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.

中文翻译：

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倾斜振动基体上液滴定向运动的表面波机制

数值研究了二维液滴在倾斜振动的基板上的定向运动。通过使用适当的正交分解（POD）方法分解与时间有关的墨滴轮廓。确定了毛细管波的两种主要POD模式。第一模式是准谐波，其导致基板振动的上坡和下坡阶段之间的表观润湿面积差异（ΔS）。它在定向运动中起关键作用。第二种模式较弱，但对ΔS的贡献很小。这两种模式在质量上与建议的“摇摆”和“传播”模式相匹配。我们的分解直接揭示了ΔS和表面波之间的联系。