Slow axial drift in three-dimensional granular tumbler flow

Models of monodisperse particle flow in partially filled three-dimensional tumblers often assume that flow along the axis of rotation is negligible. We test this assumption, for spherical and double cone tumblers, using experiments and discrete element method simulations. Cross sections through the particle bed of a spherical tumbler show that, after a few rotations, a colored band of particles initially perpendicular to the axis of rotation deforms: particles near the surface drift toward the pole, while particles deeper in the flowing layer drift toward the equator. Tracking of mm-sized surface particles in tumblers with diameters of 8-14 cm shows particle axial displacements of one to two particle diameters, corresponding to axial drift that is 1-3% of the tumbler diameter, per pass through the flowing layer. The surface axial drift in both double cone and spherical tumblers is zero at the equator, increases moving away from the equator, and then decreases near the poles. Comparing results for the two tumbler geometries shows that wall slope causes axial drift, while drift speed increases with equatorial diameter. The dependence of axial drift on axial position for each tumbler geometry is similar when both are normalized by their respective maximum values

Designing non-segregating granular mixtures

In bidisperse particle mixtures varying in size or density alone, large particles rise (driven by percolation) and heavy particles sink (driven by buoyancy). When the two particle species differ from each other in both size and density, the two segregation mechanisms either enhance (large/light and small/heavy) or oppose (large/heavy and small/light) each other. In the latter case, an equilibrium condition exists in which the two segregation mechanisms balance and the particles no longer segregate. This leads to a methodology to design non-segregating particle mixtures by specifying particle size ratio, density ratio, and mixture concentration to achieve the equilibrium condition. Using DEM simulations of quasi-2D bounded heap flow, we show that segregation is significantly reduced for particle mixtures near the equilibrium condition. In addition, the rise-sink transition for a range of particle size and density ratios matches the combined size and density segregation model predictions

Wavelength Scaling and Square/Stripe and Grain Mobility Transitions in Vertically Oscillated Granular Layers

Laboratory experiments are conducted to examine granular wave patterns near onset as a function of the container oscillation frequency f and amplitude A, layer depth H, and grain diameter D. The primary transition from a flat grain layer to standing waves occurs when the layer remains dilated after making contact with the container. With a flat layer and increasing dimensionless peak container acceleration G = 4 pi^2 f^2 A/g (g is the acceleration due to gravity), the wave transition occurs for G=2.6, but with decreasing G the waves persist to G=2.2. For 2.2<G<3.8, patterns are squares for f<f_ss and stripes for f>f_ss; H determines the square/stripe transition frequency f_ss=0.33(g/H)^0.5. The dispersion relations for layers with varying H collapse onto the curve L/H=1.0+1.1[f(H/g)^0.5]^(-1.32 +/- 0.03) (L is the wavelength) when the peak container velocity v exceeds a critical value v_gm of approximately 3 (Dg)^0.5. Local collision pressure measurements suggest that v_gm is associated with a transition in the horizontal grain mobility: for v>v_gm, there is a hydrodynamic-like horizontal sloshing motion, while for v<v_gm, the grains are essentially immobile and the stripe pattern apparently arises from a bending of the granular layer. For f at v_gm less than f_ss and v<v_gm, patterns are tenuous and disordered.Comment: 21 pages, 15 figures, submitted to Physica