An Oil-and-Water Mystery Solved

August 3, 2007

A mathematician and an engineer have unraveled a physical mystery involving oil on water.

When an oil drop sits atop water, it assumes the form of a small lens with a rounded bottom. When the oil contains a water-insoluble surfactant — a substance (such as a detergent) that reduces the surface tension of a liquid, thereby permitting easier spreading — the lens radius oscillates. Viewed from above, the throbbing lens resembles a beating heart.

It took John Bush and Roman Stocker of the Massachusetts Institute of Technology three years of sporadic work to elucidate the subtle mechanism responsible for this phenomenon: evaporation-induced variations in surface tension. "It's an easy experiment to make," Bush said. "But getting the theory for it was not straightforward."

Changes in surface tension cause the drop to expand, then contract — a process that repeats itself every few seconds until the surfactant disappears. Turning a microscope loose on the problem was key to finally understanding the effect, Bush said.

Surfactant in an oil drop moves to the bottom surface of the lens, where it interacts with water to decrease the surface tension where oil meets water. This change in tension increases the forces pulling on the outer edges of the drop, causing the drop to expand.

Because the center of the drop is deeper than the edges, more surfactant settles there, reducing the surface tension. This causes the oil and surfactant near the outer edges of the drop to circulate. This circulation creates a shear — akin to two velocities going in opposite directions — which generates tiny waves rolling towards the edge. The waves cause small droplets to erupt and escape onto the water surface outside the drop.

Using videomicroscopy, the researchers saw that when the droplets of oil and surfactant disperse on the water and decrease the surface tension of the water surface, the drop contracts.

As the surfactant evaporates, the surface tension of the water rises again, and the system is reset. As forces pull at the outer edges of the lens, the cycle begins again. The beating ceases when the oil drop is covered. Because the surfactant can't evaporate, the oil drop remains stable.

"This is a bizarre and subtle mechanism," Bush noted. Bush's recent research has included studies of how insects walk on water.

"One rationalizes the physical world by understanding the mechanisms," Bush said. "One can never predict which mechanisms will be important."

Spontaneous oscillations, in fact, are observed in many natural systems, including nerve cells, muscle tissue, and the biological clocks responsible for circadian rhythms. Previous work on the oil drop problem had been carried out by scientists interested in seeing if the mechanism could explain biological oscillations.

"Oil contamination of water resources is a prominent problem in environmental engineering," Stocker noted. "Awareness of the fundamental mechanisms governing the interaction between the two phases is critical to devise sound engineering solutions for remediation."

Stoker and Bush's paper, "Spontaneous Oscillations of a Sessile Lens," appears in the July 25 issue of the Journal of Fluid Mechanics.

Source: Massachusetts Institute of Technology, July 17, 2007