Effects of hydrostatic pressure on wetted area of submerged superhydrophobic granular coatings. Part 1: mono-dispersed coatings

Abstract

Abstract Properly designed superhydrophobic surfaces can reduce the skin-friction drag on objects submerged in moving water. This drag reduction is caused by a reduction in wetted area from air entrapped in the pores of the surface. For granular superhydrophobic surfaces, where the air–water interface is not necessarily pinned to the pore entrance, predicting the wetted area is not a trivial task, as the air–water interface can easily move into or out of the pore in response to instantaneous operating pressure or due to air dissolution into the ambient water. The relationship between wetted area and drag-reduction is complicated, and reducing the wetted area does not guarantee a reduction in drag force. However, the ability to predict the wetted area allows one to design more efficient superhydrophobic coatings to meet the specific needs of different applications. This work presents an analytical force-balance method developed to approximate the wetted area of a superhydrophobic surface made of particles of equal size but different Young–Laplace contact angles. The accuracy of our simple analytical formulations is examined using the rigorous numerical calculations of the Surface Evolver code, and reasonable agreement has been observed. Effects of particle diameter, particle contact angles, particle packing fraction, and spatial distribution on positive and negative critical hydrostatic pressures and their corresponding wetted area are predicted and discussed in detail.