Fall of Fame - Mechanisms of stripe formation in vibrated granular materials
  1. 2013 • Drop Tower Bremen - DYT2013
Physical Sciences:
  • Particle agglomeration
ZARM Drop Tower
Natacha Callens
B. Mockenhaupt (1), P. Neuner (1), R. Prach (1), T. Netter (1), T. Pöschel (1), A. Sack (1)
Friedrich-Alexander Erlangen-Nürnberg University
Naegelsbachstr. 49b
91052 Erlangen

The phenomena studied in this project belongs to the stratification category. As a result of a dynamic process, particles arrange themselves in the shape of stripes. Stratification of particles is observed when particles of different sizes, densities and surface properties are mixed in a shallow container and then subjected to horizontal vibrations. The particles rearrange themselves in stripes that are perpendicular to the direction of the shaking.

A previous experiment investigated the structural formation of mustard seeds that had a radius of approximately 1.1 mm. The particles were confined in an unpolished 50x10 cm aluminum box which was then mounted and shaken by a motor to subject it to horizontal vibrations. The formation of stripes was observed within the first few seconds. After about 10 seconds, the system reached an almost stationary state, showing only slow changes over time.

This effect can be considered as the result of a frustration effect. Free particles can roll on the bottom of the container, feeling a relatively small force of rolling friction. Particles inside the stripes are in contact with the bottom of the container, as well as with other particles, and their rolling motion is consequently suppressed due to hindrance by the much greater static friction.

Numerical simulations by D. Krengel showed that stripe formation did occur when the particles’ coefficient of static friction was set to zero.

This project intends to experimentally validate this result. In the absence of gravity, stripe formation is expected to be inhibited because of the vanishing normal force which results in a system without static friction between the jammed particles and the bottom of the container.

In order to be able to use the ZARM drop tower, the size of the box and particles were reduced. The new system contains a movable platform of about 25 x 25 cm2, on which four boxes are set up. To avoid significant influence from the side walls, each of the boxes has an area of 4 x 20 cm2. The particles used are Amaranth grains, which have a diameter of about 0.8-1.2 mm. They are put inside the boxes using different particle densities.

The boxes are made of two plexiglass panels, each around 5 mm thick. Between these panels is a thinner panel of a thickness of 1.5 mm, from which four rectangular boxes for the particles were cut out. The boxes are closed at the top and bottom with the thicker panels that are anti-static. The whole unit is fixed on a moving aluminum platform. The grains will be agitated with amplitudes varying between 32 and 36 mm and frequencies of 2.0-2.2 Hz.

Rolling effects and the so given difference between static and dynamic friction are not the only cause for stripe formation. In microgravity particles did not roll and nevertheless showed very clear stripes. This experiment has shown that wedging is one cause for stripe formation but friction with the walls and air also affect the pattern formation. 

For a detailed description of the experiment results, please, consult the "Drop Your Thesis! 2013 - Final Report" in the attachment section below.

The microgravity reached in the capsule during the catapult mode was very exact and the movement on the motor did not significantly affect it.

The theory given at the beginning of the experiment could neither be proofed nor be refuted. Rolling effects and the so given difference between static and dynamic friction is not the only cause for stripe formation. In microgravity particles did not roll and nevertheless showed very clear stripes.

With growing amplitude the number of stripes decreases while their width and density increases. This process can be fitted with a curve leading to a minimum of two stripes and a maximum amplitude of 61 mm for stripe formation. These results only are true for the used system with a length of the boxes of 20 cm, a packing between 2.5g and 4g and a frequency of 2 Hz.

The packing fraction of the boxes does not significantly affect the number of stripes, and no trend can be observed.

This experiment has shown that wedging is one cause for stripe formation but friction with the walls and air also affect the pattern formation.

One explanation for the better stripes in microgravity is, that particles receive different amounts of dynamic energy, depending on their position in the box and their contact with the walls. This leads to very different velocities and therefore to a clustering effect, where energy is dissipated. 

For a deeper understanding of this phenomenon two kinds of experiments could be possible. To explain the stripe formation in microgravity and prove the theory over the stripe forming mechanism, more measurements would be necessary, especially in parts with higher amplitudes. Additionally the frequency could be varied to check if the same parameters or a similar fit can be possible there.

To check if by eliminating the air influence and the friction with the walls the structure formation will disappear a new set up would have to be created. Here it would be very easy to eliminate the influence of air by using an evacuated box. The elimination of the influence of the walls would be very difficult because the walls always will have friction with particles that collide with them.
I.S. Aranson, L.S. Tsimring, (2009), "Granular Patterns", ISBN: 9780198712411 - Oxford University Press.
A. Betat, C.M. Dury, I. Rehberg, G.H. Ristow, M.A. Scherer, M. Schröter, G. Straßburger, (1998), "Formation of patterns in granular materials", Evolution of spontaneous structures in dissipative continuous systems, F.H. Busse, S.C. Müller, Springer.
M.P. Ciamarra, A. Coniglio, M. Nicodemi, (2006), "Dynamically induced effective interaction in periodically driven granular mixtures", Physical Review Letters, 97, DOI: http://dx.doi.org/10.1103/PhysRevLett.97.038001, pp. 038001.
D. Krengel, (2012), "Phänomen der Streifenbildung bei Schwerkraft", diploma thesis - Uni Erlangen.
D. Krengel, S. Strobl, A. Sack, M. Heckel, T. Pöschel, (2013), "Pattern formation in a horizontally shaken granular submonolayer", Granular Matter, 15, pp. 377-387.
F. Radjai, S. Roux, (1995), "Friction-induced self organization of a one-dimensional array of particles", Physical Review E, 51, pp. 6177-6187.
T. Schnautz, R. Brito, C.A. Kruelle, I. Rehberg, (2005), "A horizontal Brazil-Nut effect and its reverse", Physical Review Letters, 95, pp. 028001.
A. Washburn, (1956), "Classification of patterned ground and review of suggested origins", Geological Society of America Bulletin, 67, 7, pp. 823-865.
click on items to display

The Fall of Fame Team is made up of four bachelor students from the €œFriedrich-Alexander Universität Erlangen-Nürnberg€. They are investigating whether stripe formation caused by particle wall friction is inhibited under reduced gravity, when the normal force between particles and ground (i.e. friction) is null.

Experiment hardware.

Meet the team: Fall of Fame team

A shaky student experiment successfully completed in microgravity - 19 November 2013

"Drop Your Thesis! 2013 - Final Report"
© 2020 European Space Agency