Patterns in Flowing Sand: Understanding the Physics of Granular Flow
Tamás Börzsönyi,  Robert E. Ecke and Jim N. McElwaine
[Phys. Rev. Lett., 103, 178302 (2009)]   download:  pdf
Due to the large number of movies in this page not all of them might run continously, each of them could be seen or downloaded by clicking on the corresponding link.
Dense granular flows are often observed to become unstable and form inhomogeneous structures in nature or industry. Although recently significant advances have been made in understanding simple flows [P. Jop, Y. Forterre and O. Pouliquen, Nature 441, 727 (2006)], instabilities are often not understood in detail.  We present experimental and numerical results that show the spontaneous formation of longitudinal stripes that arise from instability of the uniform flowing state of granular media on a rough inclined plane. The form of the stripes depends critically on the mean density of the flow with a robust form of stripes at high density that consists of fast sliding pluglike regions (stripes) on top of highly agitated boiling material (see image a) - a configuration reminiscent of the Leidenfrost effect when a droplet of liquid lifted by its vapor is hovering above a hot surface.

We also show that there is a continous transition to the structure already observed [Y. Forterre and O. Pouliquen, Phys. Rev. Lett. 86, 5886 (2001)] for dilute flows where the height maxima (corresponding to the fast sliding regions) are absent and the flow is the fastest at the height minima (see image b). Both regimes can be observed for various materials such as sand, glass beads or various copper samples with different particle shape as it is presented at this page. All movies recorded at 4000 frames/sec.

Sketch of the experimental setup:

Movie of the pattern taken in the dense regime for sand of d=0.2mm:

Experimental characterization of the regimes by measuring the mean density:

Stripes are present above a critical plane inclination as it is illustrated on the following phase diagram. The average density of the flow falls in the range of 0.6-0.95 and 0.2-0.7 for the two types of stripes, respectively, in terms of the static density.

Experimental data obtained in the dense regime:

Height profiles taken at various flow thicknesses:

  Surface fluidization monitored by a reflected laser line:

Normalized wavelength as a function of the normalized mean flow thickness:

Results of numerical (Molecular Dynamics) simulations:
(Simulations done by Jim N. McElwaine at Cambridge)

The first plot (a) shows the downstream velocity while plot (b) shows the in plane velocity (streamlines included). Note that the in plane circulation is much slower compared to the modulation of the downstream velocity.
Plot (c) shows the relative density while plot (d) visulizes spatial variations of the inertial number. From these two datasets one can determine how the packing fraction depends on the inertial number, which is shown in plot (e). The most interesting data set is the nonmonotonous dependence of the effective friction on the inertial number (f). Such a dependence can obviously lead to the decomposition of the system into a plug like region of lower effective friction and a highly agitated region with moderate effective friction.

By clicking on the image below a movie of the numerical simulations can be seen.

Illustration for the change in the stripe structure as a function of the plane inclination as measured for sand with d=0.2 mm:

  Images of the pattern and the corresponding lateral velocity profiles...

...and the corresponding movies.

Movie taken at 42.6 degrees:

Movie taken at 45.8 degrees:

Movie taken at 48.5 degrees:

Movie taken at 52.2 degrees:

Example movies taken for copper particles with d=0.16mm:

Movie taken at 36.1 degrees (dense regime):

Movie taken at 42.6 degrees (dilute regime):

Example movies taken for glass beads with d=0.18mm:

Movie taken at 36.1 degrees (dense regime):

Movie taken at 42.6 degrees (dilute regime):