1/f alpha density fluctuation at the slugging transition point of granular flows through a pipe

By changing the packing rate of metallic spheres inside a pipe, we experimentally investigated a density fluctuation of metallic spheres that fall through a vertical glass pipe filled with liquid. We found that only at the intermediate packing rate p similar to 0.18 the power spectrum of the density fluctuation of falling metallic spheres P(f) obeys a power law as P(f) similar to 1/f(alpha), where f is a frequency and a is a positive constant. This intermediate packing rate corresponds to a slugging transition point from the low-packing-rate region where metallic spheres fall almost freely to the high-packing-rate region where density waves (slugs of granular materials) emerge and so metallic spheres fall in a group very slowly. We also compare our experimental results with the jamming transition and the 1/f noise that appear in a crowded traffic flow.