Horizontal Brazil Nut Effect and Its Reverse


T. Schnautz, R. Brito, C.A. Kruelle and I. Rehberg
Physical Review Letters, 95, 028001 (2005)

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The experiment

A horizontal dish is filled with many spheres (between 1000 and 2000) of equal size and density, and one intruder sphere of different size and/or density. The dish is horizontally swirled, in a motion which is a superposition of two sinusoidal vibrations of frequencies ranging between 0.5 Hz and 2 Hz and amplitudes between 0.95 cm and 2.22 cm. The motion of the particles inside the dish is recorded with a CCD zenithal camera. The setup is shown in the sketch below:

Migration

When the swirling motion is started, some intruders move towards the center of the container and other move towards the outer part of it, depending on the density and size of the intruder. In fact, the direction of motion depends only on two parameters: the ratio of sizes between the intruder and the particles and ratio of densities. The position of the intruder particle versus time is shown below for the two cases (plot taken from the Phys. Rev. Lett. referenced above):

These two segregations can be seen in these mpg movies below. In order to keep the color coding of the Phys. Rev. Lett., we should have used red color for the intruder traced in blue (migration to the center) and green color for the red one (migration towards the boundary):

Segregation towards the center (intruder: steel, diameter: 1cm, density: 7.69 g/cm3):

Click here (low resolution MPEG, 0.9Mb) or here (MPEG, 1.5Mb) or here (high resolution AVI, 27Mb)

Segregation towards the boundary (intruder: polypropylene, diameter: 1cm, density: 0.84 g/cm3):

Click here (low resolution MPEG, 0.9Mb) or here (MPEG, 1.6Mb) or here (high resolution AVI, 30Mb)

Results

Intruder of different materials and sizes migrate either to the center or to the boundary, as shown in Figure 1 of the paper:

The actual picture of the bowl and the intruders is:

Therefore, we can construct a phase space for particle properties. The plot below shows the direction of migration as a function of the intruder's particle properties (density and diameter) compared with the properties of the particles.

One can see that very heavy intruders (upper-right part of the diagram, marked in red) migrate to the center of the bowl, while lighter particles (lower-left corner, marked in green) move towards the boundary. In some cases the intruder does not show any migration trend, and we have labeled them as 'indifferent' (blue).

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