Fracture, aggregation and segregation in dry, granular flows

James T Jenkins,M.A Aguirre,L.A Pugnaloni,Michele Larcher,S Luding,R Soto

doi:10.1051/epjconf/202124903040

James T Jenkins, M.A Aguirre + Show 4 more

Open Access

https://doi.org/10.1051/epjconf/202124903040

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Abstract

Particle fracture, the formation of small particles as the result of the breakage of large ones, and aggregation, the formation of large particles as the result of the combination of small ones, have important implications in industry (e.g. food processing, pharmaceutical production) and geophysics (e.g., snow avalanches and rock debris flows). Also, the presence of particles of different size that result from fracture and aggregation can induce segregation, resulting in the migration of large and small particles to different regions of the flow. Here, we formulate simple models for fracture and agglomeration and analyze the evolution of measures of the relative concentration of two sizes of spheres due the combined effects of fracture, aggregation, and segregation in dense, dry, granular flows. Particle breakage and combination is influenced by the frequency of collisions, by the local number density of the spheres, and by the particle kinetic energy. Segregation is predicted using a kinetic theory proposed by Larcher & Jenkins [2].

Highlights

We consider a steady, dense, dry, collisional flow [1] of a binary mixture of two types of inelastic spheres down an incline at an angle q, under the influence of gravitational acceleration g
We consider a similar situation, but allow for the possibility that depending on the particle kinetic energy and the frequency of collisions, a large sphere may fracture into two smaller spheres and two small spheres may aggregate into one larger sphere, in such a way that mass is conserved
The number of large sphere collisions per unit volume can be evaluated as the product of the frequency of collisions per unit sphere referred to the mixture, given by Eq (1), and the number density of species A, nA, as nAω

Summary

Introduction

Dense, dry, collisional flow [1] of a binary mixture of two types of inelastic spheres down an incline at an angle q, under the influence of gravitational acceleration g. We consider a similar situation, but allow for the possibility that depending on the particle kinetic energy and the frequency of collisions, a large sphere may fracture into two smaller spheres and two small spheres may aggregate into one larger sphere, in such a way that mass is conserved. The local difference in the presence of the two types of spheres is described by means of the number density difference, X ≡ (nA - nB) / 2n, the kinetic.

Particle fracture

Particle aggregation

Particle segregation

An example

Conclusion