Role of fluctuations in fluid mixing

May 8, 2007

It is well known that fluctuations play a crucial role in fluid mixing in turbulent flows, and that continuum models have difficulty in capturing the fluid mixing in such flows. In the latest issue of PNAS, Kadau et al report on their atomistic simulation results of fluid mixing in turbulent systems. In addition, they also use magnetic levitation Rayleigh-Taylor instability experimental results to show that their atomistic results are in better qualitative and quantitative agreement with experiments. Here is the abstract of their paper:

A ubiquitous example of fluid mixing is the Rayleigh–Taylor instability, in which a heavy fluid initially sits atop a light fluid in a gravitational field. The subsequent development of the unstable interface between the two fluids is marked by several stages. At first, each interface mode grows exponentially with time before transitioning to a nonlinear regime characterized by more complex hydrodynamic mixing. Unfortunately, traditional continuum modeling of this process has generally been in poor agreement with experiment. Here, we indicate that 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. We performed billion-particle atomistic simulations and magnetic levitation experiments with unprecedented control of initial interface conditions. A comparison between our simulations and experiments reveals good agreement in terms of the growth rate of the mixing front as well as the new observation of droplet breakup at later times. These results improve our understanding of many fluid processes, including interface phenomena that occur, for example, in supernovae, the detachment of droplets from a faucet, and ink jet printing. Such instabilities are also relevant to the possible energy source of inertial confinement fusion, in which a millimeter-sized capsule is imploded to initiate nuclear fusion reactions between deuterium and tritium. Our results suggest that the applicability of continuum models would be greatly enhanced by explicitly including the effects of random fluctuations.

Take a look!

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