Computational investigation of actuation mechanisms of droplets on porous air-permeable substrates

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.