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Scaling behavior in the convection-driven Brazil nut effect

Prakhyat Hejmady^*, Ranjini Bandyopadhyay^†, Sanjib Sabhapandit^‡, and Abhishek Dhar^§

Raman Research Institute, CV Raman Avenue, Sadashivanagar, Bangalore 560080, India

^*phejmady@rri.res.in
^†ranjini@rri.res.in
^‡sanjib@rri.res.in
^§dabhi@rri.res.in

Phys. Rev. E 86, 050301(R) – Published 19 November, 2012

DOI: https://doi.org/10.1103/PhysRevE.86.050301

Abstract

The Brazil nut effect is the phenomenon in which a large intruder particle immersed in a vertically shaken bed of smaller particles rises to the top, even when it is much denser. The usual practice while describing these experiments has been to use the dimensionless acceleration $Γ = a ω^{2} / g$ , where $a$ and $ω$ are, respectively, the amplitude and the angular frequency of vibration and $g$ is the acceleration due to gravity. Considering a vibrated quasi-two-dimensional bed of mustard seeds, we show here that the peak-to-peak velocity of shaking $v = a ω$ , rather than $Γ$ , is the relevant parameter in the regime where boundary-driven granular convection is the main driving mechanism. We find that the rise time $τ$ of an intruder is described by the scaling law $τ \sim {(v - v_{c})}^{- α}$ , where $v_{c}$ is identified as the critical vibration velocity for the onset of convective motion of the mustard seeds. This scaling form holds over a wide range of $(a, ω)$ , diameter, and density of the intruder.

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References (24)

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Scaling behavior in the convection-driven Brazil nut effect

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