Hydrodynamic model for a dynamical jammed-to-flowing transition in gravity driven granular media

Granular material on an inclined plane will flow like a fluid if the angle theta the plane makes with the horizontal is large enough. We study chute flow down a plane using a hydrodynamic model previously used to describe granular Couette flow. Our model predicts a jammed-to-flowing transition as theta is increased even though it does not include solid friction, which might seem necessary to stabilize a state without flow. The transition is driven by coupling between mean and fluctuating velocity. In agreement with experiments and simulations, it predicts flow for layers with a thickness H larger than a critical value H(stop)(theta) and absence of flow for H相似文献   

Buchdahl limit for <Emphasis Type="Italic">d</Emphasis>-dimensional spherical solutions with a cosmological constant

We investigate the conditions for which a d-dimensional perfect fluid solution is in hydrostatic equilibrium with a cosmological constant. We find a generalization of Buchdahl inequality and obtain an upper bound for the degree of compactification. Using the Tolman–Oppenheimer–Volkoff equation to get a lower bound for the degree of compactification we analyse the regions where the solution is in hydrostatic equilibrium. We obtain the inner metric solution and the pressure for the constant fluid density model.     

准静态颗粒流流动规律的热力学分析

本文分析了颗粒流的介观结构及其特征,提出了颗粒流的双颗粒温度概念Tkin和Tconf,表征颗粒无序运动和构型无序演化的程度;进而作为非平衡变量,与经典非平衡热力学(classical irreversible thermodynamics,CIT)变量共同构成颗粒流的热力学状态变量集,确定了颗粒流的能量转换规律和熵产生率等,发展了颗粒流双颗粒温度(two granular temperate,TGT)模型.以体积恒定的简单剪切准静态颗粒流为例,结合离散元模拟(discrete element method,DEM),确定了双颗粒温度模型所需的材料参数,分析了颗粒流发展段的规律和稳恒段的有效摩擦系数.     

Cumulative author index of Volumes 351 to 360

The dynamic evolution of granular gases is fundamentally different from molecular gases due to the energy loss during collisions. Nevertheless techniques of kinetic theory are useful in a regime, when the granular particles are moving rapidly and the gas is sufficiently dilute. In these lecture notes we analyse in detail the collision of two rough particles which is inelastic due to incomplete normal and tangential restitution as well as Coulomb friction. Based on the Walton model a time evolution operator for the many particle system is introduced, a formalism which is well suited for simple approximations. We discuss free cooling of granular particles with particular emphasis on the exchange of energy between rotational and translational degrees of freedom.     

Density inversion in rapid granular flows: the supported regime

This paper presents numerical findings on rapid 2D and 3D granular flows on a bumpy base. In the supported regime studied here, a strongly sheared, dilute and agitated layer spontaneously appears at the base of the flow and supports a compact packing of grains moving as a whole. In this regime, the flow behaves like a sliding block on the bumpy base. In particular, for flows on a horizontal base, the average velocity decreases linearly in time and the average kinetic energy decreases linearly with the travelled distance, those features being characteristic of solid-like friction. This allows us to define and measure an effective friction coefficient, which is independent of the mass and velocity of the flow. This coefficient only loosely depends on the value of the micromechanical friction coefficient whereas the infuence of the bumpiness of the base is strong. We give evidence that this dilute and agitated layer does not result in significantly less friction. Finally, we show that a steady regime of supported flows can exist on inclines whose angle is carefully chosen.     

Backscattering in the vicinity of a mode cutoff

Abstract

In a recent paper to this journal (Whitman A M et al 2003 Waves Random Media 13 269–86) we derived a set of coupled equations that describe the intermodal scattering of acoustic radiation in a duct whose speed of sound varies randomly in space and time. In the paper we were mainly interested in modes that were not near cutoff. Here we study the solution of these equations in the vicinity of the cutoff. We find that near cutoff almost all the energy is reflected back independent of the other duct parameters. In addition to presenting these results, we analyse the mathematical structure of the equations in these regions in order to elucidate the reason for this behaviour.     

Shear zones and wall slip in the capillary flow of concentrated colloidal suspensions

We image the flow of a nearly random close packed, hard-sphere colloidal suspension (a "paste") in a square capillary using confocal microscopy. The flow consists of a "plug" in the center while shear occurs localized adjacent to the channel walls, reminiscent of yield-stress fluid behavior. However, the observed scaling of the velocity profiles with the flow rate strongly contrasts yield-stress fluid predictions. Instead, the velocity profiles can be captured by a theory of stress fluctuations originally developed for chute flow of dry granular media. We verified this both for smooth and rough walls.     

Monodisperse dry granular flows on inclined planes: Role of roughness

Recent studies have pointed out the importance of the basal friction on the dynamics of granular flows. We present experimental results on the influence of the roughness of the inclined plane on the dynamics of a monodisperse dry granular flow. We found experimentally that there exists a maximum of the friction for a given relative roughness. This maximum is shown to be independent of the slope angle. This behavior is observed for four planes with different bump sizes (given by the size of the beads glued on the plane) from 200 m to 2 mm. The relative roughness corresponding to the maximum of the friction can be predicted with a geometrical model of stability of one single bead on the plane. The main parameters are the size of the bumps and the size of the flowing beads. In order to obtain a higher precision, the model also takes into account the spacing between the bumps of the rough plane. Experimental results and model are in good agreement for all the planes we studied. Other parameters, like the sphericity of the beads, or irregularities in the thickness of the layer of glued particles, are shown to be of influence on the friction.     

Evaluation of the translational and rotational diffusion coefficients of a cubic particle (for the application to Brownian dynamics simulations)

By estimating the force and torque acting on the cube for the two cases of a uniform flow field and a rotational flow field, we have discussed whether or not there is a coupling between the translational and the rotational motion. From the characteristics of the friction coefficients, we may understand that there is no coupling between the translation motion and the rotational motion in the situation of the Reynolds number being sufficiently smaller than unity. In contrast, in the case of a non-slow flow field with the Reynolds number larger than unity, the coupling characteristics of the motion of a cube is certainly recognised and therefore the interaction with the ambient fluid is characterised by a variety of friction coefficients including friction coefficients that relate the forces acting on the cube to the angular velocities of the rotational motion. Hence, the employment of these translational and rotational diffusion coefficients for a cube enables the implementation of Brownian dynamics simulations for a suspension composed of cubic particles in order to analyse the dynamic characteristics of a cubic particle suspension.

Highlights

1. We have considered a flow problem around a cube in order to numerically clarify the characteristics of the translational and rotational friction or diffusion coefficients.

2. In a slow flow field the motion of the cube need only to be characterised by two friction coefficients, i.e. the translational and rotational friction coefficients.

3. In the case of a non-slow flow field, the coupling characteristics between the translational motion and the rotational motion are recognised.

4. Employment of these diffusion coefficients enables the implementation of Brownian dynamics simulations for a suspension composed of cubic particles.

     

Random Loose Packing in Granular Matter

We introduce and simulate a two-dimensional Edwards-style model of granular matter at vanishing pressure. The model incorporates some of the effects of gravity and friction, and exhibits a random loose packing density whose standard deviation vanishes with increasing system size, a phenomenon that should be verifiable for real granular matter. Research of the second named author was supported in part by NSF Grant DMS-0700120.     

Thermoconvective flow velocity in a high-speed magnetofluid seal after it has stopped

Convective flow is investigated in the high-speed (linear velocity of the shaft seal is more than 1 m/s) magnetofluid shaft seal after it has been stopped. Magnetic fluid is preliminarily heated due to viscous friction in the moving seal. After the shaft has been stopped, nonuniform heated fluid remains under the action of a high-gradient magnetic field. Numerical analysis has revealed that in this situation, intense thermomagnetic convection is initiated. The velocity of magnetic fluid depends on its viscosity. For the fluid with viscosity of 2 × 10^?4 m²/s the maximum flow velocity within the volume of magnetic fluid with a characteristic size of 1 mm can attain a value of 10 m/s.     

Polymeric particle dampers under steady-state vertical vibrations

Numerical and experimental studies are made of the power dissipated by a granular medium as it undergoes sinusoidal vibrations in the same direction as gravity. The granular medium consists of spherical elastomeric particles that partially fill a box with rectangular cross section whose walls are made of thick blocks of Perspex. Simulations are obtained using a three-dimensional Discrete Element Method code. In order to find input parameters for use in the simulation studies, a specially designed test rig is used to measure the loss factor and dynamic stiffness of the particles. The power dissipation of the granular medium obtained from simulation is compared with that from a physical experiment and found to be in good agreement. The sensitivity of power dissipation to amplitude, frequency of excitation and friction coefficient is investigated.     

Dilatancy and friction in sheared granular media

We introduce a simple model to describe the frictional properties of granular media under shear. We model the friction force in terms of the horizontal velocity and the vertical position z of the slider, interpreting z as a constitutive variable characterizing the contact. Dilatancy is shown to play an essential role in the dynamics, inducing a stick-slip instability at low velocity. We compute the phase diagram, analyze numerically the model for a wide range of parameters and compare our results with experiments on dry and wet granular media, obtaining a good agreement. In particular, we reproduce the hysteretic velocity dependence of the frictional force. Received 16 November 1999     

Evolution of Energy in Submerged Granular Column Collapse

The evolution of energy in subaerial and subaqueous granular column collapses is studied.Employing the refractive index matching method and planar laser-induced fluorescence technique,we obtain granular and liquid images simultaneously in a single experiment of subaqueous flow.Particle image velocimetry and particle tracking velocimetry are used to process the data for the fluid and granular phase.We find stepwise decreases in the total kinetic energy of the granular material.The stage of rapidly falling energy corresponds to large transverse changes in the direction of the massive granular particles.Moreover,in this stage,a major fraction of the granular kinetic energy transferred from the granular potential energy is lost or transferred.Interestingly,compared with dry granular flow,the existence of an ambient liquid seems to reduce the total dissipated energy,which may be the reason why previous studies observed similar granular runout distances in subaqueous and dry granular collapses.     

Thermodynamics and transport in an active Morse ring chain

We investigate the stochastic dynamics of an one-dimensional ring with N self-driven Brownian particles. In this model neighboring particles interact via conservative Morse potentials. The influence of the surrounding heat bath is modeled by Langevin-forces (white noise) and a constant viscous friction coefficient γ. The Brownian particles are provided with internal energy depots which may lead to active motions of the particles. The depots are realized by an additional nonlinearly velocity-dependent friction coefficient γ ₁(v) in the equations of motions. In the first part of the paper we study the partition functions of time averages and thermodynamical quantities (e.g. pressure) characterizing the stationary physical system. Numerically calculated non-equilibrium phase diagrams are represented. The last part is dedicated to transport phenomena by including a homogeneous external force field that breaks the symmetry of the model. Here we find enhanced mobility of the particles at low temperatures. Received 21 July 2001     

Phase transitions in shear-induced segregation of granular materials

We computationally study shear-induced segregation of different-sized particles in vertical chute flow. We find that, for low solid fractions, large particles segregate toward regions of low shear rates where the granular temperature (velocity variance) is low. As the solid fraction increases, this trend reverses, and large particles segregate toward regions of high shear rates and temperatures. We find that this is a global phenomenon: local segregation trends reverse at high system solid fractions even where local solid fractions are small. The reversal corresponds to the growth of a single enduring cluster of 30%-60% of the particles that we propose changes the segregation dynamics.     

Collisional granular flow as a micropolar fluid

We show that a micropolar fluid model successfully describes collisional granular flows on a slope. A micropolar fluid is the fluid with internal structures in which coupling between the spin of each particle and the macroscopic velocity field is taken into account. It is a hydrodynamical framework suitable for granular systems which consists of particles with macroscopic size. We demonstrate that the model equations can quantitatively reproduce the velocity and the angular velocity profiles obtained from the numerical simulation of the collisional granular flow on a slope using a simple estimate for the parameters in the theory.     

The memory of granular materials

Granular materials exhibit a complex variety of fluid and solid collective regimes which has led researchers to consider them as a new state of matter all on its own. In this paper we investigate the behaviour of granular materials by means of Hurst rescaled range analysis. We analyse records in time of the angle of the slope of granular materials partially filling a rotating drum and records of the local backscattered light from fluidized beds. We show that the Hurst analysis is able to identify phase transitions as well as to characterize spatio-temporal structures. The influence of interparticle attractive interactions on the memory of granular materials is also investigated.     

Shear instabilities in granular mixtures

Dynamical instabilities in fluid mechanics are responsible for a variety of important common phenomena, such as waves on the sea surface or Taylor vortices in Couette flow. In granular media dynamical instabilities have just begun to be discovered. Here we show by means of molecular dynamics simulation the existence of a new dynamical instability of a granular mixture under oscillating horizontal shear, which leads to the formation of a striped pattern where the components are segregated. We investigate the properties of such a Kelvin-Helmholtz-like instability and show how it is connected to pattern formation in granular flow and segregation.