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

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.