Dynamics and steady state of a vibrated granular binary mixture model

TL;DR

This paper models the evolution of a vibrated granular binary mixture, deriving an effective dynamics and analytical steady state distribution, revealing segregation effects based on particle composition and fugacities.

Contribution

It introduces a new analytical approach to describe the steady state of vibrated granular mixtures, highlighting segregation phenomena.

Findings

Steady state probability depends only on particle numbers, not configurations.

Segregation occurs with dominance of either small or big particles depending on fugacities.

Effective dynamics are derived in the weak vibration limit.

Abstract

A model for the dynamical evolution of a granular binary mixture is analyzed. This system is submitted to a tapping procedure, similarly to what is done in real experiments. In the weak vibration limit, an effective dynamics for the tapping process is derived, and the steady state probability distribution is analytically found. The steady probability does not depend on the details of the configuration, but only on the number of particles of each of the two species. Depending on the values of their fugacities, the system can be either almost full of small or big particles, i.e., segregation effects are present.