The current technologies for handling oil spill clean-up vary in expense and effectiveness and are largely ineffective. Oil spills occur due to accidents from wellheads and damaged facilities in the creeks of the Nigerian Delta and along the coastline of waters where hydrocarbons are prospected all over the world. They are unexpected and known to cause irreparable damage to aquatic environments and marine life. The development of a hydrophobic mesh is proposed to prevent oil from spreading into larger areas and from reaching sensitive coastlines. This will help engineers and cleanup crews in their quest to find an appropriate response to a given oil spill scenario as they race against the clock to prevent further damage and improve the oil recovery process. The overall goal of this project is to create a Numerical Simulation of meshes that repel water and attract oil using ANSYS, a Finite Element Analysis software. The mesh was modelled as a porous medium that acts like a filter that retains water on one side while allowing the passage of oil through it. In the course of this work, appropriate materials selection in fluid flow analysis was carried out. Also, the flow domain geometry was developed in such a way as to simulate a system containing an oil-water interface. Next, domain discretization (meshing) was carried out appropriately. After which appropriate boundary conditions and operating conditions were implanted in the model. Fluent was then set to initialize and run calculations. After calculations were run, results were gotten. These results were then interpreted pictorially.