Dynamics and Structure of Granular Flow Through a Vertical Pipe

We have experimentally shown how density waves of granular particles (ordinary sand) emerge, while they flow through a vertical glass pipe, by controlling air flow out of a flask attached to the bottom-end of the pipe. When a cock attached to the flask is fully open, air is dragged by falling granules and flows together with them. No density waves are observed for this situation. As the cock is gradually closed, however, the pressure gradient of air inside the pipe becomes gradually larger, inducing a velocity difference between granules and air. As a result, density waves emerge from the lower part of the pipe. The more the cock is closed, i.e., the smaller the rate of air flow, the higher the onset point (along the pipe) of the density waves. The onset of density waves is characterized by the growth of the lower frequency part of the power spectra of the time-series signals of the density waves. The power spectra of the density waves display a clear power-law form P(f) ~ f −α with the value of the exponent a = 1.33 ± 0.06, which is very close to 4/3. The value of a is robust even under the medium flow or variation of the pipe diameter, as far as density waves can be seen.