Understanding the interactions between a body of liquid and a curvy surface is important for many applications such as underwater drag force reduction, droplet filtration, self-cleaning, and fog harvesting, among many others. This study investigates ways to predict the performance of granular and fibrous surfaces for some of the above applications. More specifically, our study is focused on 1) modeling the mechanical stability of the air-water interface over submerged superhydrophobic (SHP) surfaces and their expected drag reduction benefits, and 2) predicting the mechanical stability of a droplet on a fiber in the presence of an external body force. For the first application, we modeled the air–water interface over submerged superhydrophobic coatings comprised of particles/fibers of different diameters or Young–Laplace contact angles. We developed mathematical expressions and modeling methodologies to determine the maximum depth to which such coatings can be used for underwater drag reduction as well as the magnitude of the depth-dependent drag reduction effect of the surface. For the second application, we studied the force required to detach a droplet from a single fiber or from two crossing fibers. The results of our numerical simulations were compared to those obtained from experiment with ferrofluid droplets under a magnetic field, and excellent agreement was observed. Such information is of crucial importance in design and manufacture of droplet–air and droplet–fluid separation media, fog harvesting media, protective clothing, fiber-reinforced composite materials, and countless other applications.