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] http://www.danntech.co.za

[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 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)

[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

Erosion Deposition

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