A Mathematical Model of Lubricant Film Flow Velocity on a Belt Type Oil Skimmer in a Part of Wastewater Treatment Process Using a Finite Difference Method with Quasi-Newton Iterative Technique

Oil skimmer is a useful tool in recovering all types of floating waste oils, greases and fats from water surfaces. Lubricant film flow velocity approximation is an important problem of oil skimmer belt speed adjustment. The adjustment belt speed level is up to several physical parameters of oil types. A thin lubricant film flow velocity on a moving belt oil skimmer can be modeled in a form of a nonlinear differential equation as a boundary value problem. The model is providing the lubricant film flow velocity in each thickness layers. In this research, a centered in space finite difference method and a Quasi-Newton iterative method are proposed to approximate the solutions of the nonlinear thin lubricant film flow velocity model. Their numerical simulations of a thin lubricant film flow velocity on a moving oil skimmer belt with varied physical parameters are investigated. The proposed numerical techniques give good agreement approximated solutions in several moving belts speed levels with the external force factor. These are then useful to achieve the optimum belt oil skimmer speed for each lubricant type.