Pattern scaling in axial segregation

Granular tumbled frequently segregate by grain size along the axis of partially-filled, horizontal, rotating tubes. When segregation approaches saturation at the surface, a well-defined pattern of bands with wavelength lambda emerges. The long-term dynamics of the pattern involves a much slower coarsening process. We characterized the initial saturated wavelength lambda as a function of the diameter of the tube D for a filling fraction of 30 %, for 1.9 cm <= D <= 11.5 cm. We also studied the initial growth-rate of the bands as D varies. We find that lambda/ D is not constant, but rather increases rapidly for small D. The growth-rate of bands decreases with smaller D and segregation is suppressed completely for sufficiently small D. These relatively simple features are not captured by any of the existing models of axial segregation.