Silo music: Sound emission during the flow of granular materials through tubes

The present work deals with experiments and a model related to the emission of sound during the flow of granular materials through tubes. Experiments have been conducted using tubes fitted either with pistons or orifice plates at the ends. Earlier workers have observed that the height H of the granular material above the piston or orifice must exceed a critical value H_c for the music to occur. The critical height H_c was determined using the recorded sound signal for flow velocities in the range 0.4-1.8 mm/s (piston experiments) and 3-36.2 mm/s (orifice experiments).A simple model is constructed by treating the powder column as a spring and slider in series. The slider interacts with the tube wall via a rate and state variable friction law. The model predicts that the material either moves with a constant velocity (steady sliding) or in a jerky manner (stick-slip), depending on the parameter values used. As suggested by earlier workers, we postulate that the silo music is generated by the stick-slip motion of granular material. For H < H_c, it is postulated that steady sliding occurs, and this is shown to be consistent with the model predictions. For H > H_c, the model predicts that steady sliding is unstable with respect to small perturbations. The velocity of the slider exhibits sustained oscillations, which is the expected behavior of a system undergoing stick-slip motion. The model parameters have been estimated by fitting data on the variation of H_c with the flow velocity. The predicted acceleration of the slider is similar in some respects to the data of Muite et al. (Powder Technol. 145 (2004) 190-202) for the flow of glass beads in a tube fitted with an orifice. Muite et al. found that the dominant frequency of the sound was given by c_s / (4L_a), where c_s is speed of sound in air and L_a is the length of the air column above the granular material. This expression also fits the present data for the piston experiments.