Optimizing oil-water separation using fractal surfaces

Oil has become a prevalent global pollutant, stimulating the research to improve the techniques to separate oil from water. Materials with special wetting properties - primarily those that repel water while attracting oil - have been proposed as suitable candidates for this task. However, one limitation in developing efficient substrates is the limited available volume for oil absorption. In this study we investigate the efficacy of disordered fractal materials in addressing this challenge, leveraging their unique wetting properties. Using a combination of a continuous model and Monte Carlo simulations, we characterize the hydrophobicity and oleophilicity of substrates created through ballistic deposition (BD). Our results demonstrate that these materials exhibit high contact angles for water, confirming their hydrophobic nature, while allowing significant oil penetration, indicative of oleophilic behavior. The available free volume within the substrates vary from $60\%$ to $90\%$ of the total volume of the substrate depending on some parameters of the BD. By combining their water and oil wetting properties with a high availability of volume, the fractal substrates analyzed in this work achieve an efficiency in separating oil from water of nearly $98\%$, which is significantly higher compared to a micro-pillared surfaces made from the same material but lacking a fractal design.