Size separation of granular particles

Abstract

Size separation of granular particlesG ranular 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' 1-8 . Mounting evidence indicates that differences in particle density affect size separation in mixtures of granular particles 9-11 . 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 shaking 1-5 or on granular convection 6-8 , and have implied densityindependent rising times for the larger 'intruder' particles. However, an increase in the velocity of a large intruder with increasing density has been reported 9,10 , suggesting that increased inertia might play a role. Furthermore, in computer simulations 10 , 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 mechanisms 9-11 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, ț m ). A spherical intruder (diameter, D; density, ț) was placed at a depth z 0 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, T rise , to the free surface exhibits a pronounced peak as a function of ț/ț m (Fig. 1). This peak is not affected by variations in shaking parameters, 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 ț/ț m , but more slowly when ț/ț m ഠ0.5. A monotonic dependence, T rise ഠ(ț/ț m ) ǁ1/2 , proposed for a two-dimensional system 10 , 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 intruders 9 in the absence of convection. The peak in T rise 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 T rise with ț/ț m to the left of the peak is caused by behaviour that takes place as th...

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“…The even larger realm of nonequilibrium systems similarly shows empirically that particles with different dynamic modes may segregate spontaneously. Examples include bacteria (1), granular particles under shaking (2), and active colloids (3). This concept has inspired various efforts (4,5) to extend the profound insights of statistical thermodynamics to nonequilibrium systems.…”

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“…Moreover, Mobius et al [27] did not find a regime where the large particle sank in their experiments.…”

“…Mobius et al [27] appear to indicate that interstitial air plays a prominent role in the motion of a light intruder. A non-monotonic dependence of the rise-time was found as a function of the density ratio of the intruder to the surrounding particles.…”

“…Earlier, Shinbrot and Muzzio [26] showed that a light intruder can go to the bottom of a vibrated deep granular bed, displaying what they call a reverse buoyancy. More recently, interstitial fluid including ambient air has been shown to play an important role in determining spatial distributions [27,28].…”

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