Self-similarity of contact line depinning from textured surfaces

Abstract

The mobility of drops on surfaces is important in many biological and industrial processes, but the phenomena governing their adhesion, which is dictated by the morphology of the three-phase contact line, remain unclear. Here we describe a technique for measuring the dynamic behaviour of the three-phase contact line at micron length scales using environmental scanning electron microscopy. We examine a superhydrophobic surface on which a drop’s adhesion is governed by capillary bridges at the receding contact line. We measure the microscale receding contact angle of each bridge and show that the Gibbs criterion is satisfied at the microscale. We reveal a hitherto unknown self-similar depinning mechanism that shows how some hierarchical textures such as lotus leaves lead to reduced pinning, and counter-intuitively, how some lead to increased pinning. We develop a model to predict adhesion force and experimentally verify the model’s broad applicability on both synthetic and natural textured surfaces.

Multi-height structures in injection molded polymer

“…For all surfaces the advancing angle is around 160° and the difference in hysteresis originates only from the receding angle. This is in agreement with previous findings for drops in the Cassie Baxter state rolling off the surface [13,14].. To optimize the geometry for increased water repellency one normally decreases the surface coverage of structures in contact with the water at the cost of decreasing the stability of the Cassie Baxter state [15]. For the random multi-height structures, we see that this in addition seems to lead to an increased hysteresis.…”

A dynamic Cassie–Baxter model

“…(the ratio of the grating width to pitch) of 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, and 0.8 were prepared and tested. Overall, the receding contact line periodically pinned on, slid on, and jumped across microstructures, presenting stick-slip motions consistent with observations from other researchers [8][9][10][11] . However, we were able to obtain far more details about the motion of the receding meniscus that would not have been possible without the 2-D condition and high-speed imaging.…”

“…We note that, although λ s in Eq. 10 may appear similar to the semi-empirical parameters commonly proposed in the literature 3,11,31 , λ s is fully analytical. Instead, λ s depends not only on the structure geometries but also on the receding conditions (e.g., direction), as illustrated in Figure S4.…”

Optimal Design of Permeable Fiber Network Structures for Fog Harvesting

“…As the small deposited water droplets coalesce, the growing droplets are influenced by the competition between aerodynamic drag forces ( F drag ) and surface adhesion forces ( F adhesion ). [28][29][30] When the drag force overwhelms the adhesion force, the droplets are re-entrained in the fog flow, leading to a decrease in the fog collection efficiency (Figure 3a). …”