Retention of rising oil droplets in density stratification

Following the Deepwater Horizon oil well leak in 2010, approximately 40 percent of the spilled oil remained trapped deep beneath the ocean surface. While it has been demonstrated that these trapped intrusion layers, composed of small oil droplets, are caused by interactions with the oceanic density gradient, the exact dynamics underlying the residence time of the oil in these layers is not well understood. In this study, we present results from experiments on the retention of single oil droplets rising through a two-layer density stratification. We track the motion of droplets as they rise through the water column, and delineate two timescales: an entrainment time, and a retention time. The entrainment time is a measure of the time that an oil droplet spends below its upper-layer terminal velocity and relates to the time over which the droplet entrains denser fluid. The retention time is a measure of the time that the droplet is delayed from reaching an upper threshold far from the density transition. The retention time relates to the entrainment time, as well as to the magnitude of the drop's slowdown. These two timescales are found to strongly depend on the Froude number of the system. We find that both timescales are only significantly large for Fr $\lesssim1$, indicating that trapping dynamics arise from a balance between drop inertia and buoyancy. We discuss the implications of these findings on the scale of oceanic oil spills, and propose that the size of the bulk plume of oil droplets may be the relevant length scale for trapping in that scenario.