Competition of Brazil nut effect,buoyancy, and inelasticity induced segregation in a granular mixture

It has been recently reported that a granular mixture in which grains differ in their restitution coefficients presents segregation: the more inelastic particles sink to the bottom. When other segregation mechanisms as buoyancy and the Brazil nut effect are present, the inelasticity induced segregation can compete with them. First, a detailed analysis, based on numerical simulations of two dimensional systems, of the competition between buoyancy and the inelasticity induced segregation is presented, finding that there is a transition line in the parameter space that determines which mechanism is dominant. In the case of neutrally buoyant particles having different sizes the inelasticity induced segregation can compete with the Brazil nut effect (BNE). Reverse Brazil nut effect (RBNE) could be obtained at large inelasticities of the intruder. At intermediate values, BNE and RBNE coexist and large inelastic particles are found both near the bottom and at the top of the system.     

颗粒密度对旋转筒内二元颗粒体系分离的影响

用分子动力学的方法研究了颗粒密度对旋转筒内二元颗粒体系混合与分离的影响. 当增大粒度较小的颗粒密度时, 颗粒体系表现为巴西果效应, 而增加粒度较大的颗粒密度时, 分离状态则会发生反转, 表现为反巴西果效应. 进一步的研究发现二元颗粒体系的分离指数与颗粒的密度比之间存在定量的关系, 并利用Hong的渗流与凝聚竞争机理理论对密度分离状态的反转现象给予了理论解释.     

Segregation in fluidized versus tapped packs

We compare the predictions of two different statistical mechanics approaches, corresponding to different physical measurements, proposed to describe binary granular mixtures subjected to some external driving (continuous shaking or tap dynamics). In particular we analytically solve at a mean field level the partition function of a simple hard sphere lattice model under gravity and focus on the phenomenon of size segregation. We find that the two approaches lead to similar results and seem to coincide in the limit of very low shaking amplitude. However, they give different predictions of the crossovers from Brazil nut effect to reverse Brazil nut effect with respect to the shaking amplitude, which could be detected experimentally.     

巴西果效应分离过程的计算颗粒力学模拟研究

采用离散单元模型对巴西果问题进行了模拟研究,采用本数学模型可以准确地预测出垂直机械振动导致的不同大小颗粒的分离现象.分析了影响振动床内颗粒分层的因素,讨论了振动频率、振动幅度等参数对分层的影响,发现振动频率和振动幅度会对分离效果造成较大的影响.当振动频率或振动幅度较小时,颗粒整体分离效果都较差,但分离的稳定性较好,当振动频率或振动幅度较大时,整体分离效果仍然较差,同时分离的稳定性也较差,振动分离过程中存在一个频率和振幅适中的最优操作点. 关键词： 分层 振动 模式形成 离散单元方法     

振动颗粒混合物中的周期性分聚现象与能量耗散

在垂直振动的激励下, 铜和玻璃珠组成的二元颗粒混合样品存在依次出现分界清晰的三明治, 巴西果, 反巴西果三种分聚结构的周期循环变化现象, 其中出现三明治结构的时段最长(大于90%). 循环周期随振动台频率的增加而增大, 随加速度的增加而减小. 对三种分聚结构的样品能量耗散功率的测量显示, 在相同的振动条件下反巴西果结构的能耗功率最大, 巴西果结构的最小. 利用Hong的凝聚和渗透两机理相互竞争的观点, 并结合能耗功率的测量结果, 可定性解释这个周期性分聚现象.     

Granular species segregation under vertical tapping: effects of size, density, friction, and shaking amplitude

We present extensive molecular dynamics simulations on species segregation in a granular mixture subject to vertical taps. We discuss how grain properties, e.g., size, density, friction, as well as shaking properties, e.g., amplitude and frequency, affect such a phenomenon. Both the Brazil nut effect (larger particles on the top, BN) and the reverse Brazil nut effect (larger particles on the bottom, RBN) are found and we derive the system comprehensive "segregation diagram" and the BN to RBN crossover line. We also discuss the role of friction and show that particles which differ only for their frictional properties segregate in states depending on the tapping acceleration and frequency.     

振动颗粒混合物中的三明治式分离

在竖直振动两种颗粒的混合物的实验中，观察到了一种新的分离现象——“三明治”式分离，即大而重的颗粒被夹在两层小的轻颗粒之间.这不同于“巴西果”效应导致的大而重的颗粒在上的两层有序结构.实验表明当振动加速度大于某个临界值时这种三层有序将取代两层结构，而且是稳定的.实验中观察到导致“三明治”式分离的两种不同的分离过程.对这两种过程的物理机理及其与振动加速度、振动频率及颗粒尺寸等因素的关系做了研究，并给出了相图. 关键词： 颗粒物质 振动 有序结构 三明治式分离 巴西果效应     

垂直振动作用下二元混合颗粒分层的动态循环反转

在对垂直振动下的铜颗粒和氧化铝颗粒混合物的研究中,除了观测到巴西果分层和混合分层外,还发现了一种新的随时间周期变化的分离形态. 此分离形态可随着时间的演化,在巴西果、反巴西果和三明治这几种分层构型之间进行动态的循环反转. 给出了这种反转态出现的相区,并且观测了其动态转变的规律. 根据碰撞、磨擦及空气的耗散作用所产生的耗散结构对循环反转态的出现给出了定性的解释,并通过实验证实这种分层构型与空气的存在有密切的关系. 关键词： 颗粒物质 巴西果效应 相分离     

Variational approach to hard sphere segregation under gravity

It is demonstrated that the minimization of the free energy functional for hard spheres and hard disks yields the result that excited granular materials under gravity segregate not only in the widely known "Brazil nut" fashion, i.e., with the larger particles rising to the top, but also in reverse "Brazil nut" fashion. Specifically, the local density approximation is used to investigate the crossover between the two types of segregation occurring in the liquid state, and the results are found to agree qualitatively with previously published results of simulation and of a simple model based on condensation.     

振动颗粒物质“巴西果”分离效应实验和理论研究

本文通过实验和理论研究了影响"巴西果"分离的因素及其物理机理. 分析了振动加速度、大小颗粒尺寸和密度对分离时间的影响, 并利用流体模型对分离时间作估算, 对实验结果进行定性解释. 结果表明在振动频率固定时, 调节振动加速度是控制"巴西果"分离的一个主要手段. 振动加速度存在一个临界值, 当高于此临界值时, "巴西果"分离的主要物理机理由对流机理转变为几何填空机理, 且振动加速度对分离影响变小, 大颗粒尺寸对分离的影响增大. 可通过调节大颗粒的尺寸来改变分离效果. 当大、 小颗粒密度比为1时, 仍会出现"巴西果"分离现象. 增大小颗粒尺寸或密度可以促进"巴西果"分离.     

LEVEL STATISTICS AND PARITY EFFECT ON SMALL SUPERCONDUCTING SYSTEMS

In this paper we have calculated the variations of the gap Δ'(0,d) and transition temperature T'_c in small metallic grains as functions of grain size (or the level spacing d between discrete electronic states) for the cases of odd and even numbers of electrons by applying the random matrix theory to the mean field theory. We find the presence of enhancement of superconductivity and critical d_c, where the superconductivity of small grains breaks down. This agrees with Anderson's prediction (1959 J. Phys. Chem. Solids 11 28). We find that in the grains, as the size is lowered, the transition temperature T'_c decreases and Δ'(0,d)/k_BT'_c≤πe_-γ in odd numbers of electrons, and for Gaussian orthogonal and unitary ensembles in some regimes Δ'(0,d)/k_B T'_c>πe_-γ in even numbers of electrons.     

Surface flows of granular mixtures

We present the generalization of the minimal model for surface flows of granular mixtures, proposed by Boutreux and de Gennes [J. Phys. I France 6, 1295 (1996)]. The minimal model was valid for grains differing only in their surface properties. The present model also takes into account differences in the size of the grains. We apply the model to study segregation in two-dimensional silos of mixtures of grains differing in size and/or surface properties. When the difference in size is small, the model predicts that a continuous segregation appears in the static phase during the filling of a silo. When the difference in size is wide, we take into account the segregation of the grains in the rolling phase, and the model predicts complete segregation and stratification in agreement with experimental observations. Received 9 September 1998 and Received in final form 4 November 1998     

Surface flows of granular mixtures: II. Segregation with grains of different size

We present the generalization of a theoretical model for segregation of granular mixtures due to surface flows, published in J. Phys. I France 6, 1295 (1996). Our generalized model is valid for grains differing by their size and/or their surface properties; in the present paper, we describe the case of two species with the same surface properties but two different sizes. The rolling stream is assumed to be homogeneous. Exchanges between the grains at rest and the rolling stream are modelized via binary collisions. The model predicts that during the filling of a two-dimensional silo, continuous segregation appears inside the static phase: small (respectively large) grains tend to stop uphill (respectively downhill), although both species remain present everywhere. This fits the observations when the size difference between the species is small. When the size difference is large, a different regime is observed. We argue that in this case, segregation occurs directly inside the rolling stream. Received: 25 February 1998 / Received in final form and Accepted: 6 July 1998     

Segregation in arch formation

We report new segregation phenomena in the clogging arches formed during the discharge of granular piles. Results from molecular dynamics simulations show segregation effects with respect to both size and density ratios used in piles built with bidisperse mixtures of grains. The clogging arch is preferentially constituted of large grains when size bidisperse piles were discharged, whereas for density bidisperse mixtures there is a predominance of light grains in the arch for large orifice widths but, for small widths, an inversion in the preference is observed, with a slightly higher incidence of heavy grains forming the arches. We present arguments based on the reverse buoyancy effect and the statistics collected for the avalanche size distributions to explain how these effects can be understood as a crossover between two different segregation mechanisms acting independently at small and large orifice width limits.     

Grain segregation mechanism in aeolian sand ripples

Many sedimentary rocks are formed by migration of sand ripples. Thin layers of coarse and fine sand are present in these rocks, and understanding how layers in sandstone are created has been a longstanding question. Here, we propose a mechanism for the origin of the most common layered sedimentary structures such as inverse graded climbing ripple lamination and cross-stratification patterns. The mechanism involves a competition between three segregation processes: (i) size-segregation and (ii) shape-segregation during transport and rolling, and (iii) size segregation due to different hopping lengths of the small and large grains. We develop a discrete model of grain dynamics which incorporates the coupling between moving grains and the static sand surface, as well as the different properties of grains, such as size and roughness, in order to test the plausibility of this physical mechanism. Received 19 July 1999 and Received in final form 4 August 1999     

Modeling of polysilicon diffusion sources during rapid optical annealing

A new model for polysilicon diffusion sources is presented. It considers the following effects: 1) dopant diffusion in grains, in grain boundaries and in the single-crystal silicon substrate, 2) dynamic dopant segregation between grain and grain boundary phases and between the phases of polysilicon and the single-crystal silicon substrate, 3) dynamic dopant activation or clustering in grains and in the single-crystal silicon substrate, 4) dynamic grain growth depending on local grain size and local electron density. These mechanisms with completely different time scales are modeled simultaneously. For the first time this allows the analysis of furnace and rapid optical annealing processes with arbitrary grain growth kinetics even during epitaxial realignment. The advanced model for segregation allows for the effect that dopants in grain boundaries and active dopants in grains as well as in the single-crystal silicon substrate find only a limited number of sites which can be occupied. These limitations are necessary to explain the dopant distributions in polysilicon and in the single-crystal silicon substrate. For the first time the coupling between the concentration of active dopants in grains, between the concentration of dopants in grain boundaries and between the local grain size is shown during doping enhanced grain growth.     

Structure and thermodynamics of associating rods solutions

Physical gelation in rod-like associating polymer solutions is analyzed by computer simulations and by mean field models. The structural gelation (SG) transition is determined by a rapid change in the cluster weight average. The analytically determined SG transition is in good agreement with the simulation results. At low temperatures we observe a peak in the heat capacity, which maximum is associated with phase segregation. The SG transition is sensitive to the number of associating groups per rod but nearly insensitive to the spatial distribution of associating groups around the rods. Phase segregation is strongly dependent on both the number and distribution of associating groups per rod. We find negligible overall nematic order near the SG transition and only partial local nematic order of the clusters at the phase segregation transitions.Received: 23 May 2003, Published online: 5 February 2004PACS: 61.30.Cz Molecular and microscopic models and theories of liquid crystal structure - 64.70.Md Transitions in liquid crystals     

Reverse Brazil nut problem: competition between percolation and condensation

In the Brazil nut problem (BNP), hard spheres with larger diameters rise to the top. There are various explanations (percolation, reorganization, convection), but a broad understanding or control of this effect is by no means achieved. A theory is presented for the crossover from BNP to the reverse Brazil nut problem based on a competition between the percolation effect and the condensation of hard spheres. The crossover condition is determined, and theoretical predictions are compared to molecular dynamics simulations in two and three dimensions.     

A model of binary assemblies of spheres

We propose a theoretical model of random binary assemblies of spheres at any packing fraction. We use the notion of geometrical neighborhood between grains that is defined through two generalizations of the Vorono? tessellation: the radical (or Laguerre) tessellation and the navigation map. The model is tested on different numerical packings. We find a weak local segregation for high packing fraction. We also find that the higher the size ratio of the particles, the more important the segregation. Received 19 February 2001 and Received in final form 27 June 2001     

Segregation transitions in wet granular matter

We report the effect of interstitial fluid on the extent of segregation by imaging the pile that results after bidisperse color-coded particles are poured into a silo. Segregation is sharply reduced and preferential clumping of small particles is observed when a small volume fraction of fluid V(f) is added. We find that viscous forces in addition to capillary forces have an important effect on the extent of segregation s and the angle of repose straight theta. We show that the sharp initial change and the subsequent saturation in s and straight theta occurs over similar V(f). We also find that a transition back to segregation can occur when the particles are completely immersed in a fluid at low viscosities.