Deformation of fluid free surfaces driven by high frequency vibration

Formation of surface waves on a free surface of a thin fluid layer driven by high frequency (f $\approx$ 20 MHz) surface acoustic waves (SAWs) is investigated, both numerically and experimentally. The SAWs are transmitted along a surface of a piezoelectric substrate vibrating at nanometer displacement amplitudes $\xi$. Through a perturbation expansion, the governing equations of fluid motion are decomposed into those describing a first-order acoustic field and second-order acoustic streaming. Numerical solution of these equations and use of Fourier transforms allow the fundamental and harmonic frequencies of the surface deformation to be identified. For low excitation amplitudes ($\xi$ $\sim$ 1 nm), the frequency of the perturbed free surface is approximately equal to the SAW excitation frequency. However, as the amplitude increases ($\xi$ $>$ 1 nm), the dominant resonant frequency of the fluid free surface shifts to the low frequency range (f $\sim$ 1 MHz), suggesting that, in this regime, the free surface deformation is controlled by acoustic streaming. The numerical results for $\xi$ $\sim$ 1 nm qualitatively agree with experimental laser Doppler Vibrometry measurements.