Mechanisms in the size segregation of a binary granular mixture

Abstract

A granular mixture of particles of two sizes that is shaken vertically will in most cases segregate. If the larger particles accumulate at the top of the sample, this is called the Brazil-nut effect (BNE); if they accumulate at the bottom, it is called the reverse Brazil-nut effect (RBNE). While this process is of great industrial importance in the handling of bulk solids, it is not well understood. In recent years ten different mechanisms have been suggested to explain when each type of segregation is observed. However, the dependence of the mechanisms on driving conditions and material parameters and hence their relative importance is largely unknown. In this paper we present experiments and simulations where both types of particles are made from the same material and shaken under low air pressure, which reduces the number of mechanisms to be considered to seven. We observe both BNE and RBNE by varying systematically the driving frequency and amplitude, diameter ratio, ratio of total volume of small to large particles, and overall sample volume. All our results can be explained by a combination of three mechanisms: a geometrical mechanism called void filling, transport of particles in sidewall-driven convection rolls, and thermal diffusion, a mechanism predicted by kinetic theory.

Impurity in a granular gas under nonlinear Couette flow

“…Most of the early derivations were restricted to the quasielastic limit (α ij ≈ 1), thus assuming an expansion around Maxwellians at the same temperature [3,4,5,6,7,8]. However, the nonequipartition of energy becomes significant beyond the quasi-elastic limit, as confirmed by kinetic theory [9,10,11,12], computer simulations [11,13,14,15,16,17,18,19,20,21], and real experiments [21,22,23]. A more realistic derivation of the NS transport coefficients [24,25,26,27] requires taking into account the nonequipartition of energy and applies for finite dissipation.…”

Enskog theory for polydisperse granular mixtures. I. Navier-Stokes order transport

“…This is so since the reference state is a local HCS whose parameters change throughout the system to match the physical values in each cell. Another examples of good agreement between theory and simulation [42] and experiments [43,44] include the application of the Navier-Stokes hydrodynamics to describe density/temperature profiles in vertical vibrated gases, supersonic flow past at wedge in real experiments [45], and nonequipartition and size segregation in agitated granular mixtures [27,28,46]. In summary, the Navier-Stokes hydrodynamics with the constitutive equations obtained in this paper constitute an important and useful description for many different physical situations, although more limited than for elastic gases.…”

Mass transport of an impurity in a strongly sheared granular gas

“…Recent kinetic theory results [38] based on the Navier-Stokes transport coefficients have been able to explain some experimental and/or molecular dynamics segregation results obtained in agitated granular mixtures at large shaking amplitudes [39]. Another possible direction of study is the extension of the present approach to mixtures with finite composition.…”