Flow along superhydrophobic surfaces
We have analyzed a number of flow phenomena occurring when a superhydrophobic surface is wetted by a liquid in the Cassie state, i.e. with gas pockets remaining in the indentations of the surface. The most elementary case is that of a pressure-driven or shear-driven flow over the surface. Such a scenario is depicted at the left-hand side of the figure below, where the gas filling the indentations is indicated in blue. Usually, such flows are modeled by assuming vanishing shear stress at the gas-liquid interface patches. However, especially in cases with large gas-liquid area fractions this approximation is no longer justified, since then the shear stress due to the flow inside the indentations starts playing a role. We have formulated an analytical model taking this flow into account. At the right of the figure, the corresponding streamlines are compared to streamlines obtained from numerical simulations, showing very good agreement. These results are also relevant for liquid-infused surfaces where the indentations are filled with a second immiscible liquid
Furthermore, we predict that liquid can be driven along superhydrophobic surfaces by applying a temperature gradient. The corresponding principle is depicted in the figure below. A temperature gradient gives rise to Marangoni stresses at the gas-liquid interfaces, which induce a surface-driven transport of the liquid. We have shown that substantial flow velocities of the order of centimeters per second should be achievable with temperature gradients of practical scale.
C. Schönecker, T Baier and S. Hardt, Influence of the enclosed fluid on the flow over a microstructured surface in the Cassie state, J. Fluid Mech. 740 (2014), 168-195.
T. Baier, C. Steffes and S. Hardt, Thermocapillary flow on superhydrophobic surfaces, Phys. Rev. E 82 (2010), 037301.
A broad variety of surface can be made water-repellent using the following method: The surface is coated with a thin film of silicon oil which is subsequently heated up to 300 °C. What remains after thermal treatment is a nanometer-thin solid silicon-oil residue. Then the surface is again impregnated with silicon oil. The result is a thin silicon-oil film very robustly attached to the surface, probably because of van-der-Waals forces. A water droplet wetting such a surface does not displace this film, i.e. it actually wets the silicon oil instead of the solid substrate. The contact-angle hysteresis on such surfaces is negligible, which means that a water droplet easily slides off.
Because of the negligible contact-angle hysteresis, droplets can be driven along the surface without effort, for example via Marangoni stresses due to a temperature gradient. The left part of the figure below shows two different droplets moving along the liquid-impregnated surface in a temperature gradient, where the bigger droplet overruns the smaller one. The experiments can also be performed with hanging droplets, i.e. with the whole arrangement flipped upside down, as shown at the right-hand side.
A. Eifert, D. Paulssen, S. N. Varanakkottu, T. Baier and S. Hardt, Simple fabrication of robust water-repellent surfaces with low contact-angle hysteresis based on impregnation, Adv. Mater. Interfaces 1 (2014), 1300138.
Structure of the three-phase contact region
Wetting phenomena can be observed in a wide variety of situations. Usually, the macroscopically observable parameters of a thermodynamic system, for instance the contact angle of a sessile drop on a solid substrate, are the result of a combination of several physical effects.
An example of a physical effect influencing the capillary behavior of a system is given by the formation of electric double layers (EDLs) due to ions in at least one of the fluid phases involved. The electric field due to the EDL deforms the fluid-fluid interface in the vicinity of the three-phase contact line, as depicted at the left of the figure below. Since the typical thickness of an EDL is of the order of 10 nm, the interface deformation occurs on a scale beyond the resolution limits of optical imaging. However, this effect has two macroscopically observable consequences. First of all, the macroscopically measured contact angle deviates from the microscopic one, as indicated at the right of the figure below, in which it is depicted how the fluid-fluid interface is deformed due to the presence of an EDL. Secondly, it gives a significant contribution to the line tension. We have formulated an analytical model predicting the macroscopic contact angle as well as the contribution to the line tension from EDLs. In most cases, this model predicts a negative line tension for a water droplet on a solid substrate.
A. Dörr and S. Hardt, Line tension and reduction of apparent contact angle associated with electric double layers, Phys. Fluids 26 (2014), 082105.
A. Dörr and S. Hardt, Electric-double-layer structure close to the three-phase contact line in an electrolyte wetting a solid substrate, Phys. Rev. E 86 (2012), 022601.