Fig. 1. Road map and organization of the material covered in this paper. While the flow in a tumbler exhibits differing flow regimes depending on rotation rate, here we focus exclusively on the rolling regime.

Fig. 2. Schematic representation of a cylindrical tumbler operated in the rolling regime.

Fig. 3. Experimental time evolution of the mixing process for two differing materials. (a) Sugar crystals (SC) filled to H=0.35. (b) Sugar balls (SB) filled to H=0.42. Reprinted with permission from Khakhar et al. [4]. Copyright 1997 American Institute of Physics.

Fig. 4. Experimental intensity of segregation evolution for the experiments in Fig. 3.

Fig. 5. Qualitative comparison of experiment and computation with different values of the diffusivity for sugar balls.

Fig. 6. Quantitative evaluation of the diffusivity for sugar balls.

Fig. 7. Comparison of the mixing of tracer particles in a circular, elliptical, and square mixer (assuming no particle diffusion). The inset figure on the upper left shows the Poincaré section, and the initial condition is shown in the upper right inset. Reprinted with permission from Khakhar et al., CHAOS 9(1), 1999, pp. 195–205. Copyright 1999 American Institute of Physics.

Fig. 8. Perimeter growth as mixing proceeds in different tumbler geometries. Exponential stretching is one of the signatures of chaos. Shown is the relative growth (scaled to its original length) of the perimeter of the blobs in Fig. 7. Note that the ellipse and square perimeter lengths grow exponentially, while the circle perimeter grows linearly. Reprinted with permission from Khakhar et al., CHAOS 9(1), 1999, pp. 195–205. Copyright 1999 American Institute of Physics.

Fig. 9. Mixing of tracer particles in a container with a square cross-section. Shown is a comparison of an experiment using colored glass beads (right) and a simulation using the model with D=10⁻³ (left). The number of rotations for each image is listed in the corner. The blue blobs are placed initially at the approximate location of the hyperbolic points (see Poincaré sections in Fig. 7). Reprinted with permission from Khakhar et al., CHAOS 9(1), 1999, pp. 195–205. Copyright 1999 American Institute of Physics.

Fig. 10. Variation of the dimensionless mid-layer thickness, δ_o, with the dimensionless length of the free surface, L, for different bead sizes, d, and Froude numbers, Fr. Circular and square symbols represent experiments run with 2 and 0.8 mm circular beads, respectively. Reprinted with permission from Khakhar et al., CHAOS 9(1), 1999, pp. 195–205. Copyright 1999 American Institute of Physics.

Fig. 11. A comparison of mixing at different Bo numbers for an initially segregated mixture (yellow particles began on the right and blue particles on the left) after two revolutions.

Fig. 12. Comparison of particle dynamics simulation of segregation in a chute flow with theory. Lines are fitted to data points for equilibrium segregation of different density ratios. For all three lines, a dimensionless segregation velocity of γ=68 is used.

Fig. 13. Equilibrium distribution of beads obtained experimentally (left) and from LS (right) for differing filling, H, and total fraction of more dense particles, f_T. The more dense particles are darker. Reprinted with permission from Khakhar et al., Fluids 9(12), 1997, pp. 1–14. Copyright 1997 American Institute of Physics.

Fig. 14. Time evolution of the distribution of a mixture of particles of different density with rotation of the cylinder obtained experimentally (left) and from LS (right). Darker particles have higher density. Reprinted with permission from Khakhar et al., Physics of Fluids 9(12), 1997, pp. 1–14. Copyright 1997 American Institute of Physics.

Fig. 15. Variation of the intensity of segregation with cylinder revolutions of an initially segregated mixture for different extents of filling of the cylinder. Curves are obtained from LS, points are from the experiment shown in Fig. 14.