Modeling the dynamics of an oil drop driven by a surface acoustic wave in the underlying substrate

We present a novel theoretical model, supported by recent experiments, describing the spreading dynamics of a macroscopic silicone oil (PDMS) drop driven by MHz-frequency surface acoustic waves (SAWs) in the underlying substrate. Using the long-wave approximation, we derive a reduced-order model that captures the time-dependent coupling between fluid motion and acoustic forcing. For macroscopic drops, the primary driving force comes from Reynolds stress variations caused by the attenuation of the SAW beneath the drop. An important finding is that viscous dissipation plays a significant role, and we demonstrate that neglecting its effects is inconsistent with the model development. Based on our theory and related computations, we analyze drop motion on flat substrates, showing that the drop accelerates to a nearly constant speed and leaves a thin trailing film. We then extend the model to include topographical obstacles, which contribute to the gravitational, capillary, and acoustic forces in the system. The resulting fourth-order PDE for the film height is solved numerically and produces results that qualitatively agree with experiments. Parametric studies further clarify how the drop dynamics depend on fluid and obstacle properties.