Effect of friction on the granular U-tube instability

When a granular material (like fine sand) fills a U shaped tube and is vibrated vertically, the column of grains in one branch of the tube grows while the other one empties. The height difference of the level of grains in each branch shows an exponential growth dependence with time for low frequencies of oscillation (∼10 Hz). A complete explanation of this phenomenon is still a matter of discussion. The exponential growth rate of the height difference is affected by parameters such as the amplitude and frequency of oscillation, properties of the granular material and the geometry of the U tube. This work presents an experimental study on the effect of friction between the tube walls and the granular medium, on the exponential growth rate. The internal walls of the tube were covered with sand paper of different average grain sizes (28.5 μm, 46.25 μm and 201 μm). As granular materials we used glass spheres with diameter between 180 and 300 μm. We found that increasing wall roughness lowers the exponential growth rate, and also restricts the range of amplitudes over which the effect occurs. We also compare our results with the predictions of a simple model for the instability, and show that it works only for cases with low wall roughness.