Scaling Law and Mechanism for the Formation of Stripe Patterns in a Binary Mixture of Granular Materials under Horizontal Vibration

Abstract

In this study, we performed experimental studies on the formation of stripe patterns in a granular mixture under horizontal vibration. The granular mixture was prepared by mixing brass and glass beads of 1 mm in diameter in the ratio of 1:2 by volume and immersing them in a liquid. The mixture becomes separated into glass-only and brass-only bands of random sizes. The number of bands is an increasing function of Gamma x root Re only (Gamma: acceleration relative to gravity; Re: Reynolds number based on the particle diameter). As the mechanism of stripe formation, the formation of clusters in the mixture due to local fluctuations and strong hydrodynamic interactions between particles is proposed. The initial-condition dependency also supports the cluster formation mechanism rather than the Kelvin-Helmholtz-like hydrodynamic instability.