  We present an experimental, theoretical, and computational study of the
spreading of a millimetric silicon oil drop under the excitation of a surface
acoustic wave (SAW), traveling in the underlying solid substrate. Our
theoretical model, formulated within the long wave approach, dynamically
captures the interplay between fluid dynamics and acoustic driving forces,
emphasizing Eckart streaming as the dominant mechanism over Schlichting and
Rayleigh streaming due to drop thickness. Following an initial deformation
phase to accommodate acoustic stress, the drop accelerates to a sustained
translation at nearly constant speed, leaving behind a thin wetting layer. This
speed is sustained by the quasi-steady shape of the drop's main body,
influenced by SAW attenuation. Notably, SAW attenuation becomes significant
once the wave reaches the main body of the drop, with weaker effects observed
under the air and the micron-thick liquid trail left behind the drop. The
translating drop's speed is found to be dependent on the drop size, as well as
on the SAW intensity. The drop's steady shape and speed are further informed by
analytical consideration of a simplified traveling wave type model, that
clarifies contributions from different physical effects. The theoretical
results show qualitative and sometimes even quantitative agreement with the
experiments, particularly regarding drop height and traveling speed.
