Counter-intuitive penetration of droplets into hydrophobic gaps in theory and experiment

Droplets that spontaneously penetrate a gap between two hydrophobic surfaces without any external stimulus seems counterintuitive. However, in this work we show that it can be energetically favorable for a droplet to penetrate a gap formed by two hydrophobic or in some cases even superhydrophobic surfaces. For this purpose, we derived an analytical equation to calculate the change in Helmholtz free energy of a droplet penetrating a hydrophobic gap. The derived equation solely depends on the gap width, the droplet volume and the contact angle on the gap walls, and predicts whether a droplet penetrates a hydrophobic gap or not. Additionally, numerical simulations were conducted to provide insights into the gradual change in Helmholtz free energy during the process of penetration and to validate the analytical approach. A series of experiments with a hydrophobic gap having an advancing contact angle of [Formula: see text], a droplet volume of about 10 [Formula: see text]L and different gap widths confirmed the theoretical predictions. Limits and possible deviations between the analytical solution, the simulation and the experiments are presented and discussed.