Diffusion of a granular pulse in a rotating drum

The diffusion of a pulse of small grains in an horizontal rotating drum is studied through discrete elements methods simulations. We present a theoretical analysis of the diffusion process in a one-dimensional confined space in order to elucidate the effect of the confining end-plate of the drum. We then show that the diffusion is neither subdiffusive nor superdiffusive but normal. This is demonstrated by rescaling the concentration profiles obtained at various stages and by studying the time evolution of the mean squared deviation. Finally we study the self-diffusion of both large and small grains and we show that it is normal and that the diffusion coefficient is independent of the grain size

Lateral migration of a 2D vesicle in unbounded Poiseuille flow

The migration of a suspended vesicle in an unbounded Poiseuille flow is investigated numerically in the low Reynolds number limit. We consider the situation without viscosity contrast between the interior of the vesicle and the exterior. Using the boundary integral method we solve the corresponding hydrodynamic flow equations and track explicitly the vesicle dynamics in two dimensions. We find that the interplay between the nonlinear character of the Poiseuille flow and the vesicle deformation causes a cross-streamline migration of vesicles towards the center of the Poiseuille flow. This is in a marked contrast with a result [L.G. Leal, Ann. Rev. Fluid Mech. 12, 435(1980)]according to which the droplet moves away from the center (provided there is no viscosity contrast between the internal and the external fluids). The migration velocity is found to increase with the local capillary number (defined by the time scale of the vesicle relaxation towards its equilibrium shape times the local shear rate), but reaches a plateau above a certain value of the capillary number. This plateau value increases with the curvature of the parabolic flow profile. We present scaling laws for the migration velocity.Comment: 11 pages with 4 figure

Heap Formation in Granular Media

Using molecular dynamics (MD) simulations, we find the formation of heaps in a system of granular particles contained in a box with oscillating bottom and fixed sidewalls. The simulation includes the effect of static friction, which is found to be crucial in maintaining a stable heap. We also find another mechanism for heap formation in systems under constant vertical shear. In both systems, heaps are formed due to a net downward shear by the sidewalls. We discuss the origin of net downward shear for the vibration induced heap.Comment: 11 pages, 4 figures available upon request, Plain TeX, HLRZ-101/9

Subdiffusive axial transport of granular materials in a long drum mixer

Granular mixtures rapidly segregate radially by size when tumbled in a partially filled horizontal drum. The smaller component moves toward the axis of rotation and forms a buried core, which then splits into axial bands. Models have generally assumed that the axial segregation is opposed by diffusion. Using narrow pulses of the smaller component as initial conditions, we have characterized axial transport in the core. We find that the axial advance of the segregated core is well described by a self-similar concentration profile whose width scales as $t^\alpha$, with $\alpha \sim 0.3 < 1/2$. Thus, the process is subdiffusive rather than diffusive as previously assumed. We find that $\alpha$ is nearly independent of the grain type and drum rotation rate within the smoothly streaming regime. We compare our results to two one-dimensional PDE models which contain self-similarity and subdiffusion; a linear fractional diffusion model and the nonlinear porous medium equation.Comment: 4 pages, 4 figures, 1 table. Submitted to Phys Rev Lett. For more info, see http://www.physics.utoronto.ca/nonlinear

Recent advancements in monolithic AlGaAs/GaAs solar cells for space applications

High efficiency, two terminal, multijunction AlGaAs/GaAs solar cells were reproducibly made with areas of 0.5 sq cm. The multiple layers in the cells were grown by Organo Metallic Vapor Phase Epitaxy (OMVPE) on GaAs substrates in the n-p configuration. The upper AlGaAs cell has a bandgap of 1.93 eV and is connected in series to the lower GaAs cell (1.4 eV) via a metal interconnect deposited during post-growth processing. A prismatic coverglass is installed on top of the cell to reduce obscuration caused by the gridlines. The best 0.5 sq cm cell has a two terminal efficiency of 23.0 pct. at 1 sun, air mass zero (AM0) and 25 C. To date, over 300 of these cells were grown and processed for a manufacturing demonstration. Yield and efficiency data for this demonstration are presented. As a first step toward the goal of a 30 pct. efficient cell, a mechanical stack of the 0.5 sq cm cells described above, and InGaAsP (0.95 eV) solar cells was made. The best two terminal measurement to date yields an efficiency of 25.2 pct. AM0. This is the highest reported efficiency of any two terminal, 1 sun space solar cell

Diffusive transport of light in two-dimensional granular materials

We study photon diffusion in a two-dimensional random packing of monodisperse disks as a simple model of granular material. We apply ray optics approximation to set up a persistent random walk for the photons. We employ Fresnel's intensity reflectance with its rich dependence on the incidence angle and polarization state of the light. We present an analytic expression for the transport-mean-free path in terms of the refractive indices of grains and host medium, grain radius, and packing fraction. We perform numerical simulations to examine our analytical result.Comment: 9 pages, 3 figure

Stochastic Model for the Motion of a Particle on an Inclined Rough Plane and the Onset of Viscous Friction

Experiments on the motion of a particle on an inclined rough plane have yielded some surprising results. For example, it was found that the frictional force acting on the ball is viscous, {\it i.e.} proportional to the velocity rather than the expected square of the velocity. It was also found that, for a given inclination of the plane, the velocity of the ball scales as a power of its radius. We present here a one dimensional stochastic model based on the microscopic equations of motion of the ball, which exhibits the same behaviour as the experiments. This model yields a mechanism for the origins of the viscous friction force and the scaling of the velocity with the radius. It also reproduces other aspects of the phase diagram of the motion which we will discuss.Comment: 19 pages, latex, 11 postscript figures in separate uuencoded fil

Progress toward a 30 percent-efficient, monolithic, three-junction, two-terminal concentrator solar cell for space applications

Component efficiencies of 0.2/sq cm cells at approximately 100x AMO light concentration and 80 C temperatures are not at 15.3 percent for a 1.9 eV AlGaAs top cell, 9.9 percent for a 1.4 eV GaAs middle cell under a 1.9 eV AlGaAs filter, and 2.4 percent for a bottom 1.0 eV InGaAs cell under a GaAs substrate. The goal is to continue improvement in these performance levels and to sequentially grow these devices on a single substrate to give 30 percent efficient, monolithic, two-terminal, three-junction space concentrator cells. The broad objective is a 30 percent efficient monolithic two-terminal cell that can operate under 25 to 100x AMO light concentrations and at 75 to 100 C cell temperatures. Detailed modeling predicts that this requires three junctions. Two options are being pursued, and both use a 1.9 eV AlGaAs top junction and a 1.4 eV GaAs middle junction grown by a 1 atm OMVPE on a lattice matched substrate. Option 1 uses a low-doped GaAs substrate with a lattice mismatched 1.0 eV InGaAs cell formed on the back of the substrate. Option 2 uses a Ge substrate to which the AlGaAs and GaAs top junctions are lattice matched, with a bottom 0.7 eV Ge junction formed near the substrate interface with the GaAs growth. The projected efficiency contributions are near 16, 11, and 3 percent, respectively, from the top, middle, and bottom junctions

Angle of Repose and Angle of Marginal Stability: Molecular Dyanmics of Granular Particles

We present an implementation of realistic static friction in molecular dynamics (MD) simulations of granular particles. In our model, to break contacts between two particles, one has to apply a finite amount of force, determined by the Coulomb criterion. Using a two dimensional model, we show that piles generated by avalanches have a {\it finite} angle of repose $\theta_R$ (finite slopes). Furthermore, these piles are stable under tilting by an angle smaller than a non-zero tilting angle $\theta_T$, showing that $\theta_R$ is different from the angle of marginal stability $\theta_{MS}$, which is the maximum angle of stable piles. These measured angles are compared to a theoretical approximation. We also measure $\theta_{MS}$ by continuously adding particles on the top of a stable pile.Comment: 14 pages, Plain Te

Continuous Avalanche Segregation of Granular Mixtures in Thin Rotating Drums

We study segregation of granular mixtures in the continuous avalanche regime (for frequencies above ~ 1 rpm) in thin rotating drums using a continuum theory for surface flows of grains. The theory predicts profiles in agreement with experiments only when we consider a flux dependent velocity of flowing grains. We find the segregation of species of different size and surface properties, with the smallest and roughest grains being found preferentially at the center of the drum. For a wide difference between the species we find a complete segregation in agreement with experiments. In addition, we predict a transition to a smooth segregation regime - with an power-law decay of the concentrations as a function of radial coordinate - as the size ratio between the grains is decreased towards one.Comment: 4 pages, 4 figures, http://polymer.bu.edu/~hmaks