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 physically control parameters (feed rate, particle sizes, and system size) and kinematic parameters (diffusion coefficient, flowing layer depth, and percolation velocity). The Péclet number, P e, captures the interplay of advection and diffusion, and the second dimensionless parameter, Λ, describes the interplay between segregation and advection. A parametric study of Λ and P e 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.Key words: Authors should not enter keywords on the manuscript, as these must be chosen by the author during the online submission process and will then be added during the typesetting process (see http://journals.cambridge.org/data/relatedlink/jfm-keywords.pdf for the full list) †

in Wiley Online Library (wileyonlinelibrary.com)Quantitatively predicting segregation of size-disperse granular materials is of potential value in many industrial applications. We consider granular segregation of size-bidisperse particles in quasi-2D bounded heaps, a canonical granular flow, using an advection-diffusion transport equation with an additional term to account for particle segregation. The equation is characterized by two dimensionless parameters that are functions of control parameters (flow rate, system size, and particle sizes) and kinematic parameters (flowing layer depth, diffusion coefficient, and percolation length scale). As the kinematic parameters are usually difficult to measure in practice, their dependence on the control parameters is determined directly from discrete element method simulations. Using these relationships, it is possible to determine which values of the control parameters result in a mixed or segregated heap. The approach used here is broadly applicable to a wide range of other flow geometries and particle systems. V C 2015 American Institute of Chemical Engineers AIChE J, 61: 1524AIChE J, 61: -1534AIChE J, 61: , 2015 While k can be chosen such that the surface velocity approaches a smaller fraction of the surface velocity, DEM simulations indicate that the concentration changes minimally in the normal direction below this cut-off.

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Quasi-two-dimensional bounded heap flow is a useful model for many granular flows in industry and nature. It belongs to a family of free surface flows—inclined chute flow, rotating tumbler flow and unbounded heap flow—but differs from the others in that uniform deposition of particles onto the static bed results in the uniform rise of the heap. The kinematics, however, are only partially understood. We performed discrete element method simulations to study granular flows in quasi-two-dimensional bounded heaps. The experimentally validated computational results show a universal functional form for the streamwise velocity profile for both monodisperse and bidisperse systems when velocities and coordinates are scaled by the local surface velocity and the local flowing layer thickness. This holds true regardless of streamwise location, feed rate, particle size distribution and, most surprisingly, the local particle concentration for bidisperse flows. The local surface velocity decreases linearly in the streamwise direction, while the flowing layer thickness remains nearly constant; both quantities depending only on local flow rate and local mean particle diameter. Additionally, the velocity profile normal to the overall flow, which is important in understanding segregation, can be predicted analytically from the streamwise velocity and matches the simulation results.

We model bidisperse size segregation of granular material in quasi-two-dimensional circular tumbler flow using the advection–diffusion transport equation with an additional term to account for segregation due to percolation. Segregation depends on three dimensionless parameters: the ratio of segregation to advection, ${\it\Lambda}$; the ratio of advection to diffusion, $\mathit{Pe}$; and the dimensionless flowing layer depth, ${\it\epsilon}$. The degree of segregation in steady state depends only on the ratio of segregation effects to diffusion effects, ${\it\Lambda}\,\mathit{Pe}$, and the degree of segregation increases as ${\it\Lambda}\mathit{Pe}$ increases. The transient time to reach steady-state segregation depends only on advection, which is manifested in ${\it\epsilon}$ and $\mathit{Pe}$ when ${\it\Lambda}\mathit{Pe}$ is constant. This model is also applied to unsteady tumbler flow, where the rotation speed varies with time.

Segregation and mixing of granular mixtures during heap formation has important consequences in industry and agriculture. This research investigates three different final particle configurations of bidisperse granular mixtures--stratified, segregated and mixed--during filling of quasi-two-dimensional silos. We consider a large number and wide range of control parameters, including particle size ratio, flow rate, system size, and heap rise velocity. The boundary between stratified and unstratified states is primarily controlled by the two-dimensional flow rate, with the critical flow rate for the transition depending weakly on particle size ratio and flowing layer length. In contrast, the transition from segregated to mixed states is controlled by the rise velocity of the heap, a control parameter not previously considered. The critical rise velocity for the transition depends strongly on the particle size ratio.

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Segregation of polydisperse granular materials occurs in many natural and industrial settings, but general theoretical modelling approaches with predictive power have been lacking. Here we describe a model capable of accurately predicting segregation for both discrete and continuous particle size distributions based on a generalized expression for the percolation velocity. The predictions of the model depend on the kinematics of the flow and other physical parameters such as the diffusion coefficient and the percolation length scale, quantities that can be determined directly from experiment, simulation or theory and that are not arbitrarily adjustable. The model is applied to heap and chute flow, and the resulting predictions are consistent with experimentally validated discrete element method (DEM) simulations. Several different continuous particle size distributions are considered to demonstrate the broad applicability of the approach.