Molecular-dynamics study of the viscous to inertial crossover in nanodroplet coalescence
JC Pothier and LJ Lewis, PHYSICAL REVIEW B, 85, 115447 (2012).
We have studied the coalescence of three-dimensional (3D), quasi-two- dimensional (quasi-2D), and 2D liquid, equal-size Cu and Si nanodroplets in the viscous and inertial regimes using classical molecular-dynamics simulations. At the onset of coalescence, a bridge (of radius r) between the droplets forms and develops until the merge is complete. For the 3D and quasi-2D systems, our results show a transition from a viscous- dominated regime at very short time, where r proportional to tau(1), to a regime dominated by inertial forces at longer time, with r proportional to tau(0.5), in agreement with theoretical models; the viscous regime is not observed in two dimensions, where only inertial forces seem to be operating. A detailed analysis of the 3D data suggests that the viscous-to-inertial crossover length l(c)(R-0, T) (with R-0 being the initial radius of the droplets and T being the temperature) behaves differently in the two systems. While l(c) proportional to R-0(1/2) and depends only weakly on temperature in l-Cu, as theory predicts, l(c) proportional to (R0T0.41)-T-0.96 in l-Si. We conclude from these observations and corresponding experimental data that the prefactor for the dependence of r on time in the inertial regime is not "universal" and actually depends on system properties, including initial radius, viscosity, and surface tension.
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