Line tension and morphology of a droplet and a bubble attached to the inner wall of a spherical cavity

Carbon dioxide as a line active agent: Its impact on line tension and nucleation rate

By considering a water capillary bridge confined between two flat surfaces, we investigate the thermodynamics of the triple line delimiting this solid-liquid-vapor system when supplemented in carbon dioxide. In more detail, by means of atom-scale simulations, we show that carbon dioxide accumulates at the solid walls and, preferably, at the triple lines where it plays the role of a line active agent. The line tension of the triple line, which is quantitatively assessed using an original mechanical route, is shown to be driven by the line excess concentrations of the solute (carbon dioxide) and solvent (water). Solute accumulation at the lines decreases the negative line tension (i.e., more negative) while solvent depletion from the lines has the opposite effect. Such an unprecedented quantitative assessment of gas-induced line tension modifications shows that the absolute value of the negative line tension increases upon increasing the carbon dioxide partial pressure. As a striking example, for hydrophilic surfaces, the line tension is found to increase by more than an order of magnitude when the carbon dioxide pressure exceeds 3 MPa. By considering the coupling between line and surface effects induced by gaseous adsorption, we hypothesize from the observed gas concentration-dependent line tension a nontrivial impact on heterogeneous nucleation of nanometric critical nuclei.

Line tension effects on the wetting of nanostructures: an energy method

The superhydrophobicity and self-cleaning property of micro/nano-structured solid surfaces require a stable Cassie-Baxter (CB) wetting state at the liquid-solid interface. We present an energy method to investigate how the three-phase line tension affects the CB wetting state on nanostructured materials. For some nanostructures, the line tension may engender a distinct energy barrier, which restricts the position of the three-phase contact line and affects the stability of the CB wetting state. We ascertain the upper and lower limits of the critical pressure at the CB-Wenzel transition. Our results suggest that superhydrophobicity on nanostructures can be modulated by tailoring the line tension and harnessing the curvature effect. This study also provides new insights into the sinking phenomena observed in the nanoparticle-floating experiment.

Size-dependent contact angle and the wetting and drying transition of a droplet adsorbed onto a spherical substrate: Line-tension effect

The size-dependent contact angle and the drying and wetting morphological transition are studied with respect to the volume change for a spherical cap-shaped droplet placed on a spherical substrate. The line-tension effect is included using the rigorous formula for the Helmholtz free energy in the droplet capillary model. A morphological drying transition from a cap-shaped to a spherical droplet occurs when the substrate is hydrophobic and the droplet volume is small, similar to the transition predicted on a flat substrate. In addition, a morphological wetting transition from a cap-shaped to a wrapped spherical droplet occurs for a hydrophilic substrate and a large droplet volume. The contact angle depends on the droplet size: it decreases as the droplet volume increases when the line tension is positive, whereas it increases when the line tension is negative. The spherical droplets and wrapped droplets are stable when the line tension is positive and large.

Free-Energy Barrier of Filling a Spherical Cavity in the Presence of Line Tension: Implication to the Energy Barrier between the Cassie and Wenzel States on a Superhydrophobic Surface with Spherical Cavities

The free-energy barrier of filling a spherical cavity having an inner wall of various wettabilities is studied. The morphology and free energy of a lens-shaped droplet are determined from the minimum of the free energy. The effect of line tension on the free energy is also studied. Then, the equilibrium contact angle of the droplet is determined from the generalized Young's equation. By increasing the droplet volume within the spherical cavity, the droplet morphology changes from spherical with an equilibrium contact angle of 180° to a lens with a convex meniscus, where the morphological complete drying transition occurs. By further increasing the droplet volume, the meniscus changes from convex to concave. Then, the lens-shaped droplet with concave meniscus spreads over the whole inner wall, resulting in an equilibrium contact angle of 0° to leave a spherical bubble, where the morphological complete wetting transition occurs. Finally, the whole cavity is filled with liquid. The free energy shows a barrier from complete drying to complete wetting as a function of droplet volume, which corresponds to the energy barrier between the Cassie and Wenzel states of the superhydrophobic surface with spherical cavities. The free-energy maximum occurs when the meniscus of the droplet becomes flat, and it is given by an analytic formula. The effect of line tension is expressed by the scaled line tension, and this effect is largest at the free-energy maximum. The positive line tension increases the free-energy maximum, which thus increases the stability of the Cassie superhydrophobic state, whereas the negative line tension destabilizes the superhydrophobic state.