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 z0ex{0ex}=0ex{0ex}Acos (). Above ^2/g1, convection begins, creating a heap of height L. We find that for particles of diameter d<10ex{0ex}mm the pressure P of the surrounding gas plays a key role: L0ex{0ex}=0ex{0ex}btanh (KP) +c, where b and K depend on h, the gas viscosity, d, , 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.