title: Wetting States of Droplets on Patterned Surfaces and in an Electric Field
Creators: name: Hartmann, Maximilian Roland
Publisher: name: UNSPECIFIED
Year: 2021

description: In nature, wetting of patterned surfaces by droplets is omnipresent. For example, it is used by the Stenocara desert beetle in the Namibian desert to collect moisture from the air. However, it also plays a vital role in engineering applications such as water harvesting or inkjet printing. Furthermore, the transport of droplets over substrates is possible by chemically modifying its surface to create a wetting pattern. The movement of sessile droplets can also be achieved by the application of an electrostatic field. In this case, fluid structures can occur, which are relevant, for instance, in electrospinning. In a first instance, the stability of water droplets on chemically patterned surfaces consisting of alternating hydrophilic and hydrophobic stripes is studied experimentally, numerically, and based on a scaling model. The boundary between the contact angle contrasts, leaving the droplets intact (stable) and those leading to droplet breakup (unstable), is computed numerically with the Surface Evolver, which is a numerical tool that minimizes the surface energy. The existence of a stable and unstable regime found with numerics is confirmed experimentally. In the unstable regime, when approaching droplet breakup, an H-shaped configuration with two liquid fingers on the hydrophilic stripes connected by a capillary bridge spanning the hydrophobic stripe is found. For decreasing volumes, the width of this capillary bridge decreases until a critical value is reached at which the droplet breaks up. A simple scaling model is presented, which predicts the critical bridge width. According to the model, the droplet becomes unstable when the increasing Laplace pressure inside the bridge can no longer be balanced by the pressure inside the liquid fingers on the hydrophilic stripes. The model is verified by the experiments and the Surface Evolver simulations. The breakup dynamics of the capillary bridge observed on the hydrophobic stripe in the unstable regime is studied experimentally and numerically. By considering the breakup speed as a function of the minimum capillary bridge width, the breakup dynamics can be evaluated without the uncertainty in determining the precise breakup time. The simulations are based on the Volume-of-Fluid (VOF) method. In order to construct physically realistic initial data for the VOF-simulation, Surface Evolver is employed to calculate an initial configuration consistent with experiments. It is found that the breakup of the capillary bridge cannot be characterized by a unique scaling relation. Instead, different scaling exponents are found at different stages of the breakup process, accompanied by qualitative changes in the shape of the bridge. In the final stage of the breakup, the capillary bridge forms a liquid thread that breaks up consistently with the Rayleigh-Plateau instability. Surface Taylor Cones (STCs) on hydrophilic substrates with low contact angle hysteresis are reported and investigated experimentally. STCs are structures analogous to the classical Taylor-Cones developing when a region of a liquid surface gets exposed to a strong electric field. In the present case, this region is located at the three-phase contact line, and the resulting force originating from the electric field is directed parallel to the surface. Initially, due to the Maxwell tension, only the contact angle is reduced compared to the drop without the electric field, while the drop shape itself appears to be not influenced. Subsequently, a liquid tongue is formed, which develops into a conical structure with an increasingly prominent tip, while the contact angle progressively decreases during this process. Finally, the liquid surface breaks down, and a jet emerges from the liquid cone tip that is in contact with the substrate and directed towards the electrode. It is found that the STCs can only develop on hydrophilic, low contact angle hysteresis substrates. The STC is characterized and compared to the original Taylor-Cone and a similar shape that can be observed at the receding side of droplets sliding down an inclined surface.