Subdiffusive axial transport of granular materials in a long drum mixer
Subdiffusive axial transport of granular materials
in a long drum mixer
Phys. Rev. Lett. 94, 048002 (2005).
Zeina S. Khan and Stephen W. Morris
Department of Physics,
University of Toronto, 60 St. George St., Toronto, Ontario, Canada M5S 1A7.
Granular mixtures rapidly segregate radially by size when tumbled in a partially filled horizontal drum. The smaller component moves toward the axis of rotation and forms a buried core, which then splits into axial bands. Models have generally assumed that the axial segregation is opposed by diffusion. Using narrow pulses of the smaller component as initial conditions, we have characterized axial transport in the core. We find that the axial advance of the segregated core is well described by a self-similar concentration profile whose width scales as t^alpha, with alpha ~ 0.3 < 1/2. Thus, the process is subdiffusive rather than diffusive as previously assumed. We find that alpha is nearly independent of the grain type and drum rotation rate within the smoothly streaming regime. We compare our results to two one-dimensional PDE models which contain self-similarity and subdiffusion; a linear fractional diffusion model and the nonlinear porous medium equation.