Radial segregation of granular mixtures in rotating cylinders

Abstract

Simultaneous mixing and segregation of granular materials is of considerable practical importance; the interplay among both processes is, however, poorly understood from a fundamental viewpoint. The focus of this work is radial segregation-core formation-due to density in a rotating cylinder. The flow regime considered is the cascading or continuous flow regime where a thin layer of solids flows along a nearly flat free surface, while the remaining particles rotate as a fixed bed along with the cylinder. The essence of the formation of a central segregated core of the more dense particles lies in the flow, mixing, and segregation in the cascading layer. The work involves experiments and analysis. A constitutive model for the segregation flux in cascading layers is proposed and validated by particle dynamics and Monte Carlo simulations for steady flow down an inclined plane. The model contains a single parameter, the dimensionless segregation velocity ͑␤͒, which is treated as a fitting parameter here. Experimental results for the equilibrium segregation of steel balls and glass beads are presented for different fractions and different extents of filling. There is a good match between theoretical predictions and all experimental results when the value of dimensionless segregation velocity is taken to be ␤ϭ2. The extent of segregation is found to increase with increase in the dimensionless segregation velocity and dimensionless diffusivity but is independent of the level of filling. Lagrangian simulations based on the theory and experiments demonstrate the competition between segregation and mixing. In the case of slow mixing, the intensity of segregation monotonically decreases to an equilibrium value; for fast mixing, however, there exists an optimal mixing time at which the best mixing is obtained.

Breaking size segregation waves and particle recirculation in granular avalanches

“…However, the simplicity of the hyperbolic approach lays bare the underlying structure in the low diffusive-remixing limit of more complex parabolic models (Dolgunin & Ukolov 1995;Dolgunin, Kudy & Ukolov 1998;Khakhar, McCarthy & Ottino 1997;Khakhar, Orpe & Hajra 2002;Gray & Chugunov 2006) in which smoothing is introduced by inter-particle diffusion. These models yield steady states with 'S'-shaped concentration profiles, rather than a sharp shock, and are in close agreement (Khakhar et al 1997;Gray & Chugunov 2006) with the results of three-dimensional discrete-element simulations for both density and size segregation (Khakhar, McCarthy & Ottino 1999) in high-solids-fraction flows. This, together with the experimental results of Savage & Lun (1988), Dolgunin & Ukolov (1995) and Vallance & Savage (2000), provide strong evidence for a theory with the segregation flux used in the current models.…”

Particle-size segregation and diffusive remixing in shallow granular avalanches

“…However, Savage & Lun's (1988) and Vallance & Savage's (2000) data imply that the φ(1 − φ) flux model is a good one for particle-size segregation at high solids fractions, and Khakhar, McCarthy & Ottino (1997) have also shown that Dolgunin & Ukolov (1995) approach is very good at predicting density segregation at high solids volume fractions. The models of Savage & Lun (1988), Dolgunin & Ukolov's (1995) and Gray & Thornton (2005) all have the same underlying φ(1 − φ) structure and appear to be good at predicting segregation in dense granular avalanches where there are multiple enduring frictional contacts between the grains.…”

Multi-component particle-size segregation in shallow granular avalanches

“…They occur on geophysical scales in the form of snow avalanches (Savage & Hutter 1989;Jomelli & Bertran 2001;Bartelt & McArdell 2009), rockfalls (Dade & Huppert 1998;Bertran 2003), dense pyroclastic flows (Branney & Kokelaar 1992;Calder, Sparks & Gardeweg 2000) and debris flows (Costa & Williams 1984;Pierson 1986;Iverson 1997;Iverson & Vallance 2001), as well as on much smaller scales in the form of chute flows (Gray, Wieland & Hutter 1999;Khakhar, McCarthy & Ottino 1999), during the formation of heaps (Williams 1968;Gray & Hutter 1997;Makse et al 1997), in the filling of hoppers (Baxter et al 1998) and in rotating drums (Gray & Hutter 1997;Khakhar, McCarthy & Ottino 1997;Hill et al 1999;Hill, Gioia & Amaravadi 2004;Zuriguel et al 2006). As the particle-size distribution evolves within these flows, there can be interesting feedbacks on the bulk flow itself (Phillips et al 2006;Rognon et al 2007;Gray & Ancey 2009).…”