Simple model for reverse buoyancy in a vibrated granular system

We report an experimental study of the motion of a large sphere immersed in a deep dry granular bed, subjected to vertical sinusoidal vibrations. Under certain conditions large heavy objects immersed in a homogeneous vibrated granular medium rise and similar light ones sink to the bottom. This is called reverse buoyancy. We have measured the vertical velocity of immersed large spheres, as a function of their density, under conditions for which reverse buoyancy is observed. We propose a one-dimensional mechanical model, based on the assumption that a cyclic fluidization of the medium occurs. With this model, that takes into account a buoyancy force and a frictional drag, we obtain, under the conditions of our measurements, the rising velocity for heavy objects and the sinking rate for light ones. The model yields a very good qualitative and quantitative agreement with our experiments.