Hydrodynamic boundary condition in vibrofluidized granular systems

Granular media, fluidized by a vibrating wall, is studied in the high frequency (ω→∞) small amplitude (A→0) limit. It is shown that there exists an asymptotic regime such that if the product Aω5/4 is kept constant, then the behavior of the fluid in the bulk remains independent of the actual value of the amplitude with the corresponding value of the frequency. Furthermore, we show that in this asymptotic regime the boundary condition associated to the vibrating wall can be replaced by a stationary heat source. The value of this heat flux proves to be proportional to A2ω5/2 and depends on the fluid transport coefficients and on the wall oscillation waveform. Numerical solutions of the full hydrodynamic equations confirm these predictions.