Axial band scaling for bidisperse mixtures in granular tumblers.

Axial banding in rotating tumblers has been experimentally observed, but the dependence of band formation on the relative concentration of the bidisperse particles has not been thoroughly examined. We consider axial band formation and coarsening for dry and liquid granular systems of bidisperse mixtures of glass beads where the small particle volume fraction ranges from 10% to 90% in half-filled tumblers for several rotation rates. Single bands form for small particle volume fractions as low as 10% and as high as 90%, usually near the end walls. Band formation along the entire length of the tumbler is less likely at very low or very high volume fractions. After many rotations the segregation pattern coarsens, and for small particle volume fractions of 50% and greater, the coarsening is logarithmic. For very low or very high small particle volume fractions, the rate of coarsening is either not logarithmic or coarsening does not occur within the duration of the experiment (600 rotations). When bands form, the width of the band for either the small or large particles scales with the tumbler diameter.