Devang Vipin Khakhar

This study explores the dynamics of a spherical intruder impacting a vertically vibrated granular bed using discrete element method (DEM) simulations. The system consists of 25,000 particles contained in a box with sinusoidal bottom wall vibrations ranging from 25 to 500 Hz. The intruder is dropped from a fixed height with varying initial velocities. Results show that the vibration frequency and initial velocity significantly influence the intruder’s penetration depth and hence the final resting position. Lower vibration frequencies allow deeper penetration due to reduced granular agitation, while higher impact velocities enhance penetration through increased momentum.

Hoppers are among the most widely used equipment for granular material processing in industry. We present experimental and DEM simulation results for the flow of granular material in wedge-shaped hoppers. The predictions of theory of Savage for a wedge-shaped hopper with frictionless walls and a theory using the μ–I rheology, are compared to DEM simulation results. The μ–I rheology gives a very good match to the simulation results. The velocity field in a quasi-2D wedge-shaped hopper, with front and back glass walls, is obtained experimentally using image analysis and particle tracking. We find that the radial velocity in cylindrical coordinates varies as v _r ∝ θ ² , and that the tangential velocity is non-zero, but much smaller than the radial velocity. The experimental velocity distributions closely match the DEM simulation results using calibrated parameters. DEM simulations without the front and back walls yield qualitatively similar results to the quasi- 2D case. Analysis of the flow in the exit region indicates that velocity varies smoothly over the domain and a free fall arch is not evident. The vertical acceleration data indicate that the particles experience free fall only a significant distance below the exit plane. The acceleration is larger than the acceleration due to gravity near the exit, which is explained in terms of an arch-buckling mechanism.

We study the size-based segregation in a vertically oscillating box with a sloped base connecting two flat regions at different elevations, as shown in Figure 2. Some boulders (large size) are placed at random positions inside the box, which is filled with grains (small size) to a certain depth. On vertical oscillation of the box for a long time, boulders segregate towards the flat portion at higher elevation. We attempt to understand this experimental observation by studying the velocity profile of grains and boulder trajectories through Discrete Element Method (DEM) simulations.

The shear flow of granular materials is studied in the presence of overburden pressure and gravity using the discrete element method. The system comprises particles confined between parallel walls moving with constant speed in opposite directions and with an overburden pressure applied on the top wall, which is free to move in the wall-normal direction. The overburden pressures are high enough that the stored elastic energy due to compression of the particles is significant. The variation in the average velocity, solid volume fraction, and fluctuation velocity profiles with overburden pressure is shown. For most of the overburden pressures, a coexistence of a sheared region and a pluglike region is observed. As the overburden pressure increases, a flow transition is observed from a plug in the lower region to a plug in the upper region. At intermediate overburden pressures, a wide shear zone and a fluctuating profiles are observed. The transition is found to be continuous with increasing overburden pressure, and a scaling relation for the average midplane velocity variation with pressure is obtained for different wall velocities and particle stiffness values. Analysis of different configurations of the system show that the pluglike region forms near the fluctuating wall, where pressure is applied. The instantaneous velocity profile is found to vary chaotically with time at intermediate pressures. The midline velocity distribution is found to be Gaussian in most of the cases studied with a higher standard deviation at the intermediate pressures and lower wall velocities. The work highlights the nonlinear behavior of granular shear flow as a result of overburden pressure, which includes multiplicity and chaotic velocities.

We consider the effects of temperature anisotropy in a quiescent, hard sphere gas, as a model system for flowing granular matter. Utilising kinetic theory we obtain expressions for the streaming pressure, collisional pressure and the rate of transfer of kinetic energy between the different translational degrees of freedom, assuming a Maxwell-Boltzmann velocity distribution and an isotropic pair correlation function at contact. A theory for the collisional pressure with an anisotropic pair correlation function is also presented. Event driven simulations are carried out for frictionless, elastic, hard spheres, using a thermostat that maintains a different temperature in one of the coordinate directions. The pair correlation function, the velocity distribution function, streaming and collisional pressures, and the rate of energy transfer are computed in the simulations for different temperature anisotropy values. The pair correlation function becomes significantly anisotropic with increasing temperature anisotropy and solid fraction. The streaming pressure and the energy transfer rate are well described by the theory based on the isotropic pair correlation function. The predictions of this theory for the collisional pressure match well with the results of the simulations for a solid fraction of 0.1, but increasing deviations are obtained for higher solid fractions. The theory incorporating the anisotropy in the pair correlation function gives good predictions of the collisional pressure for all the solid fractions considered. The work shows the importance of incorporating the anisotropy in the pair correlation function in kinetic theories for systems with temperature anisotropy.

Poly(vinylidene fluoride) (PVDF) is a piezoelectric polymer, with the crystalline β-phase having the highest polarity among all its phases. A multistage transformation process is developed, using molecular dynamics simulations, to compute the free energy difference between α- and β-phases of PVDF. Methods of free energy perturbation and Jarzynski's equality were used to determine Helmholtz free energy change, ΔF, for the individual stages, from which the Gibbs free energy difference, ΔG, between the α- and β-phases was calculated. Infinitely large crystals modeled using periodic boundaries with 36 chains and 12 monomers in each chain were used for the study. All-atom simulations were performed with the force fields previously developed for PVDF. In concurrence with experimental observations, the α-phase was found to be thermodynamically more stable at normal temperature and pressure conditions. The β-phase was found to be more stable at high and low temperatures and high pressure.

Granular surface flows are frequently encountered in nature as well as during handling of powders in different industries. An experimental study of granular surface flow on a heap is carried out. The heap is formed by pouring nearly monodisperse spherical particles from the rectangular slit orifice of a hopper on a rough rectangular plate. A flow of particles is developed on the heap surface, which is planar in the central region, with particles flowing over the edge of the plate into a collection chamber. The geometry considered in this study is an example of a fully three-dimensional heap without side walls. The surface velocities of the particles are measured using high-speed videography and particle tracking velocimetry for different mass flow rates with steel balls and glass beads of two different sizes, for heaps of different aspect ratios. The flow is uni-directional and fully developed in a central zone on the heap surface. The flowing layer thickness is measured in this zone by immersing a soot-coated blade into the flow. The angle of inclination of the free surface of the heap is found to be nearly constant for a ten-fold increase of the mass flow rate. The scaled flowing layer thickness is found to vary linearly with the scaled flow rate and the data for all the particles collapse to a single line over a ten-fold increase in the scaled flow rate and an increase in the aspect ratio of the heap by a factor of 1.75. The predicted scaled surface velocity and scaled shear rate using this correlation match the measured values.