Granular systems on a vibrating wall: the hydrodynamic boundary condition

Granular media, fluidized by a vibrating wall, is studied in the limit of high frequency. It is shown that if the product Aω−5/4 is kept constant, then different amplitudes A (with the corresponding frequency ω) produce the same macroscopic result. Furthermore, it is found that in the hydrodynamic equations the boundary condition associated to the vibrating wall can be replaced by a stationary heat source. Numerical solutions of the full hydrodynamic confirm these two predictions.