Numerical simulation of oscillations and rotations of a free liquid droplet using the level set method

Three-dimensional oscillations and rotations of a free liquid droplet are simulated numerically using the level set method. The oscillations of order 2, 3 and 4 are simulated, and the frequency and the damping for small-amplitude oscillations are shown to agree well with those by the linear theory. Flow fields in the inside and outside of the droplet are visualized, and three-dimensional vortex structures are found to appear around the droplet. It is also found that the number of vortices is the same as the order of oscillation. The effects of initial amplitude and rotation on the oscillation frequency are studied, and it is shown that the oscillation frequency decreases as the initial amplitude increases, while it increases as the rotation rate increases. These effects are found to be overestimated by theoretical predictions.