Surface wave mechanism for directional motion of droplet on obliquely vibrated substrate: The effects of the excitation frequency and amplitude

Abstract

Surface waves have been introduced to explore the directional motion (DM) mechanism of a droplet on an obliquely vibrated substrate (Guo et al., Phys. Fluids, 2020), where the surface wave was decomposed for analysis by using a proper orthogonal decomposition (POD) method. In this work, the elaborate responses of the POD modes are explored given varying excitation frequency (f) and amplitude. It is found the first two POD modes evolve quite differently as f changes. The first (swaying) POD mode always follows the excitation, while the second (spreading) POD mode transforms from co-frequency (linear) to double-frequency (non-linear) response as f decreases, which lets the second POD mode have a frequency of ∼2f0 constantly when f0<f<2f0 (f0 and 2f0 are the lowest natural frequencies of swaying and spreading vibration, respectively). That makes the POD modes contribute differently on the DM in different regimes, and the first POD mode may not contribute more to the DM. On the other hand, the DM speed is found to grow gradually when f decreases or the vibration acceleration amplitude increases, which is attributed to the increasing vibration nonlinearity derived from more and more kinetic energy input. This work improves the understanding of the DM from the perspective of surface waves.