Subdiffusive axial transport of granular materials in a long drum mixer

TL;DR

This study reveals that axial transport of granular materials in a long drum mixer exhibits subdiffusive behavior, with the core's width scaling as t^0.3, challenging previous diffusive assumptions and showing consistency across different conditions.

Contribution

It demonstrates that axial segregation in granular drums is subdiffusive, supported by experimental data and comparison with fractional diffusion and porous medium models.

Findings

Axial core width scales as t^0.3, indicating subdiffusion.

Subdiffusive behavior is consistent across grain types and rotation rates.

Comparison with models supports the subdiffusive transport mechanism.

Abstract

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 $\alpha \sim 0.3 < 1/2$. 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.