We study the actuation of droplets on porous substrates by air that permeates through pores. Air pockets are created between the droplets and the substrate which, eventually, incite the droplets to a quasi-moving state. We observe this mechanism computationally and verify it experimentally, using various case studies involving water droplets of different volume that are initially pinned on a porous substrate which has been set to different inclination levels and start to slide down when actuated by permeating air. The computational model employs the continuity equation and the equations of momentum transfer that are coupled with the Volume of Fluid (VOF) method, to track the shape of the droplet. We identify two dominant actuation mechanisms – seen in computations and experiments – that are given the names ‘donut’ and ‘tunnel’. Both of them are characterized by the formation of small air pockets between the droplet and the substrate that coalesce into larger ones that finally escape the droplet, by collapsing its free surface. The two mechanisms differ in the way that the free surface of the droplet collapses. The donut mechanism has the free surface collapsing at its center, thus forming a hole in the middle of the droplet (hence the name, donut), whereas the tunnel mechanism has the free surface collapsing at its rear side, forming a horizontal hole that resembles a tunnel (hence the name). We compare each mechanism in terms of the event (mechanism) occurrence frequency and droplet displacement, and also provide the dependence of the droplet speed with respect to the flow rate of permeating air, substrate inclination and droplet volume.

中文翻译：

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多孔透气基质上液滴驱动机理的计算研究†

我们研究了通过孔隙的空气对多孔基质上的液滴的驱动作用。在液滴和基底之间产生气穴，最终使液滴激发至准移动状态。我们使用各种案例研究，通过计算观察该机制并通过实验进行验证，其中涉及不同体积的水滴，这些水滴最初固定在已设置为不同倾斜度的多孔基材上，并在由渗透空气驱动时开始向下滑动。该计算模型采用与流体体积（VOF）方法耦合的连续性方程和动量传递方程来跟踪液滴的形状。我们确定了两种主要的致动机制（在计算和实验中可以看到），它们分别被命名为“甜甜圈”和“隧道”。两者的特征都在于在液滴和基材之间形成小的气穴，这些气穴会聚结成较大的空隙，最终通过塌陷其自由表面而逃逸出液滴。两种机制的不同之处在于液滴的自由表面塌陷的方式。甜甜圈机构的自由表面在其中心处塌陷，从而在液滴的中间形成一个孔（因此得名，甜甜圈），而隧道机构的自由表面在其后侧塌陷，从而形成一个类似隧道（因此得名）。我们根据事件（机制）的发生频率和液滴位移来比较每种机制，并且还提供了液滴速度与渗透空气流速，基材倾斜度和液滴体积的相关性。