Numerical Simulations of Freely Oscillating Drops

The non-linear oscillations of a viscous drop is a fundamental problem in diverse areas of science and technology. In this paper, we analyze the large-amplitude oscillations of an initially elongated liquid drop in two-dimensions by solving the free boundary problem comprised of the Navier-Stokes equations, using two different numerical codes. The drop models all start from the same deformation in vacuum with zero gravity and varied Reynolds numbers (Re). We find that non-isothermal drops undergo stronger damping than isothermal ones due to the additional dissipative effects of heat conduction. Regardless of the drop parameters and physical mechanisms of dissipation, the transition from periodic to aperiodic decay is seen to occur for $$\mathrm{Re} \le 1.5$$ in good agreement with linear theory and previous numerical simulations.