Modified inelastic bouncing ball model of the Brazil nut effect and its reverse

Abstract

© 2018, Springer-Verlag GmbH Germany, part of Springer Nature. We developed the modified inelastic bouncing ball model (mIBBM) to describe the emergence of the Brazil nut effect (BNE) and its reverse (RBNE) in a vertically-vibrated binary granular mixture. The mIBBM incorporates the container-to-grains force-transmission efficiency (transmissibility) Tr to quantify the dimensionless mean void lifetime ω⟨ δt⟩ that acts as the segregation phase indicator where ω is the vibration angular frequency. The mixture is represented as two non-interacting inelastic balls, Ball A and Ball B. Each ball bounces with a time-of-flight τA (or τB) that depends on transmissibility TrA (or TrB) and the dimensionless container acceleration Γ, i.e., τA = τA(Γ, TrA) and τB = τB(Γ, TrB). The ball dynamics are described by the bifurcation diagrams of the dimensionless times-of-flight, ωτA(Γ, TrA) and ωτB(Γ, TrB). The probability-weighted difference ω⟨ δt⟩ between branches of the two diagrams is computed and interpreted as follows: ω⟨ δt⟩ > 0 (occurrence of BNE), ω⟨ δt⟩ < 0 (RBNE) and ω⟨ δt⟩ = 0 (no segregation). Segregation phases are revealed as varying shifts and widths of ω⟨ δt⟩ across the Γ axis. The phase boundaries in the ω⟨ δt⟩ -versus-Γ diagram are sensitive to changes in TrA, TrB and ΔTr = (TrA − TrB). The mIBBM explains why the BNE is a more likely than the RBNE and predicts a segregation phase sequence that is generally consistent with related experimental results taken over a limited ω-range. Additional experiments are needed to enable a more comprehensive and precise evaluation of the mIBBM.

Source or Periodical Title

Granular Matter

ISSN

14345021

Document Type

Article

Subject

Bifurcation, Bouncing ball, Brazil nut effect, Granular segregation, Vibration

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