Phase transition characteristics of Faraday waves

Through experimentation, we have discovered that with the changing of driving conditions, the Faraday waves undergo two abrupt transitions in spatiotemporal order: onset and instability. The driving amplitudes and frequencies corresponding to these two transition points exhibit power-law relationships. The power-law exponent of the onset can be used to categorize different liquids into two distinct classes, which primarily reflects the differential contribution of surface tension and viscous forces in the surface wave dispersion relation. Meanwhile, the power-law exponent of the instability serves as an indicator of the non-Newtonian properties of the liquid. Based on our experimental data, we have developed a phenomenological theoretical model that offers a unified understanding of the Faraday pattern properties.