Dynamics of a three-dimensional oil drop driven by a surface acoustic wave over topography

We perform three-dimensional simulations of SAW-driven spreading of silicone oil drops on flat substrates and over solid obstacles. The resulting model takes the form of a three-dimensional long-wave thin-film equation incorporating capillary, gravitational, and SAW-induced acoustic stresses. A key feature of the formulation is a smooth attenuation function that localizes acoustic forcing within the bulk drop while avoiding spurious transverse discontinuities. Comparisons with results of earlier 2D formulations demonstrate qualitatively similar dynamics, albeit the additional spatial dimension permits transverse mass redistribution driven by capillarity, which leads to slower streamwise spreading and slightly lower drop apexes than predicted by 2D models. The model is applied to SAW induced dynamic wetting of flat substrates and solid obstacles and is representative of experimental geometries. Quantitative comparisons with experimental observations show good agreement for front propagation and obstacle climbing dynamics. In particular, improved agreement with the experimentally observed dependence of the liquid climbing time over obstacles on SAW amplitude is obtained when the fully three-dimensional formulation is used.