoparticles into the matrix is driven by the charging, transport, and deposition dynamics of the atomized colloid. This work examines the interaction of atomized TiO2 nanoparticles with ac electric fields in a plane-to-plane dielectric barrier discharge reactor. Experiments are performed with the discharge off to examine transport and deposition phenomena over a wide range of experimental conditions with a fixed particle charge distribution. Scanning electron microscopy reveals that the size distribution of TiO2 nanoparticles collected at different locations along the substrate surface placed on the bottom electrode of the DBD reactor can judiciously be controlled by varying the amplitude and frequency of the ac electric field. These results are also compared to the predictions of a simple particle motion model accounting for the electrostatic force, the gravitational force, and the neutral drag force in the laminar flow. It is found that while the initial charge distribution of atomized particles strongly influences the total deposition yield, its maximal position on the substrate, and the width of the deposited area, the initial size distribution of the particles at the entrance of the reactor mostly changes the size distribution at each position along the substrate surface.

Pathogenesis of developmental anomalies of the central nervous system induced by congenital cytomegalovirus infection.

In humans, the herpes virus family member cytomegalovirus (CMV) is the most prevalent mediator of intrauterine infection-induced congenital defect. Central nervous system (CNS) dysfunction is a distinguishing symptom of CMV infection, and characterized by ventriculoencephalitis and microglial nodular encephalitis. Reports on the initial distribution of CMV particles and its receptors on the blood brain barrier (BBB) are rare. Nevertheless, several factors are suggested to affect CMV etiology. Viral particle size is the primary factor in determining the pattern of CNS infections, followed by the expression of integrin β1 in endothelial cells, pericytes, meninges, choroid plexus, and neural stem progenitor cells (NSPCs), which are the primary targets of CMV infection. After initial infection, CMV disrupts BBB structural integrity to facilitate the spread of viral particles into parenchyma. Then, the initial meningitis and vasculitis eventually reaches NSPC-dense areas such as ventricular zone and subventricular zone, where viral infection inhibits NSPC proliferation and differentiation and results in neuronal cell loss. These cellular events clinically manifest as brain malformations such as a microcephaly. The purpose of this review is to clearly delineate the pathophysiological basis of congenital CNS anomalies caused by CMV.

Patterns of granular convection and separation in narrow vibration bed

Granular convection/separation of single and binary component particles are studied in a narrow vibration bed, respectively. With filling the single light particles (molecular sieve beads), the bed exhibits five different states successively by increasing the vibration frequency f from 15Hz to 70 Hz (vibration strength Γ>3), as the global convection, symmetrical heap, unsymmetrical heap, local convection and pseudo solid. Comparatively, the granular bed of the single heavy particles (steel beads) is only in pseudo solid state at the above vibration condition. By filling binary component particles (molecular sieve and same size steel beads) instead of the single component, the bed shows similar convection state with that of the single molecular sieve beads, and the heavy steel beads are aggregated in the centre of convention roll as a core. Varying the initial distribution of binary component particles, the final convection and separation are not influenced, although the aggregation process of steel beads changes.

A new class of exact solutions for Vlasov–Poisson plasmas

A new class of exact solutions of the Vlasov–Poisson equations based on the Jeans’ theorem is considered. The self-consistent solutions for the evolution of the system from given initial particle distributions make use of particular invariants of particle motion with predetermined spatial structure. The relation between the time-dependent coefficients of the latter and the macroscopic plasma quantities, or moments of the distribution function, are obtained. As an illustration, the evolution of an expanding plasma with oscillations of the electron and ion expansion fronts is presented.

Early decay of Peccei–Quinn fermion and the IceCube neutrino events

IceCube observed high-energy neutrino flux in the energy region from TeV to PeV. The decay of a massive long-lived particle in the early universe can be the origin of the IceCube neutrino events, which we call an "early decay scenario." In this paper, we construct a particle physics model that contains such a massive long-lived particle based on the Peccei-Quinn model. We calculate the present neutrino flux, taking account of realistic initial energy distributions of particles produced by the decay of the massive long-lived particle. We show that the early decay scenario naturally fits into the Peccei-Quinn model, and that the neutrino flux observed by IceCube can be explained in such a framework. We also see that, based on that model, a consistent cosmological history that explains the abundance of the massive long-lived particle is realized.

Impact of vertical and horizontal advection on nutrient distribution in the southeast Pacific

Abstract. An innovative approach is used to analyze the impact of vertical velocities associated with quasi-geostrophic (QG) dynamics on the redistribution and uptake of nitrate in the southeast Pacific (SEP). A total of 12 years of vertical and horizontal currents are derived from an observation-based estimate of the ocean state. Horizontal velocities are obtained through the application of thermal wind balance to weekly temperature and salinity fields. Vertical velocities are estimated by integration of the QG omega equation. Seasonal variability of the synthetic vertical velocity and kinetic energy associated with the horizontal currents is coincident, with peaks in austral summer (November–December) in accord with published observations. The impact of vertical velocity on SEP nitrate uptake rates is assessed by using two Lagrangian particle tracking experiments that differ according to vertical forcing (ω = ωQG vs. ω = 0). From identical initial distributions of nitrate-tagged particles, the Lagrangian results show that vertical motions induce local increases in nitrate uptake reaching up to 30 %. Such increases occur in low uptake regions with high mesoscale activity. Despite being weaker than horizontal currents by a factor of up to 10−4, vertical velocity associated with mesoscale activity is demonstrated to make an important contribution to nitrate uptake, hence productivity, in low uptake regions.

Application of a multi-component mean field model to the coarsening behaviour of a nickel-based superalloy

A multi-component mean field model has been applied to predict the particle evolution of the γ′ particles in the nickel based superalloy IN738LC, capturing the transition from an initial multimodal particle distribution towards a unimodal distribution. Experiments have been performed to measure the coarsening behaviour during isothermal heat treatments using quantitative analysis of micrographs. The three dimensional size of the γ′ particles has been approximated for use in simulation. A coupled thermodynamic/mean field modelling framework is presented and applied to describe the particle size evolution. A robust numerical implementation of the model is detailed that makes use of surrogate models to capture the thermodynamics. Different descriptions of the particle growth rate of non-dilute particle systems have been explored. A numerical investigation of the influence of scatter in chemical composition upon the particle size distribution evolution has been carried out. It is shown how the tolerance in chemical composition of a given alloy can impact particle coarsening behaviour. Such predictive capability is of interest in understanding variation in component performance and the refinement of chemical composition tolerances. It has been found that the inclusion of misfit strain within the current model formulation does not have a significant affect upon predicted long term particle coarsening behaviour. Model predictions show good agreement with experimental data. In particular, the model predicts a reduced growth rate of the mean particle size during the transition from bimodal to unimodal distributions.

Separated characteristics and global solvability for the one and one-half dimensional Vlasov Maxwell system

The motion of a collisionless plasma - a high-temperature, low-density, ionized gas - is described by the Vlasov-Maxwell (VM) system. These equations are considered in one space dimension and two momentum dimensions without the assumption of relativistic velocity corrections. The main results are bounds on the spatial and velocity supports of the particle distribution function and uniform estimates on derivatives of this function away from the critical velocity $\vert v_1 \vert = 1$. Additionally, for initial particle distributions that are even in the second velocity argument $v_2$, the global-in-time existence of solutions is shown.

Discussion on DQMOM to solve a bivariate population balance equation applied to a grinding process

A bivariate population balance equation applied to a grinding process is implemented in a model (PBM). The particles are simultaneously characterized by their size and their mechanical strength, expressed here by the minimum energy needed to break them. PBM is solved by the Direct Quadrature Method of Moments (DQMOM). The mixed moments of the distribution are expressed by the quadrature form of the population density defined for one order (N) and incorporating the weights and the abscissas defined for the two properties. The effect of the quadrature order (N=2,3,4) and the selected set of the 3N moments needed to solve the system on the accuracy of the results is discussed. For a given order of the quadrature, the selected set of the initial mixed moments slightly affects first the weights and abscissas derived from the initial particle distribution. The set of moments also affects the precision of the moments calculated versus time but only those having high orders in relation with the respective range of the solid properties considered. Problems of convergence and significant differences in the predicted mixed moments are also observed when the order of the quadrature is equal to 2. However, the changes of a bivariate distribution versus time applied to a grinding process are well predicted using the DQMOM approach, choosing a number of nodes equal to 3, associated with a smart selection of the moment set, incorporating all the moments of interest.

The propagation of particulate gravity currents in a V-shaped triangular cross section channel: Lock-release experiments and shallow-water numerical simulations

In this study, we investigate the motion of particulate gravity currents in a horizontal V-shaped channel. The particulate currents consisted of particles whose size varied between 0 and 100 μm but whose mean size increased. Particles were poorly sorted as the variance of the grain size distributions varied between 50 and 200. While the phases of propagation of homogeneous currents in such a geometry have been studied in the literature, this study considers the effects of the grain size on the propagation. The distance of propagation and front velocity of full-depth high-Reynolds-number lock-release experiments and shallow-water equation simulations were analyzed as the mean grain size of the initial particle distributions, defined by mass, was increased from 19 to 58 μm. Similar to the homogeneous currents, three consecutive phases of the front velocity could be identified but their characteristics and extent depend on the particle size. The initial phase, in particular, depends on a dimensionless settling number β that is defined as the ratio of two characteristic time scales, the propagation time x0/U, where U is the scale for the front speed and x0 the lock length, and the settling time h0/vs, where vs is the scale for the settling velocity and h0 the initial height of the current. For dimensionless settling numbers less than 0.001, the initial phase is characterized by a constant velocity for over about 6-7 lock lengths that is alike the initial slumping phase of perfectly constant velocity of the homogeneous currents. For dimensionless settling numbers greater than 0.001 and less than 0.015, the initial phase is no longer characterized by a constant velocity but an almost constant velocity for over about a similar 6-7 lock lengths. For dimensionless settling numbers greater than 0.015, however, as such, this phase is no longer seen. This initial phase is followed by a continuous decrease of the front advance, which results from the sedimentation of the particles. Unlike the homogeneous currents, this phase is a non-self-similar propagation. This phase is ended by a viscosity-dominated phase appearing to vary as ∼t1/7. The good agreement between the front advance of the experiments and shallow-water equation simulations demonstrates that the mean size by mass is a fairly good proxy of poorly sorted particles.

Influence of SPH Regularity and Parameters in Dynamic Fracture Phenomena

The Smoothed Particle Hydrodynamics (SPH) method can be used with advantage in the field of fracture mechanics, which is especially true when quasi-brittle materials are involved. The advantages of the SPH method are more evident when loading speed increases and dynamic material fractures start to occur. Since the SPH method is a meshfree method, the large deformation and eventual fragmentation of material during simulations can be solved without major complications. This happens because of the phase of the SPH method in which a search is made for neighbouring particles and the constraints created between them within a chosen time interval. The number of neighbouring particles depends on the size of the area where the search takes place. This area – the support domain – may therefore be considered as one of the key control elements in simulations using the SPH method. The influence of the number of particles and their initial distribution on the results is also a question. Particle clusters (areas with increased particle concentration) may be formed in cases of poor regularity. Consequently, false (numerical) cracks which bypass these clusters may appear in the simulation. The article describes an experiment concerning the dynamic loading of concrete L-specimens simulated by the SPH method. Different density distributions and initial particle distribution regularities are chosen in the simulation. The results show that it is especially necessary for the initial configuration to exhibit regular particle distribution if simulations are to be executed successfully. False cracks tend to occur more frequently with increasing particle distribution irregularities. A certain degree of compensation can be achieved via the appropriate choice of support domain size with its variations during the simulation.

Concentration of microparticles and bubbles in standing waves.

This paper studies the collective dynamics of microparticles in plane and cylindrical resonators. Based on the known results regarding the motion of a single particle under the action of acoustic radiation force, concentration and separation of particles in standing waves are investigated. As an example, spherical particles (cells) with a slightly larger density and sound speed than those in ambient fluid are considered. Initial particle distribution is assumed to be almost homogeneous at the considered intervals. The formation of concentration peaks in plane standing waves and on the axis of a cylindrical system is demonstrated; additional concentration along the axis is possible. The possibility of an opposite process, i.e., keeping particles stirred by periodic change of acoustic wavelength, is confirmed as well. Distribution and separation of microbubbles of different sizes in a standing wave is also studied. Examples of available experimental data illustrating the relevance of the theory are given.

Modified variable mass incompressible SPH method for simulating internal fluid flows

In the conventional divergence free incompressible smoothed particle hydrodynamics method, the density and mass of the particles assumed to be constant over the simulation time. So, the particles are assumed to have constant volumes. At each time step, particles are moved according to the imposed acceleration and so the initial distribution of particles is changed. This paper presents a modified scheme for the incompressible SPH method. The contributions of this work are updating the volume of the particles at each time step and introducing an extra term to the pressure Poisson equation. In the proposed scheme, the mass of the particles are updated in each time step to keep the density of the particles constant and the divergence of convective term of the momentum equation is added to the source term of the pressure Poisson equation. The validity of the proposed scheme is verified, and to show the ability of the presented method, two internal fluid flow examples are solved.

Zebra pattern in rocks as a function of grain growth affected by second-phase particles

In this communication we present a simple microdynamic model which can explain the beginning of the zebra pattern formation in rocks. The two dimensional model consists of two main processes, mineral replacement along a reaction front, and grain boundary migration affected by impurities. In the numerical model we assume that an initial distribution of second-phase particles is present due to sedimentary layering. The reaction front percolates the model and redistributes second-phase particles by shifting them until the front is saturated and drops the particles again. This produces and enhances initial layering. Grain growth is hindered in layers with high second-phase particle concentrations whereas layers with low concentrations coarsen. Due to the grain growth activity in layers with low second-phase particle concentrations these impurities are collected at grain boundaries and the crystals become very clean. Therefore the white layers in the pattern contain large grains with low concentration of second-phase particles, whereas the dark layers contain small grains with a large second-phase particle concentration.

On natural solutal convection in magnetic fluids

An experiment was carried out to investigate natural solutal convection in a magnetic fluid caused by non-homogeneous initial distribution of colloidal particles in a vertical Hele-Shaw cell. For experiment, we used a dilute magnetic fluid of the “magnetite–kerosene–oleic acid” type. The initial distribution of particles was formed by magnetophoresis of the drop-like aggregates and their sedimentation on the surface of the diamagnetic disk located in the center of the cell. Application of the magnetic field on the system led to the onset of the Rayleigh-Taylor instability and formation of descending convective jets. The velocity of the flow at the front of descending jets was measured for different values of cell thickness (up to 0.18 mm) and strength of the magnetic field generating the drop-like aggregates (up to 21 kA/m). The solutal Rayleigh numbers varied in the range Ra = 50–105. It was shown that the intensity of the convective flow characterized by the Reynolds number Re, increases with the Rayleigh number according to the power law: Re = 1.16 × 10−5Ra0.86.