Granular media differ from other materials in their response to stirring or jostling — unlike two-fluid systems, bi-disperse granular mixtures will separate according to particle size when shaken, with large particles rising, a phenomenon termed the 'Brazil-nut effect'1,2,3,4,5,6,7,8. Mounting evidence indicates that differences in particle density affect size separation in mixtures of granular particles9,10,11. We show here that this density dependence does not follow a steady trend but is non-monotonic and sensitive to background air pressure. Our results indicate that particle density and interstitial air must both be considered in size segregation.
Explanations of the Brazil-nut effect, which has been known since the 1930s, have focused either on infiltration of small particles into voids created underneath larger ones during shaking1,2,3,4,5 or on granular convection6,7,8, and have implied density-independent rising times for the larger 'intruder' particles. However, an increase in the velocity of a large intruder with increasing density has been reported9,10, suggesting that increased inertia might play a role. Furthermore, in computer simulations10, a 'reverse' Brazil-nut effect was found, in which groups of larger particles, if heavy enough, segregate to the bottom.
A monotonic density dependence implied by such mechanisms9,10,11 is incompatible with our measurements of intruder rising times over a wide range of size and density ratios (Fig. 1). We tracked an intruder particle in the presence of granular convection produced by vertically shaking a three-dimensional cylinder filled with smaller background particles (density, ρm). A spherical intruder (diameter, D; density, ρ) was placed at a depth z0 below the surface; a hollow acrylic ball filled with foam and lead shot was used to tune the intruder density. Material properties other than density, such as coefficients of restitution and friction, had no measurable impact.
For a fixed intruder diameter, the measured rising time, Trise, to the free surface exhibits a pronounced peak as a function of ρ/ρm (Fig. 1). This peak is not affected by variations in shaking para-meters, background medium (glass beads, poppy seeds) and system size. Compared with convection measured in the absence of an intruder (dotted line), the intruder rises faster both at large and small ρ/ρm, but more slowly when ρ/ρm ≈ 0.5. A monotonic dependence, Trise≈(ρ/ρm)−1/2, proposed for a two-dimensional system10, is incompatible with our data. The presence of a large intruder perturbs the convective flow of the background particles. Data above the horizontal dotted lines in Fig. 1 therefore do not necessarily imply sinking intruders9 in the absence of convection. The peak in Trise becomes significant for diameter ratios D/d > 10, increasing with increasing intruder size (Fig. 1, inset).
Measurements of intruder velocity as a function of depth show that the increase in Trise with ρ/ρm to the left of the peak is caused by behaviour that takes place as the particle approaches the upper surface. Deeper inside the pile, Trise decreases monotonically with ρ/ρm. The peak is sensitive to the background air pressure, P, in the cylinder. It decreases in magnitude and shifts to lower ρ/ρm with decreasing P, and vanishes as P approaches 1 torr. At this low pressure, the intruder velocity (both at the surface and within the bulk) no longer depends on ρ/ρm and co-incides, within our resolution, with the non-zero convection velocity of the background particles in the absence of the intruder.
Our results indicate an intricate interplay between vibration-induced convection and fluidization, drag by interstitial air12, and intruder motion. The rising time of a large intruder in a bed of smaller particles emerges as a sensitive probe of these interactions. Understanding the phenomenon described here may require a new approach that describes intruder motion in the presence of two 'fluids': background particles and interstitial air.
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Möbius, M., Lauderdale, B., Nagel, S. et al. Size separation of granular particles. Nature 414, 270 (2001). https://doi.org/10.1038/35104697
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