# Experimental evidence of thermal-like behaviour in dense granular suspensions

## TL;DR

This study demonstrates that dense granular suspensions under stationary sedimentation exhibit thermal-like behavior, with an equation of state linking pressure and packing fraction, suggesting an effective temperature and insights into phase transitions.

## Contribution

The paper provides experimental evidence of thermal-like behavior in dense granular suspensions and derives a semi-analytical equation of state for the system.

## Key findings

- Granular pressure and packing fraction follow an equation of state.
- Identification of an effective temperature related to buoyant energy.
- System behavior at high packing fractions and phase transition implications.

## Abstract

We experimentally investigate the statistical behaviour of a model two-dimensional granular system undergoing stationary sedimentation. Buoyant cylindrical particles are rotated in liquid-filled drum, thus confined in a harmonic centripetal potential with tunable curvature, which competes with gravity to produce various stationary states: though heterogeneous, the packing fraction of the system can be tuned to be fully dispersed to fully crystallised as the rotation rate is increased. We show that this dynamical system is in mechanical equilibrium in the confining potential and exhibits a thermal-like behaviour, where the granular pressure and the packing fraction are related through an equation of state. We obtain a semi-analytical expression of the equation of state allowing to probe the nature of the hydrodynamic interactions between the particles. This description is valid in the whole range of the physical parameters we investigated and reveals a buoyant energy scale that we interpret as an effective temperature. We finally discuss the behaviour of our system at high packing fractions and the relevance of the equation of state to the liquid-solid phase transition.