The ultimate goal of this project has been to develop a computational model for quantifying the interactions between of a body of fluid and a fibrous surface. To achieve this goal, one has to develop a model to create virtual structures that resemble the morphology of a fibrous surface (Objective-1) as well as a model that can simulate the flow of a fluid over these virtual surfaces (Objective-2). To achieve the first objective, we treated fibers as an array of beads interconnected through viscoelastic elements (springs and dampers). The uniqueness of our algorithm lies in its ability to simulate the curvature of the fibers in terms of their rigidity, fiber diameter, and fiber orientation. Moving on to Objective-2, we considered woven screens for their geometric periodicity, as a starting point. We studied how fiber diameter, fiber spacing, and contact angle can affect the skin-friction drag of a submerged hydrophobic woven screen, and how such surfaces resist against water intrusion under elevated hydro-static pressures (a requirement for providing drag reduction benefits). We also studied the impact of surface geometry and wetting properties on droplet mobility over these surfaces. Laboratory experiment was conducted at various stages throughout this investigation, and good agreement was observed between the experimental data and the results from our numerical simulation.