Radiation Stress Links Faraday Waves to the Shrinkage of Holes in Capillary Surfaces

When subjecting a liquid film to vertical vibrations, a phenomenon known as Faraday instability can occur. Its characteristic waves become increasingly chaotic with stronger vibrations. In the absence of vibrations, stable holes in a bounded liquid film are described by the Young-Laplace equation. Combining both phenomena raises the question of how the waves affect the hole. We present a quantitative model that incorporates the underlying physics and describes the time-averaged size of the hole. Remarkably, we find that the experimentally obtained hole size can still be described by the Young-Laplace equation using an effective capillary length. We establish a relationship between this effective capillary length and the dynamic system by mapping it to the required wave radiation stress for the measured hole shrinkage. In addition, we determine the radiation stress by measuring the wave energy through spectral surface deformation measurements. Comparing these independent measurements of the radiation stress shows good quantitative agreement in the highly dynamic regime of chaotic Faraday waves. This agreement holds irrespective of the initial hole size and exciter frequency. Our results demonstrate the possibility of quantifying the radiation stress due to chaotic Faraday waves solely by observing the time-averaged shrinkage of a hole.