Convection in vibrated annular granular beds

The response to vibration of a granular bed, consisting of a standard cylindrical geometry but with the addition of a dissipative cylindrical inner wall, has been investigated both experimentally (using positron emission particle tracking) and numerically (using hard sphere molecular dynamics simulation). The packing fraction profiles and granular temperature distributions (in both vertical and horizontal directions) were determined as a function of height and distance from the axis. The two sets of results were in reasonable agreement. The molecular dynamics simulations were used to explore the behavior of the granular bed in the inner wall-outer wall coefficient of restitution phase space. It was observed that one could control the direction of the toroidal convection rolls by manipulating the relative dissipation at the inner and outer walls via the coefficients of restitution, and with several layers of grains it was seen that double convection rolls could also be formed, a result that was subsequently confirmed experimentally.

Anisotropic energy distribution in three-dimensional vibrofluidized granular systems

We examine the energy flows in a three-dimensional model of a granular system consisting of N inelastic hard spheres contained in an open cylinder of radius R under the influence of gravity. Energy is supplied to the system in the vertical direction by a vibrating base and is transferred to the perpendicular directions through particle-particle collisions. We examine how the local and global dissipation of energy by particle-particle and particle-wall collisions depends on the number of particles, the velocity of the vibrating base, and the restitution coefficients.

Mass and size effects in three-dimensional vibrofluidized granular mixtures

We examine the steady state properties of binary systems of driven inelastic hard spheres. The spheres, which move under the influence of gravity, are contained in a vertical cylinder with a vibrating base. We computed the trajectories of the spheres using an event-driven molecular dynamics algorithm. In the first part of the study, we chose simulation parameters that match those of experiments published by Wildman and Parker. Various properties computed from the simulation including the density profile, granular temperature, and circulation pattern are in good qualitative agreement with the experiments. We then studied the effect of varying the mass ratio and the size ratio independently while holding the other parameters constant. The mass and size ratio are shown to affect the distribution of the energy. The changes in the energy distributions affect the packing fraction and temperature of each component. The temperature of the heavier component has a nonlinear dependence on the mass of the lighter component, while the temperature of the lighter component is approximately proportional to its mass. The temperature of both components is inversely dependent on the size of the smaller component.

Stochastic simulation of the partition mechanism with a heterogeneous surface phase

A three-dimensional stochastic model of chromatography has been used to determine the effect of multiple sites on the partition mechanism. The effect of additional sites on mass transfer rates, zone profiles, and their statistical moments are investigated as a function of the partition coefficient, diffusion coefficient, and interfacial barrier to mass transfer. These studies have demonstrated that changes in the partition coefficient alone are not sufficient to alter the system response from that of a single site. Changes in the diffusion coefficient and the barrier to mass transfer do cause changes in the response compared to that of a single site. The zone profiles produced by the systems become more asymmetric as the difference between the diffusion coefficients or the barriers to mass transfer increases. The site with the slower mass transfer rate plays the dominant role in the total system response.