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Scaling behavior in the convection-driven Brazil-nut effect

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 ωare 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= aω, 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 τof an intruder is described by the scaling law τ~ (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.