Effects of Ambient Gases on Granular Materials under Vertical Vibration

We consider layers of noncohesive granular materials of mean height h subject to vertical vibration z0ex0ex=0ex0exAcos(ωt). Above γ≡Aω²/g1, convection begins, creating a heap of height L. We find that for particles of diameter d<10ex0exmm the pressure P of the surrounding gas plays a key role: L0ex0ex=0ex0exbtanh(KP)+c, where b and K depend on h, the gas viscosity, d, γ, and A. Convection is significantly suppressed if the shaker sidewalls are permeable, showing that gas trapped in the granular material is a major source of heaping. We consider criteria to determine when gas effects are relevant.