Accidental oil spills in the ocean have a big impact on aquatic environments and human activities, and one of the most promising clean-up techniques is the use of hydrophobic and oleophilic meshes. It is important to understand the underlying physics of these meshes and their behavior under different conditions. Here, a mesh is conceptualized as an equivalent porous medium where the oil recovery and water breakthrough depend on the fluid column height and material properties. A model of two-phase flow through the mesh was implemented in COMSOL Multiphysicse (R). Hydrophobicity, contact angles and surface tension effects are considered through a capillary retention curve, while flow properties are represented by permeability functions. The model was verified and tested with existing experimental data. It constitutes a powerful tool for future research and optimization of environmental solutions based on hydrophobic and oleophilic meshes. (C) 2017 Elsevier Ltd. All rights reserved.