Using digital subtraction radiography, we study the basic modes of a granular material (here sand) flowing through a flat hopper. These modes take the form of density waves whose formation and propagation is controlled by several parameters, including the mass flow rate M and the hopper angle θ. We consider the effect of roughness on pattern formation in this system using mixtures of smooth and faceted sand and show the existence of a bifurcation at a mass fraction of faceted sand X≊0.2. Propagating patterns form in faceted sand but not in smooth sand of the same size.

• Received 23 November 1988

DOI:https://doi.org/10.1103/PhysRevLett.62.2825