Granular flow in a rotating tumbler is of theoretical and industrial significance. However, in spite of its relative simplicity, little is known about the dynamics of the top flowing layer. Here we present an experimental study of the velocity field within the fluidized layer of monodisperse particles in a quasi-2D (two-dimensional) rotating tumbler in the rolling flow regime using particle tracking velocimetry. The granular flow is illuminated by a laser flash and recorded using a charge coupled device camera. Image processing is used to remove the experimental noise and to achieve sub-pixel accuracy in calculating the particle displacements. The ensemble-averaged streamwise and transverse velocity profiles are calculated based on the particle displacements for three angular velocities and three bead sizes. The normalized streamwise velocity profile is linear throughout the fluidized layer, but becomes logarithmic as it enters the “fixed” bed where slow particle rearrangements dominate. The rms velocities appear to be exponentially related to the depth in the layer. Nondimensionalizing the number density in the fluidized layer with a geometric factor based on the square packing results in collapse of the data over a range of bead sizes and angular velocities.

Predicting segregation of granular materials composed of different-sized particles is a challenging problem. In this paper, we develop and implement a theoretical model that captures the interplay between advection, segregation and diffusion in size bidisperse granular materials. The fluxes associated with these three driving factors depend on the underlying kinematics, whose characteristics play key roles in determining particle segregation configurations. Unlike previous models for segregation, our model uses parameters based on kinematic measures from discrete element method simulations instead of arbitrarily adjustable fitting parameters, and it achieves excellent quantitative agreement with both experimental and simulation results when applied to quasi-two-dimensional bounded heaps. The model yields two dimensionless control parameters, both of which are only functions of control parameters (feed rate, particle sizes, and system size) and kinematic parameters (diffusion coefficient, flowing layer depth, and percolation velocity). The Péclet number, $\mathit{Pe}$ , captures the interplay of advection and diffusion, and the second dimensionless parameter, $\Lambda $ , describes the interplay between segregation and advection. A parametric study of $\Lambda $ and $\mathit{Pe}$ demonstrates how the particle segregation configuration depends on the interplay of advection, segregation and diffusion. The model can be readily adapted to other flow geometries.