Onset of visible capillary waves from high-frequency acoustic excitation

Abstract

Remarkably, the interface of a fluid droplet will produce visible capillary waves when exposed to acoustic waves. For example, a small ($\sim\! 1 \mu$L) sessile droplet will oscillate at a low $\sim\!10^2$~Hz frequency when weakly driven by acoustic waves at $\sim\!10^6$~Hz frequency and beyond. We measured such a droplet's interfacial response to 6.6~MHz ultrasound to gain insight into the energy transfer mechanism that spans these vastly different timescales, using high-speed microscopic digital transmission holography, a unique method to capture three-dimensional surface dynamics at nanometer space and microsecond time resolutions. We show that low-frequency capillary waves are driven into existence via a feedback mechanism between the acoustic radiation pressure and the evolving shape of the fluid interface. The acoustic pressure is distributed in the standing wave cavity of the droplet, and as the shape of the fluid interface changes in response to the distributed pressure present on the interface, the standing wave field also changes shape, feeding back to produce changes in the acoustic radiation pressure distribution in the cavity. A physical model explicitly based upon this proposed mechanism is provided, and simulations using it were verified against direct observations of both the microscale droplet interface dynamics from holography and internal pressure distributions using microparticle image velocimetry. The pressure-interface feedback model accurately predicts the vibration amplitude threshold at which capillary waves appear, the subsequent amplitude and frequency of the capillary waves, and the distribution of the standing wave pressure field within the sessile droplet responsible for the capillary waves.