Scaling Laws in Directional Spreading of Droplets on Wettability-Confined Diverging Tracks

Spontaneous pumpless transport of droplets on wettability-confined tracks is important for various applications, such as rapid transport and mixing of fluid droplets, enhanced dropwise condensation, biomedical devices, and so forth. Recent studies have shown that on an open surface, a superhydrophilic track of diverging width, laid on a superhydrophobic background, facilitates the transport of water from the narrower end to the wider end at unprecedented rates (up to 40 cm/s) without external actuation. The spreading behavior on such surfaces, however, has only been characterized for water. Keeping in mind that such designs play a key role for a diverse range of applications, such as handling organic liquids and in point-of-care devices, the importance of characterizing the spreading behavior of viscous liquids on such surfaces cannot be overemphasized. In the present work, the spreading behavior on the aforementioned wettability-patterned diverging tracks was observed for fluids of different viscosities. Two dimensionless variables were identified, and a comprehensive relationship was obtained. Three distinct temporal regimes of droplet spreading were established: I), a Washburn-type slow spreading, II) a much faster Laplace pressure-driven spreading, and III), a sluggish density-augmented Tanner-type film spreading. The results offer design guidance for tracks that can pumplessly manage fluids of various viscosities and surface tensions.