Accurate buoyancy and drag force models to predict particle segregation in vibrofluidized beds

Abstract

The segregation of large intruders in an agitated granular system is of high practical relevance, yet the accurate modelling of the segregation (lift) force is challenging as a general formulation of a granular equivalent of a buoyancy force remains elusive. Here, we critically assess the validity of a granular buoyancy model using a generalization of the Archimedean formulation that has been proposed very recently for chute flows. The first model system studied is a convection-free vibrated system, allowing us to calculate the buoyancy force through three different approaches, i.e. a generalization of the Archimedean formulation, the spring force of a virtual spring and through the granular pressure field. The buoyancy force obtained through these three approaches agree very well, providing strong evidence for the validity of the generalization of the Archimedean formulation of the buoyancy force which only requires an expression for the solid fraction of the intruder, hence allowing for a computationally less demanding calculation of the buoyancy force as coarse-graining is avoided. In a second step, convection is introduced as a further complication to the granular system. In such a system, the lift force is composed of granular buoyancy and a drag force. Using a drag model for the slow velocity regime, the lift force, directly measured through a virtual spring, can be predicted accurately by adding a granular drag force to the generalization of the Archimedean formulation of the granular buoyancy. The developed lift force model allowed us to rationalize the dependence of the lift force on the density of the bed particles and the intruder diameter, and the independence of the lift force on the the intruder diameter, and the independence of the lift force on the intruder density and the vibration strength (once a critical value is exceeded).

Intruder trajectory tracking in a three-dimensional vibration-driven granular system: Unveiling the mechanism of the Brazil nut effect

“…For a fully fluidized particle bed, the intruder may experience a volume-related buoyancy force similar to a liquid. [30] For a sufficiently light intruder, it may move upward under the effect of "buoyancy," resulting in the Brazil-nut effect (BNE). However, it is worth noting that in this study, the vibration strength is not sufficient for the particle bed to be fully flu-idized.…”

“…The complexity of granular segregation arises from the interplay of diverse influencing factors, including particle size, density, interaction between interstitial fluid and particles, and friction between particles and container walls. [4,24,25] Various segregation mechanisms, such as convection, [26,27] voidfilling, [28] buoyancy, [29,30] inertia, [31] and cohesion, [10,13] have been identified, each inducing gradients in different ways. [32,33] Given the complexity, physicists have attempted to simplify the problem by studying the motion of a single large particle embedded in a granular bed [34,35] to infer the mechanisms underlying the bulk particle segregation.…”

Resonance‐induced acceleration of theRBNE‐BNEsegregation inversion

“…Various segregation agitation methods, that is, shear and vibration, have been used to separate and mix binary grains 13–17 . Many physical mechanism based on material properties, that is, percolation and buoyancy, have also been proposed to drive the segregation of binary mixtures 18–22 . Although great progress has been made, the underlying physical mechanism for the segregation remains interesting, and how to achieve a fast segregation of binary mixtures is expected to be deeply discovered and investigated for scientific relevance and practical operation.…”

“…[13][14][15][16][17] Many physical mechanism based on material properties, that is, percolation and buoyancy, have also been proposed to drive the segregation of binary mixtures. [18][19][20][21][22] Although great progress has been made, the underlying physical mechanism for the segregation remains interesting, and how to achieve a fast segregation of binary mixtures is expected to be deeply discovered and investigated for scientific relevance and practical operation. When a granular system of binary mixtures with identical size is subjected to vertical vibration, mass density plays a key role in the segregation process.…”

Resonance-induced acceleration of the RBNE-BNE segregation inversion of granular mixtures

“…Various segregation agitation methods, i.e., shear and vibration, have been used to separate and mix binary grains [13][14][15][16][17]. Many driving mechanism based on materials properties, i.e., percolation and buoyancy, have also been proposed to describe the segregation of binary mixtures [18][19][20][21][22]. Although great progress has been made, the underlying physical mechanism for the segregation remains interesting, and how to achieve a fast segregation of binary mixtures is expected to be deeply discovered and investigated for scientific relevance and practical operation.…”