The relationship between oil droplet size and upper ocean turbulence

Oil spilled at sea often forms oil droplets in stormy conditions. This paper examines possible mechanisms which generate the oil droplets. When droplet Reynolds numbers are large, the dynamic pressure force of turbulent flows is the cause of droplet breakup. Using dimensional analysis, Hinze (1955, A.I.Ch.E. Journal 1, 289–295) obtained a formula for the maximum size of oil droplets that can survive the pressure force. When droplet Reynolds numbers are small, however, viscous shear associated with small turbulent eddies is the cause of breakup. For the shear mechanism, we obtain estimates of droplet size as a function of energy dissipation rate, the ratio of oil-to-water viscosity and the surface tension coefficient. The two formulae are applied to oil spills in the ocean. At dissipation rates expected in breaking waves, the pressure force is the dominant breakup mechanism and can generate oil droplets with radii of hundreds of microns. However, when chemical dispersants are used to treat an oil slick and significantly reduce the oil-water interfacial tension, viscous shear is the dominant breakup mechanism and oil droplets with radii of tens of microns can be generated. Viscous shear is also the mechanism for disintegrating water-in-oil emulsions and the size of a typical emulsion blob is estimated to be tens of millimeters.