Penetration of liquid droplets into hydrophobic fibrous materials under enhanced gravity

Abstract

In this paper, experimental and numerical simulations were devised to study and formulate the force required for forcing a droplet to penetrate into a thin nonwetting fibrous structure. Due to the complexity of the problem at hand, we considered only thin fibrous structures comprised of parallel or orthogonally layered fibers. The experiments were conducted using ferrofluid droplets placed on electrospun polystyrene fibrous coatings. A permanent magnet was used to apply a body force to the droplets from below, and the assembly was placed on a sensitive scale for measuring the applied force. Numerical simulations were conducted using the Surface Evolver finite element code validated through comparison with dedicated experimental results. We studied how the force needed to initiate droplet spontaneous penetration into a thin fibrous coating varies with varying the volume of the droplet or the geometric properties of the coating. Using a combination of simulation results and experimental observations, easy-to-use but approximate expressions were derived and used to predict the force required to initiate droplet spontaneous penetration into the above-mentioned fibrous material. These analytical expressions allow one to circumvent the need for running a numerical simulation for each and every droplet-coating combination of interest and thereby expand the application of our work to conditions different from those considered here.