Kuniyasu Saitoh

Effect of cohesion on shear banding in quasistatic granular materials.

Cohesive powders have widely different bulk behavior due to their peculiar interactions. We use discrete element simulations to investigate the effect of contact cohesion on the steady state flow of dense powders in a slowly sheared split-bottom Couette cell, which imposes a wide stable shear band. The intensity of cohesive forces can be quantified by the granular Bond number (Bo), namely the ratio between maximum attractive force and average force due to external compression. We find that the shear banding phenomenon is almost independent of cohesion for Bond numbers Bo<1, however for Bo≥1 cohesive forces start to play an important role, as both width and center position of the band increase. Inside the shear band, the mean normal contact force is independent of cohesion and depends only on the confining stress. In contrast, when the behavior is analyzed focusing on the eigendirections of the local strain rate tensor, a dependence on cohesion shows up. Forces carried by contacts along the compressive and tensile directions are symmetric about the mean force (larger and smaller respectively), while the force along the third, neutral direction follows the mean force. This anisotropy of the force network increases with cohesion, just like the heterogeneity in all (compressive, tensile and neutral) directions.

Role of gravity or confining pressure and contact stiffness in granular rheology

The steady-state shear rheology of granular materials is investigated in slow quasistatic and inertial flows. The effect of gravity (thus the local pressure) and the often-neglected contact stiffness are the focus of this study. A series of particle simulations are performed on a weakly frictional granular assembly in a split-bottom geometry considering various magnitudes of gravity and contact stiffnesses. While traditionally the inertial number, i.e., the ratio of stress to strain-rate time scales, is used to describe the flow rheology, we report that a second dimensionless number, the ratio of softness and stress time scales, must also be included to characterize the bulk flow behavior. For slow, quasistatic flows, the density increases while the effective (macroscopic) friction decreases with increase in either particle softness or local pressure. This trend is added to the

Negative Normal Restitution Coefficient Found in Simulation of Nanocluster Collisions

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Simulation of cohesive fine powders under a plane shear

rheology and can be traced back to the anisotropy in the contact network, displaying a linear correlation between the effective friction coefficient and deviatoric fabric in the steady state. When the external rotation rate is increased towards the inertial regime, for a given gravity field and contact stiffness, the effective friction increases faster than linearly with the deviatoric fabric.

Weakly nonlinear analysis of two dimensional sheared granular flow

The oblique impacts of nanoclusters are studied theoretically and by means of molecular dynamics. In simulations we explore two models--Lennard-Jones clusters and particles with covalently bonded atoms. In contrast with the case of macroscopic bodies, the standard definition of the normal restitution coefficient yields for this coefficient negative values for oblique collisions of nanoclusters. We explain this effect and propose a proper definition of the restitution coefficient which is always positive. We develop a theory of an oblique impact based on a continuum model of particles. A surprisingly good agreement between the macroscopic theory and simulations leads to the conclusion that macroscopic concepts of elasticity, bulk viscosity, and surface tension remain valid for nanoparticles of a few hundred atoms.

Kinetic theory for dilute cohesive granular gases with a square well potential

Three-dimensional molecular-dynamics simulations of cohesive dissipative powders under a plane shear are performed. We find the various phases depending on the dimensionless shear rate and the dissipation rate as well as the density. We also find that the shape of clusters depends on the initial condition of velocities of particles when the dissipation is large. Our simple stochastic model reproduces the non-Gaussian velocity distribution function appearing in the coexistence phase of a gas and a plate.

Simulation of Depositions of a Lennard-Jones Cluster on a Crystalline Surface

Weakly nonlinear analysis of a two dimensional sheared granular flow is carried out under the Lees-Edwards boundary condition. We derive the time dependent Ginzburg–Landau equation of a disturbance amplitude starting from a set of granular hydrodynamic equations and discuss the bifurcation of the steady amplitude in the hydrodynamic limit.

Quantitative test of the time dependent Gintzburg-Landau equation for sheared granular flow in two dimensions

We develop the kinetic theory of dilute cohesive granular gases in which the attractive part is described by a square well potential. We derive the hydrodynamic equations from the kinetic theory with the microscopic expressions for the dissipation rate and the transport coefficients. We check the validity of our theory by performing the direct simulation Monte Carlo.

Collective motion of macroscopic spheres floating on capillary ripples: dynamic heterogeneity and dynamic criticality.

Depositions of amorphous Lennard-Jones clusters on a crystalline surface are numerically investigated. From the results of the molecular dynamics simulation, we found that the deposited clusters exhibit a transition from multilayered adsorption to monolayered adsorption at a critical incident speed. Employing the energy conservation law, we can explain the behavior of the ratio of the number of atoms adsorbed on the substrate to the cluster size. The boundary shape of the deposited cluster depends strongly on the incident speed, and some unstable modes grow during the spread of the deposited cluster on the substrate. We also discuss the wettability between different Lennard-Jones atoms. Subject Index: 023, 331, 335, 545

Time Dependent Ginzburg-Landau Equation for Sheared Granular Flow

We examine the validity of the time-dependent Ginzburg-Landau equation of granular fluids for a plane shear flow under the Lees-Edwardsboundary condition derivedfrom a weakly nonlinear analysis through the comparison with the result of discrete element method.We verify quantitative agreements in the time evolution of the area fraction and the velocityfields, and also find qualitative agreement in the granular temperature.