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 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 nu = 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 similar to (nu - nu(c))(-alpha), where nu(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.