[O-09] Kitchen Earth Science: its potential for producing diverse goals by hands-on experiments

[O09-P02] Particle clustering and stripe pattern induced by forced oscillation★Invited Papers

*Hidetsugu Sakaguchi¹ (1.Nihon University)

Keywords:

forced oscillation,clustering,pattern formation

When powder is set at the bottom of a cup of water and the cup is shaken, the powder sometimes aggregates into several clusters and forms a stripe pattern. In the well-known Kundt's experiment, cork powder vibrates owing to the sound wave and forms a stripe pattern whose wavelength is much shorter than that of the sound wave. We propose a simple mathematical model for particle gathering due to forced oscillation and perform numerical simulations. Inspired by Einstein's viscosity law, which states that the viscosity increases with particle density, we assume that the viscous friction of a particle increases owing to neighboring particles. The model has a form of forced oscillation with a damping term that depends on the distances between neighboring particles. When particles are initially placed at equal intervals along a straight line, the uniform distribution is unstable and splits into several clusters. When particles are initially placed on an equidistant square lattice, a stripe pattern of particle aggregates is formed. The wavelength of the stripe pattern is found to roughly match the most unstable wavelength in the linear stability analysis.