From antinode clusters to node clusters: The concentration dependent transition of floaters on a standing Faraday wave

TL;DR

This study investigates how the collective behavior of floating spheres on a standing wave transitions from clustering at antinodes to nodal lines as the concentration increases, revealing an energy-based explanation for this pattern inversion.

Contribution

It introduces a concentration-dependent transition in floating particle patterns on standing waves and explains it through potential energy considerations.

Findings

At low concentration, particles form antinode clusters due to energy minimization.

Beyond a critical concentration, particles switch to forming nodal line clusters.

The transition is explained by a reversal in the energetic favorability of the patterns.

Abstract

A hydrophilic floating sphere that is denser than water drifts to an amplitude maximum (antinode) of a surface standing wave. A few identical floaters therefore organize into antinode clusters. However, beyond a transitional value of the floater concentration $\phi$, we observe that the same spheres spontaneously accumulate at the nodal lines, completely inverting the self-organized particle pattern on the wave. From a potential energy estimate we show (i) that at low $\phi$ antinode clusters are energetically favorable over nodal ones and (ii) how this situation reverses at high $\phi$, in agreement with the experiment.