Segregation in a fluidized binary granular mixture: Competition between buoyancy and geometric forces

Abstract

Starting from the hydrodynamic equations of binary granular mixtures, we derive an evolution equation for the relative velocity of the intruders, which is shown to be coupled to the inertia of the smaller particles. The onset of Brazil-nut segregation is explained as a competition between the buoyancy and geometric forces: the Archimedean buoyancy force, a buoyancy force due to the difference between the energies of two granular species, and two geometric forces, one compressive and the other-one tensile in nature, due to the size-difference. We show that inelastic dissipation strongly affects the phase diagram of the Brazil nut phenomenon and our model is able to explain the experimental results of Breu et al. [16].

Theory of Dilute Binary Granular Gas Mixtures

“…Recently, a theory for granular mixtures [13,14] has been worked out to study the transition between the BN and RBN effects (it also treats finite concentrations of intruders). Slightly different approaches, still based on kinetic theory, have been invoked to obtain a segregation criterion [24,51,47]. These approaches consider the temperature gradient as input, and therefore only partly address the case of a vibrated system; they may capture though some of its qualitative segregation properties for known temperature profiles.…”

Mutiscale Modeling of Segregation in Granular Flows

“…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.…”

“…For > 1 with small amplitudes and high frequencies, where the granulate is fluidized without convection, a "buoyancy force" analogous to fluid buoyancy has been proposed to predict the Brazil nut effect (Shishodia and Wassgren, 2001;Trujillo et al, 2003). 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).…”

Convection, Segregation and Pattern Formation in Horizontally Vibrated Granular Materials

“…in vertically vibrated systems. Segregation in vertically vibrated granular systems also reveals extensive range of interesting phenomena [28][29][30][31][32][33][34][35][36] . A variety of segregation patterns [37][38][39][40][41][42][43][44][45][46][47] are also observed in vertically vibrated systems, such as stripe patterns [46] wave-like patterns [27] , BNE and RBNE [34,47] etc.…”