Analysis of radial segregation of granular mixtures in a rotating drum

This paper considers the segregation of a granular mixture in a rotating drum. Extending a recent kinematic model for grain transport on sandpile surfaces to the case of rotating drums, an analysis is presented for radial segregation in the rolling regime, where a thin layer is avalanching down while the rest of the material follows rigid body rotation. We argue that segregation is driven not just by differences in the angle of repose of the species, as has been assumed in earlier investigations, but also by differences in the size and surface properties of the grains. The cases of grains differing only in size (slightly or widely) and only in surface properties are considered, and the predictions are in qualitative agreement with observations. The model yields results inconsistent with the assumptions for more general cases, and we speculate on how this may be corrected. Received 4 June 1999 and Received in final form 28 September 1999     

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     

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     

Shapes of heaps and in silos

Experimental investigations on the shape of a heap formed in a Hele Shaw cell either on a flat base or in a two-dimensional silo are presented. We have focused our attention on the shape dependence on mass flux and initial energy of particles poured into the cell. Two kinds of granular media are considered: glass beads and sand and we shall point out their different behaviors. We described the variations of the angle of repose and of the size of the tail as a function of the experimental parameters. We also report the time evolution of the angle of repose during the formation of the heap. Received 28 September 1998 and Received in final form 20 January 1999     

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     

Humidity effects on the stability of a sandpile

Humidity is well-known to significantly affect the mechanical properties, static as well as dynamic, of granular materials. We present the method of humidification of granular media from an under-saturated vapor that we designed in order to experimentally quantify such moisture-induced effects under accurately-controlled humidity conditions. We report the quantitative measurements of the maximum angle of stability of a pile made of small glass beads, as a function of the relative vapor pressure, up to close to saturation. The results obtained with liquids differing in their wetting properties on glass, namely water and heptane, are presented. It is shown that the wetting properties of the liquid on the grains have a strong influence on the cohesion of the non-saturated granular medium. Received 26 October 1998 and Received in final form 30 March 1999     

The dust emission law in the wind erosion process on soil surface

The dust emission models to date cannot describe the relation between the transport rate of different sized grains and their grain size composition in soil surface, so Aeolian grain transport on a soil-like bed composed of fine sand and silt powder was measured in a wind tunnel. Six types of soil-like beds with different silt fractions have been tested in this experiment. The mass flux profiles of silt dust and sand grains are much different due to their different motion modes. Analysis of the vertical distribution of the powder and sand grains reveals that for a given soil bed, the ratio of the horizontal dust flux to the horizontal sand flux is directly proportional to their mass ratio in the bed. The dust flux is closely linked to the sand flux by the bombardment mechanism. For a given wind velocity and grain size of the bed, the slopes of the vertical mass flux profiles of sand grains larger than 100 μm are nearly equal in a log-linear plot and the ratio between the fraction of transport rate of each size group to the whole transport rate and the mass fraction of each size group in the bed is a constant only dependent on grain size. With this law, the transport rate of dust and different sized grains can be related with the grain size composition in the soil surface. Supported by the National Natural Science Foundation of China (Grant No. 50706031) and the Natural Science Foundation of Shanxi Province of China (Grant No. 2008021005)     

A computer simulation study of the ground-state configurations of Fe and Fe-Al clusters

Using the noncentral embedded atom model potential recently proposed by Besson and Morillo for bulk alloys (), we performed computer simulations to predict the ground-state configurations of and clusters (). The computed structures of clusters are in general agreement with such theoretical results as have been obtained by density functional calculations (i.e. for ). The results for Fe-rich clusters show surface segregation of Al, which is in keeping with the findings of a previous study of clusters. Received 29 April 1999     

Formation of metallic nanophases in silica by ion beam mixing. Part II: cluster formation

2 matrix by ion-beam mixing of SiO₂/Ag multilayers is studied via Rutherford backscattering spectrometry, optical absorption, and transmission electron microscopy experiments. In a first step, irradiation with MeV heavy ions transforms the continuous Ag layers into a string of micrometer-sized Ag inclusions. This mechanism can be attributed to lateral segregation of metallic atoms induced by irradiation. In a second step, the Ag inclusions are broken up by incoming ions and Ag nanoclusters are formed by agglomeration of mobile Ag atoms. The latter mechanism is likely due to a combination of ballistic mixing and radiation-induced segregation or radiation-enhanced diffusion processes. The size of the metallic nanoclusters formed depends also on the irradiation temperature. Received: 27 October 1997/Accepted: 3 February 1998     

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     

Scaling approach of the convective drying of a porous medium

We propose a simplified, theoretical approach of the evolution of liquid distribution during the convective drying of a granular packing. In the absence of gravity effects three regimes are distinguished according to the relative importance of surface evaporation, capillarity or evaporation from the interior of the sample. The evolution of the drying rate as a function of the saturation can be inferred from the characteristic velocities associated to each of these effects. We also carried out drying experiments of bead packings saturated with ethanol, at four different velocities of the boundary convection current, and with bead size ranging from 4.5 to 100 μm. The drying curves exhibit different regimes with a scaling as a function of particle radius and current velocity as predicted by the theory. Received 7 June 1999 and Received in final form 25 October 1999     

Air-Driven Segregation in Binary Granular Mixtures with Same Size but Different Densities

We investigate the segregation effect of binary granular mixtures with the same size but different densities under vibration at different air pressures. Our experiments show that the segregation state is seriously dependent on the air pressure and there is a new type of partially segregated state at high air pressure, which has the characteristic that the lighter grains tend to stay at the bottom and form a pure layer, while heavier grains and remained lighter ones tend to rise and to form a mixed layer on the top of the system. We redefine the order parameter to study the variation of the segregation effect with the air pressure and vibration parameter in detail. Finally, the mechanism of the air-driven segregation is illustrated by the faster acceleration due to the airflow through the granular bed for lighter particles.     

In situ X-ray diffraction investigation of porous silicon strains induced by the freezing of a confined organic fluid

High resolution X-ray diffraction is used to perform an in situ measurement of the variations of the lattice parameter of the nanometer size crystallites of porous silicon, induced by the freezing of a confined organic fluid, dodecane. Two p⁺ type PS layers of 60 and 70% porosity are investigated, and the variations of their lattice parameter with the temperature (in the range 150–300 K) are measured. The experimental curves are discussed in relation with the results of a previous calorimetric study of the freezing of confined dodecane. We explain the observed strains by the presence of capillary stresses, that appear in the layer due to the formation of internal liquid-vapour meniscus during the freezing process of the confined fluid. Received 22 October 1999 and Received in final form 25 March 2000     

Microstructure, microhardness, composition, and corrosive properties of stainless steel 304 I. Laser surface alloying with silicon by beam-oscillating method.

Laser surface alloying (LSA) with silicon was conducted on austenitic stainless steel 304. Silicon slurry composed of silicon particle of 5 μm in average diameter was made and a uniform layer was supplied on the substrate stainless steel. The surface was melted with beam-oscillated carbon dioxide laser and then LSA layers of 0.4–1.2 mm in thickness were obtained. When an impinged energy density was adjusted to be equal to or lower than 100 W mm⁻², LSA layers retained rapidly solidified microstructure with dispersed cracks. In these samples, Fe₃Si was detected and the concentration of Si in LSA layer was estimated to be 10.5 wt.% maximum. When the energy density was equal to or greater than 147 W mm⁻², cellular grained structure with no crack was formed. No iron silicate was observed and alpha iron content in LSA layers increased. Si concentration within LSA layers was estimated to be 5 to 9 wt.% on average. Crack-free as-deposited samples exhibited no distinct corrosion resistance. The segregation of Si was confirmed along the grain boundaries and inside the grains. The microstructure of these samples changed with solution-annealing and the corrosion resistance was fairly improved with the time period of solution-annealing. Received: 2 September 1999 / Accepted: 6 September 1999 / Published online: 1 March 2000     

Kinematic segregation of granular mixtures in sandpiles

We study the segregation of granular mixtures in two-dimensional silos using a recently proposed set of coupled equations for surface flows of grains. We study the thick flow regime, where the grains are segregated in the rolling phase. We incorporate this dynamical segregation process, called kinematic sieving, free-surface segregation or percolation, into the theoretical formalism and calculate the profiles of the rolling species and the concentration of grains in the bulk in the steady state. Our solution shows the segregation of the mixture with the large grains being found at the bottom of the pile in qualitative agreement with experiments. Received: 6 July 1998 / Revised and Accepted: 13 August 1998     

A deterministic sandpile automaton revisited

The Bak-Tang-Wiesenfeld (BTW) sandpile model is a cellular automaton which has been intensively studied during the last years as a paradigm for self-organized criticality. In this paper, we reconsider a deterministic version of the BTW model introduced by Wiesenfeld, Theiler and McNamara, where sand grains are added always to one fixed site on the square lattice. Using the Abelian sandpile formalism we discuss the static properties of the system. We present numerical evidence that the deterministic model is only in the BTW universality class if the initial conditions and the geometric form of the boundaries do not respect the full symmetry of the square lattice. Received 19 August 1999     

A nonlinear model for aeolian sand ripples

Starting from the phenomenological model for sand ripple formation developed in [#!Bouchaud98!#], we proposed a new interpretation in the light of recent experiments. Furthermore, we derive, close to the threshold of ripple instability, a nonlinear equation for the spatio-temporal evolution of the sand bed profile, which to leading order has a quadratic nonlinearity. This equation is identical to that derived recently on the basis of geometry and conservation law [#!Csahok98!#]. Our derivation connects the coefficients of the nonlinear equation to the underlying physical mechanisms (reptation length...). This equation reveals ripple structures which then undergo a coarsening process, as observed in wind tunnel experiment. Small, fast moving ripples are absorbed by larger, slower forms resulting in a growth of the mean wavelength. Received 5 January 1999     

Discrete particle simulation of radial segregation in horizontally rotating drum: Effects of drum-length and non-rotating end-plates

The radial segregation phenomena of a mixture of two different size grains in a horizontal rotating drum are studied by DEM simulations. The grano-dynamics of radial segregation phenomena is examined as a function of the axial length and the friction between grains and not-rotating end-plates of the drum. The results indicate that, in the longer drums, the radial segregation ratio is higher and the friction on the end-plates shows little effect. Whereas in the shorter drums, the radial segregation is very slow or negligible; however, decreasing the friction on non-rotating end-plates increases the segregation ratio. If we increase the friction further (greater than the frictions between the grain-grain and the grains and the inner wall), the segregation ratio drops in the longer drums while in the shorter drums mixing is seen instead. The cause of these phenomena lies in the mechanism of diffusion in granular flows due to shearing strain by the end-plates. For more roughened end-plates, this shearing activity increases the granular temperature of the system and only the mixing can be observed instead of the segregation.     

Strain relaxation at cleaved surfaces studied by atomic force microscopy

Atomic force microscopy (AFM) in air is used to study the (110) cleaved surface of strained (100) In_xGa_1-xAs/ InP heterostructures for different compositions and thicknesses of the ternary compound layers. We find that the elastic strain relaxation induces a surface undulation of a few ? amplitude, even for very small misfits, provided the layers are thick enough. Using finite-element calculations of the strain relaxation near the cleaved edge, we reproduce quantitatively the AFM observations for compressive- as well as for tensile-strained layers with an accuracy better than 0.1 nm. This demonstrates the ability of AFM to quantify strain distributions by making use of surface profile measurements. Received: 9 November 1998 / Accepted: 11 March 1999 / Published online: 7 July 1999     

Porous structure of membranes of an acrylonitrile copolymer. Porosity, 1H-NMR permeability

Nanoporous polymer membranes (porosity ) used for dialysis are studied from NMR relaxation times of water confined in the pore space. Fast interpore water diffusion is observed. Two structural parameters are evidenced: i) a reduced NMR relaxation time, , which reflects the width of the pore-size distribution; ii) the average polymer-grain size of the solid matrix deduced from NMR experiments performed on membranes partially filled by water. A relation is found between the ratio , where k is the permeability to water and the porosity. This relation is in qualitative agreement with numerical simulations reported in the literature on low-porosity systems and with experimental results obtained for sedimentary rocks and for fused glass model systems. It supports the idea that is the relevant structural parameter to describe convective transport in a wide class of porous systems. Received 8 July 1999