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.