| Summary: | <p>In this thesis, we model the breakup of oil droplets in a turbulent jet and the effect of surfactants in enhancing this process. The problem is motivated by deep-sea oil spills where, hundreds of metres below the sea surface, a pipe transporting oil ruptures and a turbulent oil jet is released into the sea. The jet’s turbulent mixing breaks up the oil into smaller droplets. These droplets are then eaten by microbes in the sea. To encourage this natural clean-up process, surfactants are added to the oil jet to reduce the oil-water surface tension and encourage droplet breakup. Our aim is to understand how to best apply the surfactant to maximise droplet breakup. To do so, we first examine and unify the large scale jet and small scale droplets without the presence of surfactants. We then incorporate the effect of surfactant addition to these models.</p> <p>We begin by modelling an axisymmetric turbulent oil jet. Our key approach is to take advantage of the self-similarity of a jet to find similarity solutions for its velocity field and energy. Scaling laws are then used to understand the breakup of droplets due to turbulent mixing. We combine these large-scale jet models and small-scale drop models, using droplet population models to predict the droplet size distributions at different locations in the jet. We first do so numerically. We then find similarity solutions for the drop size distribution, by taking advantage of the self-similarity of the jet.</p> <p>Finally we include the effect of surfactants. We use numerical and asymptotic methods to model their effect on the drop size distribution. This allows us to address two important questions: how much surfactant should be used and where should it be injected.</p>
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