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 = aω(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 = 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 τ of 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.