The importance of fluctuations in fluid mixing

Abstract

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.atomistic simulation ͉ magnetic levitation ͉ Rayleigh-Taylor A s early as 400 B.C., the Greek philosopher Democritus of Abdera postulated that matter is comprised of indivisible units, and that it therefore can change its character due to the constant motion and temporary clustering of these ''atoms.'' Today, the existence of atoms can be verified directly via electron microscopy. Therefore, when modeling a sample of material, it is desirable to take into account the dynamics of the atoms, which ultimately are responsible for the macroscopic properties of the gas, liquid, or solid of interest. However, such calculations of the underlying atomistic dynamics have not previously been attempted for a complex fluid flow because it was thought that the number of atoms required was too large for even the most powerful computers. The physical problem has usually been approximated by a continuum description, in which the spatially and temporally averaged properties of a large number of atoms are described. Such descriptions are usually adequate when the scales of interest are large compared with the atomistic scale.A continuum obviously describes many physical situations very well, such as the fluid flow around a car or low-altitude aircraft. However, the continuum hypothesis must fail when the mean distance between atoms is not very small compared with the characteristic length of flow features, as is the...

Nonideal Rayleigh–Taylor mixing

“…The above cited papers achieved values for α consistent with experiment using a special code (FronTier) based on front tracking and designed to eliminate numerical mass diffusion and to model correctly physical mass diffusion. Particle methods (10), also known to have low levels of numerical mass diffusion, achieve values of α consistent with experiment. A combined experimental-simulation study (11,12) addressed both the initial condition issue and the numerical mass diffusion and achieved agreement with experiment.…”

Algorithm Refinement for Fluctuating Hydrodynamics

“…A heavy fluid sits above a light fluid, and spontaneous microscopic fluctuation at the interface between the fluids leads to turbulent mixing throughout the domain. Kadau and co-workers have recently studied the development of this turbulence at the atomic scale [5,6]. That group's atomistic simulations indicate that thermal fluctuations are an important driver of the behavior of complex flows, certainly at the smallest scales and perhaps at all scales.…”

Computational fluctuating fluid dynamics

“…Specifically, we consider the Rayleigh-Taylor instability, which occurs when a heavy fluid rests upon a light fluid [57], and the KelvinHelmholtz instability that arises from the instability of a shear layer. The importance of fluctuations has recently been highlighted in the study of such instabilities by molecular simulations [31,32].…”

“…Rayleigh-Bernard convection (both single species [63] and mixtures [53]), Kolmogorov flow [5,6,43], RayleighTaylor mixing [31,32], combustion and explosive detonation [40,50], and reaction fronts [46].…”