Mathematical Simulation of Random Interface Between Heavy and Light Liquids

May 17, 2007

The interface between a heavier fluid floating atop a lighter one is unstable and has been difficult, if not impossible, to simulate accurately. Now, researchers report that they have mathematically modeled the mixing of immiscible fluids when the heavier material moves downward and the lighter material moves upward in a gravitational field.

This effect is known as the Rayleigh-Taylor instability. The development of the interface between the liquids goes through stages, starting with depressions and fingers that grow exponentially, then transitioning to highly complicated patterns as the fluids intermingle further. Standard simulations that assume that fluids are continuous have proved inadequate for characterizing this evolving interface.

By performing billion-particle atomistic simulations and magnetic levitation experiments, the scientists were able to match simulations with experiments, revealing "good agreement" in terms of the "growth rate of the mixing front" and the subsequent "droplet breakup."

"The natural, random fluctuations of the flow field present in any fluid, which are neglected in continuum models, can lead to qualitatively and quantitatively better agreement with experiment," Kai Kadau of the Los Alamos National Laboratory and his colleagues conclude.

Their results, the researchers contend, will "improve our understanding of many fluid processes," which range from the complex interface phenomena in supernovas to the technology of inkjet printing to how ordinary drops of water slowly detach themselves from a kitchen faucet.

Source: Proceedings of the National Academy of Sciences, May 8, 2007