Effects of Ambient Gases on Granular Materials under Vertical Vibration

Abstract

We consider layers of noncohesive granular materials of mean height $h$ subject to vertical vibration $z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}A\mathrm{cos}(\ensuremath{\omega}t)$. Above $\ensuremath{\gamma}\ensuremath{\equiv}A{\ensuremath{\omega}}^{2}/g\ensuremath{\simeq}1$, convection begins, creating a heap of height $L$. We find that for particles of diameter $d<1\phantom{\rule{0ex}{0ex}}\mathrm{mm}$ the pressure $P$ of the surrounding gas plays a key role: $L\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}b\mathrm{tanh}(\mathrm{KP})+c$, where $b$ and $K$ depend on $h$, the gas viscosity, $d$, $\ensuremath{\gamma}$, 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.