Particle-size segregation patterns in convex rotating drums

1. Particle-size segregation patterns in convex rotating drums By D.G.Mounty & J.M.N.T Gray

2. Motivation for the problem [1] • Industrially important • Segregation is important in rotating kilns and mixers used in bulk chemical, mining and pharmaceutical industries [1] http://www.danntech.co.za

3. Axial Banding Band in Band Segregation [2] • In long drums, axial segregation can develop over longer time scales • We want to understand the 2D base segregation problem [2] Newey et al. (2004) Europhys. Lett. 66 (2)

4. Thin two-dimensional rotating drums • Focus on strong segregation • Sharp transition between regions of large and small particles • Thins drum suppress the axial instability • We can perform experiments on the 2D base flow [3] Hill et al. (1997) Phys. Rev. Lett. 78 [4] Gray & Hutter (1997) Contin. Mech. & Thermodyn. 9(6)

5. Particle-size segregation and remixing • Mixture theory framework for segregation in dense flows • Small particle concentration 0≤Φ≤1 • Segregation-Remixing equation [7][8] • No small particle flux boundary conditions • We will study the non diffusive-remixing limit Dr = 0 [5] Savage & Lun (1988) J. Fluid. Mech. 189 [6] Dolgunin & Ukolov (1995) Powder Technol. 83 [7] Gray & Thornton (2005) Proc. R. Soc. 461 [8] Gray & Chugunov, J. Fluid. Mech (In Press)

6. Concentration shocks [9] • Velocity field must be prescribed • Construct exact steady and unsteady solutions • Concentration shocks idealize sharp transitions • Use shock-capturing numerical methods for general problems [9] Gray et al. (2006) Proc. R. Soc. 462

7. Geometry of the full system Erosion Deposition • Base flow has two domains • Dense avalanche at free surface • Solid rotating body underneath • Use segregation theory to compute concentrations in avalanche region

8. Segregation in the Avalanche Large Mixed Small Erosion Deposition • Solve in the parabolic avalanche domain • Jump in velocities and behavior at boundary

9. Segregation in the full system • What you might actually see • Thin avalanche, sharp segregation

10. Simplified model • Find the surface by conservation of area • Projection of all free surface positions

11. The mapping method • Integrate each species between surfaces • Place sorted material down slope

12. Triangle experiment

13. Triangle simulation

14. Varying ratio

15. Varying fill

16. Symmetry 8.3% 25.0% 41.7% 91.7% 75.0% 58.3% • Symmetry of corresponding low and high fill levels • We may restrict analysis to fills over 50%

17. Fifty percent • Not what the simulation predicts • Different time scale • Dynamics of avalanche and segregation within are critical [10] Zuriguel et al. (2006) Phys. Rev. E 73

18. Various Figures • More sides implies shorter lobes • Circle is limiting case

19. Square simulation

20. Overview • Fills over 60% and under 40% are well predicted • Below 40% is more “industrially important”

21. Difference time series • At long time there seem to be two groups • Fifty percent seems to be a special case

22. Possible Bifurcation • Very marked jump between 65%/70% • More thorough study required