Turbulent mixing in the microscale: A 2D molecular dynamics simulation

Results of 2D molecular dynamics (MD) method are presented for the mixing phenomenon in the microscale, where the length and time are measured in terms of microns and nanoseconds, respectively. Particle ensembles consisting of 0.7-3 × 10⁶ particles in 1.3-5×10⁵ timesteps were simulated. We focus on the temporal evolution of mixing layer between two superimposed Lennard-Jones particle systems in a gravitational field directed from the heavier to the lighter particle fluid, and compare its properties with those observed in the macroworld. It is shown that the bubble-and-spikes stage of mixing process is similar in both the molecular scale and in the macroworld. The mixing layer growth constant A, which can be estimated using MD, is approximately the same as that obtained for 2D simulations in the macroscale, where the Navier-Stokes equations are used. For the closed particle systems, we show that the value A remains stable for changing physical conditions, as it is in the macroscale. For the open particle systems with a free surface A is 20% higher and reaches the value 0.07, i.e., the same as that obtained in laboratory experiments. The influence of fluid granularity on the speed of mixing can be observed at a very early stage. This start-up time is connected with spontaneous instabilities formation, which appears as the cumulative result of thermal fluctuations. The occurrence of Rayleigh-Taylor instability in the microscale, and its similarity to the same process in the macroscale, can also expand the scope of the term "turbulence" to microscaled flows on the molecular scale.