Density waves and sand swimmers

Spontaneously unbounded fluctuations in the density or the forces against the wall can appear when a granular medium flows through pipes or hoppers.

With Gongwen Peng we formulated a cellular automaton which predicted density waves in pipe flow and a background power spectrum following a power-law with exponent 4/3. The first paper was published in Phys. Rev. E. 49 (1994) R1796. A longer paper showing that the power law spectrum is always present with periodic boundary conditions but only appears at a certain flux in the open pipe was published in Phys. Rev. E 51 (1995) 1745-1756. A clear experimental verifications came several years later by the group of Matsushita ().

Simulations of outflowing hoppers as performed with Gerald Ristow show that the fluctuations in density have a power spectrum of 1/f noise (see paper in Phys. Rev. 50, R5 (1994)). The forces acting against the walls also follow a power law in their spectrum if the opening angle is not too large (see paper in Physica A 213, 474-481 (1995)). You can also see how the pipe in the figure clogs .

A particularly interesting type of waves are those of small amplitude namely sound waves.

In a collaboration with the group of Jean Pierre Hulin at the FAST in Orsay we studied density waves of glass beads flowing through a vertical pipe. With Tareck Raafat we analyzed the time series for different humidities and fluxes and found various phases as described in a paper published in Phys. Rev. E, Vol. 53, 4345-4350 (1996). Pressure measurements are reported in the paper published in J. Fluid Mech. Vol. 458, 317-345 (2002).

A technical implementation of the above phenomenon is realized in pneumatic transport. In a DFG joint collaboration with Prof. Karl Sommer of the chemical engineering department at the Technical University of Munich we studied with Martin Strauss in detail plug motion for vertical pipes as seen in this movie and as discussed in a preprint and compared it to the results from experiments by Gerhard Niederreiter in a proceedings for PARTEC 2004. We also studied horizontal pipe flow as seen in this movie and presented in our recent preprint .

With Takashi Shimada, Troy Shinbrot and Dirk Kadau we investigated swimming inside sand as it is realized for instance buy the sand skink. We introduced a push-me-pull-you mechanism of two disks connected by a spring and calculated its velocity and energy consumption as function of its geometry and frequency as published in Phys.Rev.E Vol. 80, p.020301 (2009) and commented in News and Views of Nature Physics Vol.5, p.709 (2009).