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     

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     

倾斜沙漏流与颗粒休止角研究

本文发现在测量误差内颗粒物质的下列三个临界角度相等: 1)从直径为D的倾斜孔洞流出的Beverloo颗粒流的流量开始停止的临界倾角θ_c 向大孔径极限线性外推θ_c∞≡θ_c(D→∞) 的补角θ_s∞= 180°-θ_c∞;2) 从靠近堆顶的点源向光滑底板缓慢下落颗粒形成的圆锥形堆的休止角θ_r; 3) 直接剪切矩形颗粒固体测得的库仑内摩擦角φ. 该结果倾向支持倾斜孔洞和颗粒堆自由表面的固-液转变与颗粒固体内部的库仑屈服均来自材料的同一临界性质. 由于三种情况样品的内部应力和变形等都是目前还远不能定量分析的复杂非均匀分布, 我们仅从定性角度对此给出一些讨论.     

Boundary effects on the maximal angle of stability of a granular packing

We have studied the maximal angle of stability of a granular packing confined between two walls. The effect of the walls is to increase the angle dramatically. The decay of the angle with the distance between the walls is exponential with a characteristic length which is a function of the beads diameter. The effect of the roughness of the walls has been also studied. Received 1 April 1999     

Time of avalanche mixing of granular materials in a half filled drum

The avalanche mixing of granular solids in a slowly rotated 2D upright drum is studied. We demonstrate that the account of the difference δ between the angle of marginal stability and the angle of repose of the granular material leads to a restricted value of the mixing time τ for a half filled drum. The process of mixing is described by a linear discrete difference equation. We show that the mixing looks like linear diffusion of fractions with the diffusion coefficient vanishing when δ is an integer part of π. Introduction of fluctuations of δ suppresses the singularities of τ(δ) and smoothes the dependence τ(δ). Received 27 October 2000 and Received in final form 13 March 2001     

Characteristics of large three-dimensional heaps of particles produced by ballistic deposition from extended sources

Abstract

This paper reports a detailed numerical investigation of the geometrical and structural properties of three-dimensional heaps of particles. Our goal is the characterization of very large heaps produced by ballistic deposition from extended circular dropping areas. First, we provide an in-depth study of the formation of monodisperse heaps of particles. We find very large heaps to contain three new geometrical characteristics: they may display two external angles of repose, one internal angle of repose, and four distinct packing fraction (density) regions. Such features are found to be directly connected with the size of the dropping zone. We derive a differential equation describing the boundary of an unexpected triangular packing fraction zone formed under the dropping area. We investigate the impact that noise during the deposition has on the final heap structure. In addition, we perform two complementary experiments designed to test the robustness of the novel features found. The first experiment considers changes due to polydispersity. The second checks what happens when letting the extended dropping zone to become a point-like source of particles, the more common type of source.     

Affine turbulence

We present a generalization of the multiplicative model for velocity increments involving an affine process. The consequences on the shape of the probability distribution functions for the velocity increments are explored, and shown to be better compatible with the existence of a scale variation of the skewness. Received 29 March 1999 and Received in final form 14 September 1999     

Where does a cohesive granular heap break?

In this paper, we consider the effect of cohesion on the stability of a granular heap and compute the maximum angle of stability of the heap as a function of the cohesion. We show that the stability is strongly affected by the dependence of the cohesion on the local pressure. In particular, this dependence is found to determine the localization of the failure plane. While for a constant adhesion force, slip occurs deep inside the heap, surface failure is obtained for a linear variation of the cohesion on the normal stress. Such a transition allows to interpret some recent experimental results on cohesive materials.Received: 6 May 2004, Published online: 29 June 2004PACS: 45.70.-n Granular systems - 61.43.Gt Powders, porous materials     

Magnetisation of isolated single crystalline Fe-nanoparticles measured by a ballistic Hall micro-magnetometer

We present here the first magnetisation measurements on isolated single crystalline Fe-nanoparticles performed with a ballistic Hall micro-magnetometer. The measurements have a sensitivity of and thus provide us the possibility to study the mechanisms of magnetisation reversal in a single nanoparticle. The magnetic properties of the nanoparticles are influenced by their crystal structure and shape, and the presence of an oxide surface layer. They exhibit curling of the magnetic moments, but also a novel hysteresis behaviour. The spin configurations found for the system agree well with numerical calculations based on a Heisenberg Hamiltonian including the exchange and dipole interaction and surface anisotropy. Received: 1st September 1998 and Received in final form 21 June 1999     

X-ray scattering by nano-particles within granular thin films, investigation by grazing angle X-ray reflectometry

It is shown here that the observation of the phenomenon of like small angle scattering of X-rays in very thin heterogeneous films, can be made comparatively easily by using grazing angle reflectometry of X-rays. The feasibility was achieved with co-sputtered thin films of approximately 600 ? thickness, made up by crystalline platinum clusters embedded in an amorphous alumina matrix. The experimental reflectivity profiles are simulated by the intensity superposition of two components: (i) the specular part caused by the usual interference phenomenon between the partial waves reflected from the air-film and film-substrate interfaces, and (ii) the like-small angle scattering part due to diffraction by platinum clusters. It is found that the shape of such clusters is spherical characterized by mean values of diameter and inter-cluster distance of the order 29 ? and 45 ? respectively with standard deviations and of the order of 3 ?. Such an observation of both the interference and diffraction phenomena indicates that the thin granular film exhibits both its continuous and heterogeneous aspects together. Received: 19 February 1998 / Accepted: 25 August 1998     

Droplet suction on porous media

We study the forced aspiration of small ( mm) and large ( cm) liquid drops, deposited on prewetted porous membranes, and pumped mechanically with a constant current J. Two kinds of membranes are used where the pores are i) disconnected, cylindrical and calibrated or ii) interconnected “sponge-like”. Whatever the size of the drops and the intensity J of the current, two suction regimes are observed versus time: 1) a “locked” regime, when the drop is pinned, with a dynamic contact angle decreasing from advancing () to finite receding () contact angle; 2) an “unlocked” regime, where the contour line recedes with a constant contact angle closed to . In both regimes, the shape of the drop remains quasistatic, during the suction process, i.e. a spherical cap for small drops and a flat “gravity pancake” for large ones. Received 19 January 2000     

Fluid membranes in hydrodynamic flow fields: Formalism and an application to fluctuating quasispherical vesicles in shear flow

The dynamics of a single fluid bilayer membrane in an external hydrodynamic flow field is considered. The deterministic equation of motion for the configuration is derived taking into account both viscous dissipation in the surrounding liquid and local incompressibility of the membrane. For quasi-spherical vesicles in shear flow, thermal fluctuations can be incorporated in a Langevin-type equation of motion for the deformation amplitudes. The solution to this equation shows an overdamped oscillatory approach to a stationary tanktreading shape. Inclination angle and ellipticity of the contour are determined as a function of excess area and shear rate. Comparisons to numerical results and experiments are discussed. Received 20 August 1998     

Microscopic membrane elasticity and interactions among membrane inclusions: interplay between the shape, dilation, tilt and tilt-difference modes

A phenomenological Landau elasticity for the shape, dilation, and lipid-tilt of bilayer membranes is developed. The shape mode couples with the sum of the monolayers' tilt, while the dilation mode couples with the difference of the monolayers' tilts. Interactions among membrane inclusions within regular arrays are discussed. Inclusions modifying the membrane thickness and/or inducing a tilt-difference due to their convex or concave shape yield a dilation-induced attraction and a tilt-difference-induced repulsion. The resulting interaction can stabilize 2D crystal phases, with the possible coexistence of different lattice spacings when the dilation-tilt-difference coupling is large. Inclusions favoring crystals are those with either a long-convex or a short-concave hydrophobic core. Inclusions inducing a local membrane curvature due to their conical shape repel one another. At short inclusions separations, a tilt comparable with the inclusion's cone angle develops: it relaxes the membrane curvature and reduces the repulsion. At large separations the tilt vanishes, whatever the value of the shape-tilt coupling. Received 23 October 1998 and Received in final form 12 January 1999     

Optical response of thin plasma-polymer films with non-spherical silver nanoparticles

The size and shape of silver nanoparticles which are embedded in a plasma-polymer matrix were obtained by transmission electron microscopy and analyzed with optical image processing. We used a sample in which silver particles were present before and after reshaping caused by thermal annealing in adjacent regions. As most of the particles appeared as elongated rotational ellipsoids, the major and minor half axis were determined for each particle. We adopted the model of Gans in the Rayleigh approximation to calculate for each investigated particle the extinction spectra from to using the data from the image processing. The various spectra for 368 silver particles were added to get total extinction spectra for the sample as deposited and after reshaping, respectively. We found good agreement with the experimental spectra. The blue shift of the plasma-resonance absorption, which occurs due to the reshaping of the silver particles during thermal annealing, was also confirmed by using only changes in the particle sizes and shapes. Received: 23 July 1997 / Revised: 27 October 1997 / Accepted: 3 December 1997     

Rolling as a “continuing collision”

We show that two basic mechanical processes, the collision of particles and rolling motion of a sphere on a plane, are intimately related. According to our recent findings, the restitution coefficient for colliding spherical particles , which characterizes the energy loss upon collision, is directly related to the rolling friction coefficient for a viscous sphere on a hard plane. We quantify both coefficients in terms of material constants which allows to determine either of them provided the other is known. This relation between the coefficients may give rise to a novel experimental technique to determine alternatively the coefficient of restitution or the coefficient of rolling friction. Received 5 May 1999     

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     

The topological structure of 2D disordered cellular systems

We analyze the structure of two dimensional disordered cellular systems generated by extensive computer simulations. These cellular structures are studied as topological trees rooted on a central cell or as closed shells arranged concentrically around a germ cell. We single out the most significant parameters that characterize statistically the organization of these patterns. Universality and specificity in disordered cellular structures are discussed. Received: 23 September 1997 / Received in final form: 14 January 1998 / Accepted: 29 January 1998     

Statics and dynamics of a single ferrofluid-peak

We consider a single peak of a ferrofluid resulting from the Rosensweig instability for a small fluid container. Minimizing the total energy of the system by a variational method we determine the shape of the peak in a static field as well as the characteristics of the subcritical bifurcation leading to its formation. The latter are in very good agreement with experiment. Generalizing the approach to dynamic situations we qualitatively reproduce the complicated subharmonic response of the peak to an oscillating part in the external magnetic field found in recent experiments. Received 14 December 1999 and Received in final form 31 May 2000     

Model of populations colonizing a new habitat

We propose a model suitable for investigating the conditions under which a population, adapted to a given environment, may colonize a new neighbouring, spatially separated, habitat. We find out how similar the two regions must be for such a colonization to succeed and what will be the spatial distribution of genetic pools of the two populations after the process. It is found that between the two populations each adapted to the different region, a hybrid zone, characterized by increased heterozygosity, may be formed. The dependence of the shape of the hybrid zone on the external (environmental) parameters is determined. When the differences between the two regions are significant, the populations are separated by a depopulated zone. We show that the conditions in the colonized habitat influence the genetic pool of the population living in the first region. Computer simulations based on the standard Monte Carlo technique are used. Received 11 December 1998 and Received in final form 17 December 1998     

Doubly excited states in the negative hydrogen ion

We present a detailed analysis of doubly excited resonances in H^- of both and symmetry. Both resonance positions and total widths for auto-detachment are calculated using complex coordinate scaling in a Sturmian-type basis in perimetric coordinates. The resonances are classified by approximate quantum numbers with help of their Lewis structures. For the first time, a new class of shape resonances is reported which can be understood as resulting from couplings between different adiabatic potentials with both binding and repulsive character. In addition, we present an analysis of the so called mass polarisation term which gives rise to specific isotope shifts. Received 10 March 1999 and Received in final form 18 October 1999