Size segregation in vertically shaken binary granular mixture

animated mixing of Brazilnuts and Sunflower seeds

Figure 1
The so called Brazil Nut Effect. The bigger brazil nuts accumulate at the top when the mixture is shaken or tapped.

If mixtures of different sized particles are shaken, they can segregate. Often the big particles accumulate at the top surface, a behaviour known as the Brazil Nut Effect. A lot of products in the chemical, pharmaceutical and food industry are such mixtures and their segregation during transport and handling is often a problem. However the physics leading to segregation are not well understood; in recent years 10 different, sometimes contradictory, mechanisms have been suggested.

Experimental Setup

Figure 2
Left: Experimental Setup. The particles are shaken vertically in an evacuated square glass tube. Pictures are taken from the top and the bottom (using a mirror) of the granular sample.
Right: An image of the bottom plate. All big particles detected by the image processing are marked with black circles.

In our experiments we shake mixtures of two sizes of brass spheres sinusoidally in a rectangular, evacuated glass container. For a quantitative characterization of the segregation state, we use image analysis to count the number of big particles visible at the top and bottom surface of the sample after shaking. These experimental results are also reproduced with molecular dynamics simulations, which then provide further inside in the underlying mechanism.

Results

Figure 3
Experimental segregation results as a function of the shaking amplitude. The different symbols correspond to different shaking frequencies. These experiments exhibit the BNE except for those with f=15 Hz and shaking amplitudes larger than 1.7 particle diameters. The container is filled with 128 large and approximately 1040 small brass spheres (correspoonding to equal volumes); their diameter ratio is 2.

Figure 4
Number density and granular temperature in simulations with periodic boundaries. As predicted by kinetic theory, the larger particles accumulate preferentially at the minimum of the granular temperature. This mechanism is called thermal diffusion. The sample contains one monolayer (measured in units of d_L) each of small (open circles) and large (closes triangles) particles with a diameter ratio of two. The RBNE observed in the experiment at 15 Hz is in accord with the relative positions of the arrows, which show the height of the centers of mass for the small and large particles.

Conclusion

We have found that three mechanisms are sufficient to explain our results:

At a shaking frequency of 80 Hz all samples exhibited a strong Brazil-nut effect due to the geometrical mechanism called void filling.
At a shaking frequency fo 15 Hz and shaking amplitudes up to 1.5 large particle diameters, a strong Brazil-nut effect is induced by sidewall-driven convection.
If the shaking amplitude is increased above 1.5 large particle diameters, the sample starts to resemble a granular gas and the thermal diffusion mechanism becomes significant. Thermal diffusion describes the tendency of large particles to accumulate in the minimum of the granular temperature profile. In a shallow layer, thermal diffusion eventually becomes stronger than convection, which leads to the reverse Brazil-nut effect. If the total layer height is increased, the temperature minimum is within the sample and no increased number of large particles at the bottom is observed.