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 $z=A\cos \left(\omega t\right)$. Above $\gamma \equiv A{\omega }^2/g\simeq 1$, convection begins, creating a heap of height $L$. We find that for particles of diameter $d<\mathrm{}1\mathrm{mm}$ the pressure $P$ of the surrounding gas plays a key role: $L=b\tanh \left(\mathrm{KP}\right)+c$, where $b$ and $K$ depend on $h$, the gas viscosity, $d$, $\gamma$, 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.