Scaling behavior in the convection-driven Brazil-nut effect

TL;DR

This study reveals that in the convection-driven Brazil-nut effect, the peak-to-peak shaking velocity v is the key parameter, and the intruder's rise-time follows a specific scaling law related to a critical velocity v_c.

Contribution

The paper demonstrates that the shaking velocity v, not the dimensionless acceleration Gamma, governs the convection-driven Brazil-nut effect, introducing a new scaling law for rise-time.

Findings

Rise-time scales as  au  (v - v_c)^{-\u03b1}

Shaking velocity v is the relevant parameter, not Gamma

Scaling law holds across various particle sizes and densities

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 \Gamma=a \omega^2/g, where a and \omega 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\omega, rather than \Gamma, is the relevant parameter in the regime where boundary-driven granular convection is the main driving mechanism. We find that the rise-time \tau of an intruder is described by the scaling law \tau ~ (v-v_c)^{-\alpha}, 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,\omega), diameter and density of the intruder.