Initial growth of the Rayleigh-Taylor instability via molecular dynamics

At small length scales, the fluctuations that are neglected in most continuum descriptions of fluids become important. In this work, we explore the emergence of the Navier-Stokes equations as the ensemble mean of these fluctuations, which are inherent in the fundamental molecular processes underlying a fluid. This is accomplished by examining the initial growth of the Rayleigh-Taylor instability via hundreds of large-scale molecular dynamics simulations. A comparison of the mean growth rate spectra with the corresponding continuum predictions yields good agreement over a range of length scales from similar to 1 mu m to as small as similar to 10 nm. However, individual simulations exhibit significant variations from the continuum prediction. This work helps pave the way to a more fundamental understanding of fluid dynamics on small scales, and the mechanisms by which macroscopic, continuum models emerge. Such an understanding is essential, for example, in the rapidly growing field of nanotechnology.