Surface wave mechanism for directional motion of droplet on an obliquely vibrated substrate

Abstract

The directional motion of a two-dimensional droplet on an obliquely vibrated substrate is studied numerically. The time dependent droplet profile is decomposed by using a proper orthogonal decomposition (POD) method. Two dominant POD modes of the capillary wave are identified. The first mode is quasi-harmonic, which leads to an apparent wetted area difference between uphill and downhill stages of the substrate vibration (ΔS). It plays a key role in the directional motion. The second mode is weak but contributes to ΔS subtly. The two modes qualitatively match the proposed “swaying” and “spreading” modes. Our decomposition directly reveals the connection between ΔS and the surface waves.