We develop a numerical framework for simulating the coalescence and jumping of microdroplets on superhydrophobic surfaces. The framework combines the volume of fluid (VOF) method with models for advancing and receding contact angles on a number of superhydrophobic surfaces. We demonstrate the temporal and spatial convergence of the framework and show agreement between our numerical results and other experimental studies. The capillary-inertial scaling is investigated together with the existence of a cut-off behaviour frequently observed in the lower size-range of that regime. We investigate findings in some of the previous studies that the cut-off behaviour can be attributed to viscosity effects and dissipation due to interaction with surface microstructures. We exemplify specific features related to the jumping process and the corresponding energy budget analysis when microdroplets coalesce and jump. We have tested droplets of a radius as small as 0.5 μm that are still jumping but recorded a decrease in the jumping velocity and the degree of energy conversion compared to the jumping of larger droplets. We argue and prove that strong capillary forces originating from the high curvature oscillations dissipate the energy of the system significantly faster in the case of microdroplets.

中文翻译：

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超疏水表面上聚结诱导的微滴跳跃——数值研究

我们开发了一个数值框架来模拟超疏水表面上微滴的聚结和跳跃。该框架将流体体积 (VOF) 方法与用于在多个超疏水表面上前进和后退接触角的模型相结合。我们展示了框架的时间和空间收敛性，并显示了我们的数值结果与其他实验研究之间的一致性。毛细管惯性缩放与在该状态的较低尺寸范围内经常观察到的截止行为的存在一起进行了研究。我们调查了一些先前研究中的发现，即截止行为可归因于粘度效应和由于与表面微结构相互作用而引起的耗散。我们举例说明了与跳跃过程相关的特定特征以及微滴聚结和跳跃时相应的能量收支分析。我们测试了半径小至 0.5 μm 的液滴仍在跳跃，但与较大液滴的跳跃相比，跳跃速度和能量转换程度有所下降。我们论证并证明，在微滴的情况下，源自高曲率振荡的强毛细力会显着更快地消散系统的能量。