Investigating terminal film thickness in oil spreading dynamics under opposing net surface tension force on calm water

Heavy oils, particularly in cold water, spread slowly and eventually stop at a certain film thickness, known as the terminal film thickness. A few studies have specifically addressed the conditions and physical mechanisms that terminate the spreading process. However, traditional models for oil spreading on calm water do not predict this behavior, which may be due to a net negative surface tension effect. This paper aims to extend the existing spreading models to include the impact of net negative surface tension, where surface tension slows down and eventually stops gravity-driven spreading. Nihoul's spreading equation with negative surface tension is first analytically solved, and a physical equation for terminal thickness is derived. A Finite Element model is then developed and validated against analytical results for instantaneous spills. Finally, the model is extended to continuous spills, and the results for terminal film thickness and slick radius are compared with experimental measurements.