Microscopic model for a granular solid-liquid-like phase transition

TL;DR

This paper introduces a microscopic model explaining the phase transition and coexistence between solid and liquid states in vibrated granular matter, aligning well with experimental and simulation data.

Contribution

It proposes a microscopic origin for granular solid-liquid phase transitions, modeling the solid as an effective particle and deriving a power balance equation.

Findings

Model predictions match experimental results

Effective particle approach captures collective particle motion

Power equation relates velocities to microscopic parameters

Abstract

Forced granular matter in confined geometries presents phase transitions and coexistence. Depending on the system and forcing parameters, liquid-vapor and liquid-solid co-existing states are possible. For the solid-liquid coexistence that is observed in quasi-two-dimensional vibrated systems, both first- and second-order transitions have been reported. Experiments show that particles in the solid cluster move collectively, synchronized with the cell's vibration, in a similar way to the collect-and-collide regime observed in granular dampers. Here, we present a model that proposes a microscopic origin of this granular phase transition and co-existence. Imposing synchronicity, we model the solid cluster as an effective particle of zero restitution coefficient. In addition, we use the mechanical equilibrium between the two phases, with an equation of state validated for hard spheres relating the horizontal velocities in each phase. Balancing energy input and dissipation per unit time we obtain a global power equation, which relates the characteristic vertical and horizontal velocities to the microscopic relevant parameters (geometric and dissipation coefficients) as well as to the vibration amplitude and solid cluster's size. The predictions of the model compare quite well with our experimental results and with the experimental and dynamic simulation results reported elsewhere.