Oil capture from a water surface by a falling sphere

Motivated by contaminant remediation, we study the volume of oil (oleic acid) removed from a liquid lens by a falling particle. When a spherical particle is dropped from a fixed height into an oil lens that floats on top of a water surface, a portion of the oil adheres to the sphere. Once the sphere comes to rest at the subsurface, the oil forms an equilibrium pendant drop that remains attached to the sphere. We find in experiments with spheres of different sizes and materials, that the pendant drop volume is an increasing function of sphere mass for each material and a decreasing function of sphere density. By contrast, the normalized droplet volume in all of our experiments scales with sphere mass following Voil/Vsphere ~ M-0.544. Thus, for a given size, lighter spheres capture more oil relative to their own volume than do heavier spheres and are more efficient at removing oil from a water surface in our experiments. Estimates for the upper bound of the normalized droplet volume, determined from the continuous family of solutions of the Young-Laplace equation, show the same qualitative dependence on the sphere mass.

Duke Scholars

Author Thomas P. Witelski Mathematics