The Gulf of Mexico Oil Spill is perhaps the most significant environmental disaster in US history with a significant portion of the US coastline affected by the approaching crude. Cleanup of beaches is important for both environmental reasons and for the tourist trade. This research program addresses fundamental questions of the dynamics of oil and sand of direct relevance to the cleanup problem. The work builds on recent studies of the Principal Investigator on mathematical models for oil-sand mixtures on slopes, including work on critical inclination angles for separation of oil-sand mixtures and modeling of shear-induced migration in oil/particulate films. The current research effort addresses such basic questions as whether there is a critical angle of incline for beach sand dunes that result in oil collecting in the dune vs. flowing to the bottom of the dune. The study of periodic patterns of shearing due to waves is also important for this research project.
The dynamics of particulates (e.g. sand) in oil is a complex process involving hindered settling dynamics and dynamics of the fluid such as shear. Recently the research group of the PI has found the dominant physics for particle-oil film mixtures on an incline and can explain quantitatively the bifurcation that occurs between regimes of particle settling downstream of the flow and clear fluid separating out from the flow. The equilibrium theory compares shear-induced migration due to the bulk flow properties with hindered settling due to gravity, and matches well with laboratory experiments. The current research program develops dynamic theories for particle-sand mixtures on inclines of particular relevance to the current crude oil spill. In addition to basic time-dependent flow problems the study considers oil-water mixtures and periodic time dependent shear such as what might result from wave motion and tidal forces on beaches.
This research program addresses fundamental questions of the dynamics of oil and sand of direct relevance to the cleanup problem. The work builds on recent studies of the Principal Investigator on mathematical models for oil-sand mixtures on slopes, including work on critical inclination angles for separation of oil-sand mixtures and modeling of shear-induced migration in oil/particulate films. The research effort addresses such basic questions as whether there is a critical angle of incline for terrain that result in oil collecting on the slope vs. flowing to the bottom of the slope. The dynamics of particulates (e.g. sand) in oil is a complex process involving hindered settling dynamics and dynamics of the fluid such as shear. Recently the research group of the PI has found the dominant physics for particle-oil film mixtures on an incline and can explain quantitatively the bifurcation that occurs between regimes of particle settling downstream of the flow and clear fluid separating out from the flow. The equilibrium theory compares shear-induced migration due to the bulk flow properties with hindered settling due to gravity, and matches well with laboratory experiments. The research program develops dynamic theories for particle-oil mixtures on inclines. This work led to new analysis for spiral separators – used to segregate particulates from liquids and to segregate different types of particulates. This program also developed new numerical algorithms for simulating these particulate flows including the role of surface tension on the free surface. Numerical schemes for surface tension driven flows were also extended to other physics problems such as ion bombarded surfaces.
