Levitating granular cluster: statics and oscillations

The granular Leidenfrost state consists of a dense granular cluster levitating above a hot granular gas. The density of particles inside the cluster can be very high and even close to the density of crystalline packing. To describe this state theoretically, one needs to know the density dependence of constitutive relations (pressure, heat losses, thermal conductivity) at these very high densities. We measured the constitutive relations at high densities in molecular dynamics simulations in three different settings: a uniform freely cooling dense granulate (to measure heat losses), a uniform ensemble of elastically colliding particles (to measure pressure), and a dense granular medium between two thermal walls under gravity (to measure thermal conductivity). Next, the hydrodynamic equations with the resulting expressions were solved to describe the levitating cluster state in various parameter regimes. Separate molecular dynamics simulations were performed to test the theoretical predictions, and a good agreement with theoretical results was observed. In some cases, however, the agreement with the static levitating cluster theoretical solution was not good, since the cluster developed high amplitude low frequency oscillations. We will discuss these oscillations in some detail.