Numerical simulation for the initial state of avalanche in polydisperse particle systems

Numerical simulation is employed to investigate the initial state of avalanche in polydisperse particle systems.Nucleation and propagation processes are illustrated for pentadisperse and triadisperse particle systems,respectively.In these processes,particles involved in the avalanche grow slowly in the early stage and explosively in the later stage,which is clearly different from the continuous and steady growth trend in the monodisperse system.By examining the avalanche propagation,the number growth of particles involved in the avalanche and the slope of the number growth,the initial state can be divided into three stages:T1(nucleation stage),T2(propagation stage),T3(overall avalanche stage).We focus on the characteristics of the avalanche in the T2 stage,and find that propagation distances increase almost linearly in both axial and radial directions in polydisperse systems.We also consider the distribution characteristics of the average coordination number and average velocity for the moving particles.The results support that the polydisperse particle systems are more stable in the T2 stage.

Effect of distribution shape on the melting transition, local ordering,and dynamics in a model size-polydisperse two-dimensional fluid

We study the effect of particle size polydispersity(δ) on the melting transition(T*), local ordering, solid–liquid coexistence phase and dynamics of two-dimensional Lennard–Jones fluids up to moderate polydispersity by means of computer simulations. The particle sizes are drawn at random from the Gaussian(G) and uniform(U) distribution functions.For these systems, we further consider two different kinds of particles, viz., particles having the same mass irrespective of size, and in the other case the mass of the particle scales with its size. It is observed that with increasing polydispersity,the value of T*initially increases due to improved packing efficiency(φ) followed by a decrease and terminates at δ ≈8%(U-system) and 14%(G-system) with no significant difference for both mass types. The interesting observation is that the particular value at which φ drops suddenly coincides with the peak of the heat capacity(CP) curve, indicating a transition. The quantification of local particle ordering through the hexatic order parameter(Q_6), Voronoi construction and pair correlation function reveals that the ordering decreases with increasing δ and T. Furthermore, the solid–liquid coexistence region for the G-system is shown to be comparatively wider in the T –δ plane phase diagram than that for the U system. Finally, the study of dynamics reveals that polydisperse systems relax faster compared to monodisperse systems;however, no significant qualitative differences, depending on the distribution type and mass polydispersity, are observed.

Modeling of anisotropic polydispersed composites by progressive micromechanical approach

A progressive micromechanical method is presented in order to predict the elastic constants of polydispersed composites including multi-directional or randomly ori- ented reinforcement particles. Heterogeneities of various types are introduced into the matrices in a gradual manner. At each step, the Mori-Tanaka method is used to ob- tain the stiffness tensor of the intermediate medium used as a matrix of the following step. The proposed method is capable of introducing any kind of heterogeneities based on their dimensions, orientations, mechanical properties, and volume fractions to the ma- trix. Furthermore, suitable probability density functions can be defined for physical and structural parameters of the composite, including the level of the filler-matrix interfacial bonding, the aspect ratio, and the orientation of reinforcement particles. The efficiency of the iterative approach and the convergence of the solution are studied by computing the stiffness tensors of unidirectional and bidirectional particulate composites. The results of the present study are also compared with the literature data for a randomly oriented particulate composite.

Non-Gaussian and Clustering Behavior in One-Dimensional Polydisperse Granular Gas System

We present a one-dimensional dynamic model of polydisperse granular mixture with the fractal characteristic of the particle size distribution, in which the particles are subject to inelastic mutual collisions and are driven by Gaussian white noise. The inhomogeneity of the particle size distribution is described by a fractal dimension D. The stationary state that the mixture reaches is the result of the balance between energy dissipation and energy injection. By molecular dynamics simulations, we have mainly studied how the inhomogeneity of the particle size distribution and the inelasticity of collisions influence the velocity distribution and distribution of interparticle spacing in the steady-state. The simulation results indicate that, in the inelasticity case, the velocity distribution strongly deviates from the Gaussian one and the system has a strong spatial clustering. Thus the inhomogeneity and the inelasticity have great effacts on the velocity distribution and distribution of interparticle spacing. The quantitative information of the non-Gaussian velocity distribution and that of clustering are respectively represented.

Global Pressure of One-Dimensional Polydisperse Granular Gases Driven by Gaussian White Noise

We study the global pressure of a one-dimensional polydisperse granular gases system for the first time, in which the size distribution of particles has the fractal characteristic and the inhomogeneity is described by a fractal dimension D. The particles are driven by Gaussian white noise and subject to inelastic mutual collisions. We define the global pressure P of the system as the impulse transferred across a surface in a unit of time, which has two contributions, one from the translational motion of particles and the other from the collisions. Explicit expression for the global pressure in the steady state is derived. By molecular dynamics simulations, we investigate how the inelasticity of collisions and the inhomogeneity of the particles influence the global pressure. The simulation results indicate that the restitution coefficient e and the fractal dimension D have significant effect on the pressure.

Dynamic Properties of Two-Dimensional Polydisperse Granular Gases

We propose a two-dimensional model of polydisperse granular mixtures with a power-law size distribution in the presence of stochastic driving. A fractal dimension D is introduced as a measurement of the inhomogeneity of the size distribution of particles. We define the global and partial granular temperatures of the multi-component mixture. By direct simulation Monte Carlo, we investigate how the inhomogeneity of the size distribution influences the dynamic properties of the mixture, focusing on the granular temperature, dissipated energy, velocity distribution, spatial clusterization, and collision time. We get the following results： a single granular temperature does not characterize a multi-component mixture and each species attains its own ＂granular temperature＂; The velocity deviation from Gaussian distribution becomes more and more pronounced and the partial density of the assembly is more inhomogeneous with the increasing value of the fractal dimension D; The global granular temperature decreases and average dissipated energy per particle increases as the value olD augments.

Steady-State Properties of Driven Polydisperse Granular Mixtures

We represent a two-dimensional model of polydisperse granular mixtures with a power-law size distribution. The model consists of smooth hard disks in a rectangular box with inelastic collisions,driven by a homogeneous heat bath at zero gravity.The width of particle size distribution is characterized by the only parameter,namely,the fractal dimension D.The energy dissipation of the mixture is increased as D increases or as e decreases.Furthermore,it is found that the steady-state properties of the mixture such as the collision rate,granular temperature,kinetic pressure and velocity distribution depend sensitively on size distribution parameter D.

Simulation of fine polydisperse particle condensational growth under an octadecane-nitrogen atmosphere

The evolution of particle size distribution （PSD） of fine polydisperse particles at high number concen- trations （7105 cm-3） was simulated through a combined model employing direct quadrature method of moments （DQMOM） with heat and mass transfer equations. The PSD was assumed to retain log-normal distribution during the heterogeneous condensation process. The model was first verified by exact solu- tion and experimental data prior to investigating the influence of initial conditions on final PSD under an octadecane-nitrogen atmosphere. Low particle number concentrations and high vapor concentrations were beneficial to shift the PSD to larger particles having a narrower distribution. Additionally, vapor depletion has more influence on the final PSD than the heat release parameter for a number concentra- tion of 10^6 cm^-3. This study may assist the design process of a gas-solid separating cyclone, to eliminate dust from high-temperature volatiles by pyrolysis of solid fuels.

Using the discrete element method to assess the mixing of polydisperse solid particles in a rotary drum

Despite the wide applications of powder and solid mixing in industry, knowledge on the mixing of polydisperse solid particles in rotary drum blenders is lacking. This study investigates the mixing of monodisperse, bidisperse, tridisperse, and polydisperse solid particles in a rotary drum using the dis- crete element method. To validate the model developed in this study, experimental and simulation results were compared. The validated model was then employed to investigate the effects of the drum rotational speed, particle size, and initial loading method on the mixing quality. The degree of mixing of polydis- perse particles was smaller than that for monodisperse particles owing to the segregation phenomenon. The mixing index increased from an initial value to a maximum and decreased slightly before reaching a plateau for bidisperse, tridisperse, and polydisperse particles as a direct result of the segregation of par- ticles of different sizes. Final mixing indices were higher for polydisperse particles than for tridisperse and bidisperse particles. Additionally, segregation was weakened by introducing additional particles of intermediate size. The best mixing of bidisperse and tridisperse particles was achieved for top-bottom smaller-to-larger initial loading, while that of polydisperse systems was achieved using top-bottom smaller-to-larger and top-bottom larger-to-smaller initial loading methods.

Study of fluid cell coarsening for CFD-DEM simulations of polydisperse gas–solid flows

Particle polydispersity is ubiquitous in industrial fluidized beds,which possesses a significant impact on hydrodynamics of gas-solid flow.Computational fluid dynamics-discrete element method(CFD-DEM)is promising to adequately simulate gas-solid flows with continuous particle size distribution(PSD)while it still suffers from high computational cost.Corresponding coarsening models are thereby desired.This work extends the coarse-grid model to polydisperse systems.Well-resolved simulations with different PSDs are processed through a filtering procedure to modify the gas-particle drag force in coarse-grid simulations.We reveal that the drag correction of individual particle exhibits a dependence on filtered solid volume fraction and filtered slip velocity for both monodisperse and polydisperse systems.Subsequently,the effect of particle size and surrounding PSD is quantified by the ratio of particle size to Sauter mean diameter.Drag correction models for systems with monodisperse and continuous PSD are developed.A priori analysis demonstrates that the developed models exhibit reliable prediction accuracy.

Effects of coefficient of friction and coefficient of restitution on static packing characteristics of polydisperse spherical pebble bed

The effects of the coefficient of friction and coefficient of restitution on the static packing characteristics of a polydisperse spherical pebble bed are numerically investigated using the discrete element method.Several important static packing characteristics under different coefficients of friction and restitution are presented and discussed.The results show that the coefficients of friction and restitution impose opposite effects on the packing heights and global packing factor.Neither the coefficient of friction nor restitution affected the oscillation width of the wall,whereas their effects are primarily reflected in the oscillation amplitude of the radial local packing factor and the axial local packing factor distribution at the top of the pebble bed.In both the contact force distribution and coordination number distribution,a left-shifted phenomenon appearing as the coefficient of friction occurred,and only the magnitude of the maximum frequency is affected when the coefficient of restitution changed from 0.1 to 0.9.In all simulation cases,the effects of the coefficients of friction and restitution are similar to that of cross-impact.

Representative elementary volume analysis of polydisperse granular packings using discrete element method

The representative elementary volume （REV） for three-dimensional polydisperse granular packings was determined using discrete element method simulations. Granular mixtures of various sizes and particle size distributions were poured into a cuboid chamber and subjected to uniaxial compression, Findings showed that the minimum REV for porosity was larger compared with the REV for parameters such as coordination number, effective elastic modulus, and pressure ratio. The minimum REV for porosity and other parameters was found to equal 15,10, and 5 times the average grain diameter, respectively. A study of the influence of sample size on energy dissipation in random packing of spheres has also confirmed that the REV size is about 15 times the average grain diameter. The heterogeneity of systems was found to have no effect on the REV for the parameters of interest for the narrow range of coefficient of uniformity analyzed in this paper. As the REV approach is commonly applied in both experimental and numerical studies, determining minimum REV size for polydisperse granular packings remains a crucial issue.

Parameterization of below-cloud scavenging for polydisperse fine mode aerosols as a function of rain intensity

The below-cloud aerosol scavenging process by precipitation is one of the most important mechanisms to remove aerosols from the atmosphere.Due to its complexity and dependence on both aerosol and raindrop sizes,wet scavenging process has been poorly treated,especially during the removal of fine particles.This makes the numerical simulation of below-cloud scavenging in large-scale aerosolmodels unrealistic.To consider the slip effects of submicron particles,a simplified expression for the diffusion scavenging was developed by approximating the Cunningham slip correction factor.The derived analytic solution was parameterized as a simple power function of rain intensity under the assumption of the lognormal size distribution of particles.The resultant approximated expression was compared to the observed data and the results of previous studies including a 3D atmospheric chemical transport model simulation.Compared with the default GEOS-Chem coefficient of 0.00106R0.61 and the observation-based coefficient of 0.0144R0.9268,the coefficient of a and b in∧m=aRb spread in the range of 0.0002-0.1959 for a and 0.3261-0.525 for b over a size distribution of GSD of 1.3–2.5 and a geometric mean diameter of 0.01-2.5μm.Overall,this study showed that the scavenging coefficient varies widely by orders of magnitude according to the size distribution of particles and rain intensity.This study also demonstrated that the obtained simplified expression could consider the theoretical approach of aerosol polydispersity.Our proposed analytic approach showed that results can be effectively applied for reduced computational burden in atmospheric modeling.

Machine Learning for heat radiation modeling of bi-and polydisperse particle systems including walls

We investigated the ability of four popular Machine Learning methods i.e.,Deep Neural Networks(DNNs),Random Forest-based regressors(RFRs),Extreme Gradient Boosting-based regressors(XGBs),and stacked ensembles of DNNs,to model the radiative heat transfer based on view factors in bi-and polydisperse particle beds including walls.Before training and analyzing the predictive capability of each method,an adjustment of markers used in monodisperse systems,as well as an evaluation of new markers was performed.On the basis of our dataset that considers a wide range of particle radii ratios,system sizes,particle volume fractions,as well as different particle-species volume fractions,we found that(i)the addition of particle size information allows the transition from monodisperse to bi-and polydisperse beds,and(ii)the addition of particle volume fraction information as the fourth marker leads to very accurate predictions.In terms of the overall performance,DNNs and RFRs should be preferred compared to the other two options.For particle-particle view factors,DNN and RFR are on par,while for particle-wall the RFR is superior.We demonstrate that DNNs and RFRs can be built to meet or even exceed the prediction quality standards achieved in a monodisperse system.

Universal Concentration Scaling on Rheometric Properties of Polydisperse and High Molecular Weight Polyacrylamide Aqueous Solutions

A great progress has been made over the last decades in studying concentration scaling on rheometric properties of monodisperse polymer solutions.However,the effects of polydisperse polymer solutions on such a concentration scaling remain elusive.In this work,rheometric properties of industrially relevant polydisperse and high molecular weight polyacrylamide(PAAm)aqueous solution have been studied.The results show a concentration scaling of the characteristic relaxation time,the plateau modulus and the zero-shear viscosity across a concentration range from 10c^(*)to 250c^(*).The time-concentration superposition principle is validated and extended in the data analysis of the terminal dynamic regime.The concentration scaling exponent of their shifting factors is significantly smaller than the results of monodisperse polymer solutions in good andθsolvents reported in the literature.The steady shear viscosity and shear stress of 18M PAAm aqueous solutions with relatively lower concentration(≤35c^(*))could also be superimposed into a master curve with the shear-thinning exponent of 0.73±0.03 and0.27±0.03,respectively,over a wide range of shear rates in about six orders of magnitudes.However,for 18M PAAm aqueous solutions with higher concentration(≥48c^(*))in an intermediate shear thinning regime,the scaling exponent shows a pronounced concentration dependence.The shear thinning exponent of steady shear viscosity varies from 0.73 to 0.57 as concentration is increased,and then increases from 0.57 to 0.90from sufficiently high shear rate.Further increasing shear rate,the shear-thinning exponent of 18M PAAm aqueous solutions at all concentrations converges to the lower bounded value observed in the relatively less concentrated(≤35c^(*))18M PAAm aqueous solutions,i.e.,0.73±0.02 for shear viscosity and 0.27±0.02 for steady shear stress,respectively.It reveals that the concentration effects of polydisperse polymer solutions could be greatly reduced by the dynamic"molecular individualism”in strong shear flow.

Morphologies of a spherical bimodal polyelectrolyte brush induced by polydispersity and solvent selectivity

It is commonly realized that polydispersity may significantly affect the surface modification properties of polymer brush systems. In light of this, we systematically study morphologies of bidisperse polyelectrolyte brush grafted onto a spherical nanocolloid in the presence of trivalent counterions using molecular dynamics simulations. Via varying polydispersity, grafting density, and solvent selectivity, the effects of electrostatic correlation and excluded volume are focused, and rich phase behaviors of binary mixed polyelectrolyte brush are predicted, including a variety of pinned-patch morphologies at low grafting density and micelle-like structures at high grafting density. To pinpoint the mechanism of surface structure formation, the shape factor of two species of polyelectrolyte chains and the pair correlation function between monomers from different polyelectrolyte ligands are analyzed carefully. Also, electrostatic correlations, manifested as the bridging through trivalent counterions, are examined by identifying four states of trivalent counterions. Our simulation results may be useful for designing smart stimuli-responsive materials based on mixed polyelectrolyte coated surfaces.

Effects of Shape of Crowders on Dynamics of a Polymer Chain Closure

Using 3D Langevin dynamics simulations, we investigate the effects of the shape of crowders on the dynamics of a polymer chain closure. The chain closure in spherical crowders is dominated by the increased medium viscosity so that it gets slower with the increasing volume fraction of crowders. By contrast, the dynamics of chain closure becomes very complicated with increasing volume fraction of crowders in spherocylindrical crowders. Notably, the mean closure time is found to have a dramatic decrease at a range of volume fraction of crowders 0.36-0.44. We then elucidate that an isotropic to nematic transition of spherocylindrical crowders at this range of volume fraction of crowders is responsible for the unexpected dramatic decrease in the mean closure time.

Analytical modeling and simulation of porous electrodes: Li-ion distribution and diffusion-induced stress

A new model of porous electrodes based on the Gibbs free energy is developed, in which lithium-ion(Liion) diffusion, diffusion-induced stress(DIS), Butler–Volmer(BV) reaction kinetics, and size polydispersity of electrode particles are considered. The influence of BV reaction kinetics and concentration-dependent exchange current density(ECD) on concentration profile and DIS evolution are numerically investigated. BV reaction kinetics leads to a decrease in Li-ion concentration and DIS. In addition, concentrationdependent ECD results in a decrease in Li-ion concentration and an increase in DIS. Size polydispersity of electrode particles significantly affects the concentration profile and DIS.Optimal macroscopic state of charge(SOC) should consider the influence of the microscopic SOC values and mass fractions of differently sized particles.

Polydispersity effects on the magnetization of diluted ferrofluids:a lognormal analysis

Based on a lognormal particle size distribution, this paper makes a model analysis on the polydispersity effects on the magnetization behaviour of diluted ferrofluids. Using a modified Langevin relationship for the lognormal dispersion, it first performs reduced calculations without material parameters. From the results, it is extrapolated that for the ferrofluid of lognormal polydispersion, in comparison with the corresponding monodispersion, the saturation magnetization is enhanced higher by the particle size distribution. It also indicates that in an equivalent magnetic field, the lognormally polydispersed ferrofluid is magnetically saturated faster than the corresponding monodispersion. Along the theoretical extrapolations, the polydispersity effects are evaluated for a typical ferrofluid of magnetite, with a dispersity of σ = 0.20. The results indicate that the lognormal polydispersity leads to a slight increase of the saturation magnetization, but a noticeable increase of the speed to reach the saturation value in an equivalent magnetic field.