Intruders in the Dust: Air-Driven Granular Size Separation

Abstract

Using MRI and high-speed video we investigate the motion of a large intruder particle inside a vertically shaken bed of smaller particles. We find a pronounced, non-monotonic density dependence, with both light and heavy intruders moving faster than those whose density is approximately that of the granular bed. For light intruders, we furthermore observe either rising or sinking behavior, depending on intruder starting height, boundary condition and interstitial gas pressure. We map out the phase boundary delineating the rising and sinking regimes. A simple model can account for much of the observed behavior and show how the two regimes are connected by considering pressure gradients across the granular bed during a shaking cycle.PACS numbers: 45.70. Mg, 64.75.+g, 83.80.Fg Unlike thermal systems which favor mixing to increase entropy, granular systems tend to separate under an external driving mechanism such as vibrations [1,2]. This is commonly known as the Brazil Nut Effect, in which a large particle, the "intruder", rises to the top of a bed of smaller background particles [3,4,5]. More recently, new behavior was discovered for the limit of very small bed particles ("dust"), in particular the sinking of light intruders [6,7], and a non-monotonic dependence of the rise time on density [8,9,10]. A number of theory and experimental papers explored different aspects of this surprising behavior [11,12,13,14,15,16], but so far there has been no consensus about either the underlying mechanisms or the relative importance of various system parameters in driving the intruder motion.Here we present results from a systematic investigation of both the intruder motion and the bed particle flow. Our central finding is that there is a phase diagram which delineates rising and sinking behavior of the intruder as a function of interstitial gas pressure, intruder density, and initial intruder height within the container. Our results lead to a physical model that provides a unifying framework to describe both rising and sinking regimes. In this way, the work presented here connects previously disjointed pieces of a puzzle that pointed to the importance of pressure gradients [7,8,9] but approached the two regimes as separate phenomena. As a consequence, our findings directly contrast with the mechanisms proposed in Refs. [6,10,14,16] that neglect interstitial gas flow.We placed granular material inside an acrylic cylinder (inner diameter 8.2 cm) mounted on a shaker and used individual, well-spaced sine wave cycles ("taps") of frequency f and amplitude A to vibrate the vessel vertically. The cell could be evacuated to a gas pressure, P . Both smooth and rough cells (created by gluing glass beads to the interior walls of an otherwise smooth cell) were used to study the effect of wall friction. A large intruder sphere of diameter D was buried in the bed of background spheres (diameter d) at a height h s measured from the vessel bottom to the intruder top (See Fig. 1(a)). A range of diameter ratios D/d, shaking parameters, and bac...

Role of Air in Granular Jet Formation

“…When an object impacts on a bed of fine, loose grains, it is quickly engulfed and a surprisingly vigorous jet shoots upward from the surface of the sand [1][2][3][4], similar to what happens in a liquid [5][6][7]. Royer et al [4] found a granular jet created at reduced ambient pressure to be smaller than at atmospheric pressure, highlighting the relevant role that interstitial air plays in systems with very small grains (<100 m) [8][9][10].…”

Mutiscale Modeling of Segregation in Granular Flows

“…Other mechanisms from topological considerations have also been proposed, such as arching (Duran et al, 1993) and "void filling" beneath large particles (Rosato et al, 2002). In addition to these mechanisms, air-driven segregation has also been found to be important in the case of very fine particles (Mobius et al, 2001;Burtally et al, 2002;Mobius et al, 2004). Despite the variety of mechanisms proposed, many important details of the microscopic dynamics driving the segregation remain unknown.…”

“…It has recently gained more attention in fundamental experimental (Mobius et al, 2001;Breu et d., 2003;NahmadMolinari et al, 2003;Huerta and Ruiz-SuGrez, 2004b;Mobius et al, 2004) and theoretical studies (Rosato et al, 1987;Shishodia and Wassgren, 2001;Hong et al, 2001;Trujillo et al, 2003). Efforts have been made in these studies to explain segregation from the non-equilibrium, dissipative nature of granular material and to establish hydrodynamics models for segregation behavior.…”

Size Segregation in Granular Media Induced by Phase Transition

“…Mg, 64.75.+g, 05.50.+q In the last decades a great attention has been devoted to the study of the problem of vertically shaken granular mixtures under gravity. It was observed that such systems depending on the control parameters can mix or segregate their components spontaneously according to a mechanism which is still largely unclear, although of deep practical and conceptual relevance [1,2]. Rosato et al [3] showed that large grains surrounded by a sea of smaller ones rise to the top when subjected to vertical shaking.…”