滑动液滴的形态转变：动力学和分叉
Morphological transitions of sliding drops: Dynamics and bifurcations
摘要：
我们研究完全三维的液滴，采用薄膜方程，占毛细作用，润湿性，并在小梯度（或长波）近似的横向驱动力的倾斜下滑。特别是，我们专注于定性变化的形态和行为的固定滑动滴。我们采用基板的倾斜角作为控制参数，并使用连续技术来分析几个固定的液滴尺寸的固定液滴的分岔图，其线性稳定性，和相关的本征模式。通过直接的数值模拟，也被用来调查一个分支的时间周期性的行为（对应于重复的分裂-合并周期，其中的分裂也被称为珍珠）出现在一个全球性的不稳定性，相关的滞后行为，和周期加倍级联的存在范围和不稳定性的预测进行测试。本文还研究了具有有限长尾的液滴系统的非平凡振荡行为。最后，它示出的分岔图的主要特征遵循标度律在几十年的液滴尺寸。
英文摘要：
We study fully three-dimensional droplets that slide down an incline by employing a thin-film equation that accounts for capillarity, wettability, and a lateral driving force in small-gradient (or long-wave) approximation. In particular, we focus on qualitative changes in the morphology and behavior of stationary sliding drops. We employ the inclination angle of the substrate as control parameter and use continuation techniques to analyze for several fixed droplet sizes the bifurcation diagram of stationary droplets, their linear stability, and relevant eigenmodes. The obtained predictions on existence ranges and instabilities are tested via direct numerical simulations that are also used to investigate a branch of time-periodic behavior (corresponding to repeated breakup-coalescence cycles, where the breakup is also denoted as pearling) which emerges at a global instability, the related hysteresis in behavior, and a period-doubling cascade. The nontrivial oscillatory behavior close to a Hopf bifurcation of drops with a finite-length tail is also studied. Finally, it is shown that the main features of the bifurcation diagram follow scaling laws over several decades of the droplet size.
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