Quantfying rich patterns in agglomeration of floating beads

TL;DR

This study investigates how floating beads form diverse patterns on a standing Faraday wave, revealing a systematic transition from antinode to node clustering as bead concentration increases, characterized by Minkowski functionals.

Contribution

The paper introduces a modified Minkowski functional approach to quantitatively analyze and characterize the morphology of patterns formed by floating beads on a Faraday wave.

Findings

Pattern morphology shifts systematically with bead concentration.

Low concentration: antinode clusters; high concentration: node clusters.

Modified Minkowski functionals effectively quantify cluster properties.

Abstract

Macroscopic spherical particles spontaneously form rich patterns on a standing Faraday wave. These patterns are found to follow a very systematic trend depending on the floater concentration $\phi$: The same floaters that accumulate at amplitude maxima (antinodes) of the wave at low $\phi$, surprisingly move towards the nodal lines when $\phi$ is beyond a certain value. In more detail, circular irregularly packed antinode clusters at low $\phi$ give way to loosely packed filamentary structures at intermediate $\phi$, and are then followed by densely packed grid-shaped node clusters at high $\phi$. Here, we successfully characterize the morphology of these rich patterns using a metric analysis, i.e., the Minkowski functionals. We modify the Minkowski functionals such that we are able to measure the physical quantities of the clusters such as area, perimeter, and aspect ratio.