## Abstract

Granular materials fluidized by a rapidly vibrating bottom plate often

develop a fascinating density inversion: a heavier layer of granulate supported by a

lower-density region. We employ the Navier-Stokes granular hydrodynamics to follow

a density inversion as it develops in time. Assuming a dilute low-Mach-number flow,

we derive a reduced time-dependent model of the late stage of the dynamics. The

model looks especially simple in the Lagrangian coordinates. The time-dependent

solution describes the growth of a density peak at an intermediate height. A transient

temperature minimum is predicted to develop in the region of the density peak.

The temperature minimum disappears at later times, as the system approaches the

steady state. At late times, the predictions of the low-Mach-number model are in

good agreement with a numerical solution of the full hydrodynamic equations. At

an early stage of the dynamics, pressure oscillations are predicted

develop a fascinating density inversion: a heavier layer of granulate supported by a

lower-density region. We employ the Navier-Stokes granular hydrodynamics to follow

a density inversion as it develops in time. Assuming a dilute low-Mach-number flow,

we derive a reduced time-dependent model of the late stage of the dynamics. The

model looks especially simple in the Lagrangian coordinates. The time-dependent

solution describes the growth of a density peak at an intermediate height. A transient

temperature minimum is predicted to develop in the region of the density peak.

The temperature minimum disappears at later times, as the system approaches the

steady state. At late times, the predictions of the low-Mach-number model are in

good agreement with a numerical solution of the full hydrodynamic equations. At

an early stage of the dynamics, pressure oscillations are predicted

Original language | American English |
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Title of host publication | Granular Gas Dynamics |

Editors | Thorsten Pöschel, Nikolai Brilliantov |

Place of Publication | Berlin ; Heidelberg ; New York |

Publisher | Springer |

Pages | 251-266 |

Number of pages | 16 |

DOIs | |

State | Published - 2003 |

### Publication series

Name | Lecture notes in physics |
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Volume | 624 |