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

Motivation for the problem  Industrially important  Segregation is important in rotating kilns and mixers used in bulk chemical, mining and pharmaceutical industries [1] [1]

Axial Banding  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) [2] Band in Band Segregation

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)

Particle-size segregation and remixing  Segregation-Remixing equation  No small particle flux boundary conditions  We will study the non diffusive-remixing limit D r = 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) [7][8]  Mixture theory framework for segregation in dense flows  Small particle concentration 0≤Φ≤1

Concentration shocks  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] [9] Gray et al. (2006) Proc. R. Soc. 462

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

Segregation in the Avalanche Large Small Mixed ErosionDeposition  Solve in the parabolic avalanche domain  Jump in velocities and behavior at boundary

Segregation in the full system  What you might actually see  Thin avalanche, sharp segregation

Simplified model  Find the surface by conservation of area  Projection of all free surface positions

The mapping method  Integrate each species between surfaces  Place sorted material down slope

Triangle experiment

Triangle simulation

Varying ratio

Varying fill

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

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

Various Figures  More sides implies shorter lobes  Circle is limiting case

Square simulation

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

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

Possible Bifurcation  Very marked jump between 65%/70%  More thorough study required