Segregation in a fluidized binary granular mixture Competition between buoyancy and geometr.pdf

a r X i v : c o n d - m a t / 0 3 0 6 5 5 8 v 1 [ c o n d - m a t .s o f t ] 2 3 J u n 2 0 0 3 Segregation in a Fluidized Binary Granular Mixture: Competition between Buoyancy and Geometric Forces Leonardo Trujillo1, Meheboob Alam2,3 and Hans J. Herrmann1,2 1Laboratoire de Physique et Me?canique des Milieux He?te?roge?nes (UMR CNRS 7636), E?cole Supe?rieure de Physique et de Chimie Industrielles, 10 rue Vauquelin, 75231 Paris Cedex 05, France 2Institut fu?r Computeranwendungen 1, Pfaffenwaldring 27, D-70569 Stuttgart, Germany 3Engineering Mechanics Unit, JNCASR, Jakkur Campus, Bangalore 560064, India (Dated: February 2, 2008) 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]. PACS numbers: 45.70.Mg;05.20.Dd I. INTRODUCTION Segregation is a process in which a homogeneous mix- ture of particles of different species becomes spatially non-uniform by sorting themselves in terms of their size and/or mass [1, 2, 3, 4, 5, 6, 7]. Monte Carlo simulations of Rosato et al. [3] clearly demonstrated that the larger particles immersed in a sea of smaller particles rise to the top when subjected to strong vertical shaking. This is the well-known Brazil nut phenomenon (BNP). It has been explained using the geometrical ideas of percolation theory, i.e. in a vibrated-bed the smaller particles are more likely to fin