Lattice Boltzmann Simulation of Droplet Impact on an Oscillating Horizontal Surface

Abstract

In this work, the droplet impact on a sinusoidally oscillating hydrophobic substrate is numerically simulated using the lattice Boltzmann method. We focus particularly on energy transfer and the maximum droplet spreading diameter (${\beta }_m$) as functions of substrate oscillation parameters, the Weber number, and the wettability of the substrate. Our analysis shows that the maximum spreading diameter scales linearly with the tangential Weber number ($W{e}_s$), calculated from the substrate velocity amplitude. Notably, the spreading dynamics exhibit a nonmonotonic, resonance-like response, peaking when the spreading time coincides with half the oscillation period. Additionally, decreasing the contact angle strengthens interfacial adhesion to amplify horizontal migration, whereas superhydrophobic surfaces severely attenuate this tangential momentum exchange through inherent slip. Furthermore, the analysis of the normal Weber number ($W{e}_n$) uncovers a “forgetting” mechanism, whereby the droplet ultimately converges to a consistent dynamic response across different $W{e}_n$ as the initial kinetic energy dissipates. The study further elucidates the distinct regulatory effects of amplitude and period: amplitude primarily shifts the overall ${\beta }_m$-$W{e}_n$ scaling relation, while period significantly alters its slope. Based on these insights, we propose a universal scaling law that decomposes the maximum spreading factor into a normal-inertia-dominated term and a tangential vibration-coupling term. A semi-empirical correlation is subsequently derived, which quantifies the significant spreading enhancement induced by long-period oscillations and captures the attenuation of this gain at high $W{e}_n$.