Capillary wave motion excited by high frequency surface acoustic waves

This paper presents a numerical and experimental study of capillary wave motion excited by high frequency surface acoustic waves (SAWs). The objective of this study is to provide insight into the dynamic behavior of the fluid free surface and its dependence on the excitation amplitude. A two-dimensional numerical model that couples the motion of the piezoelectric substrate to a thin liquid layer atop the substrate is constructed. A perturbation method, in the limit of small-amplitude acoustic waves, is used to decompose the equations governing fluid motion to resolve the widely differing time scales associated with the high frequency excitation. While this model focuses on the free surface dynamics in the low-amplitude flow regime, the experimental study focuses on the high-amplitude flow regime. Transformation of time series data from both experiments and simulations into the frequency domain reveals that, in the low-amplitude regime, a fundamental resonant frequency and a superharmonic frequency are found in the frequency spectra. The former is found to be identical to that of the applied SAW, and the free surface displacement magnitude is comparable to that of the substrate displacement. Our numerical results also confirm previous speculation that the separation distance between two displacement antinodal points on the free surface is $δSt≈λSAW/2$ for a film and $δSt≈λf/2$ for a drop, where $λSAW$ and $λf$ denote the SAW wavelength and the acoustic wavelength in the fluid, respectively. Finally, in the high-amplitude regime, strong nonlinearities shift the acoustic energy to a lower frequency than that of the SAW; this low-frequency broadband response, quite contrary to the subharmonic half-frequency capillary wave excitation predicted by the classical linear or weakly nonlinear Faraday theories, is supported by a scaling analysis of the momentum equations.