Double bursting jets from a suspended water drop under one cycle of oscillation

Abstract

We found that a hemispherical water drop of radius of the capillary length ${\ell }_c$ suspended on a substrate can generate a pair of bursting jets after experiencing one cycle of oscillation. The drop of initial base radius $R_0$ first undergoes the downward acceleration stage and reaches a peak velocity $V_p$ with a characteristic Weber number $We\equiv \rho V_p^2{R}_0/\gamma$. At the end of the downward acceleration, the drop is compressed into a pancake shape with the maximum spreading diameter that scales with ${We}^{1/10}$. Subsequently, the acceleration is reversed to upward, pulling up a cylindrical cavity. The depth of the cavity increases with larger We. The axisymmetric cavity pinch-off is logarithmically slow and the variation of neck radius $r$ with time $\tau$ exhibits the scaling law: $r\propto {\tau }^{1/2}{e}^{-\sqrt{-log\tau }/2}$ (Eggers et al., 2007). The collapse of a small cavity does not trap any bubble, forming a single Worthington-type jet. The intermediate sized cavity collapses to form two opposite bursting jets, and the inner jet is absorbed by the enclosed bubble. The collapse of the sufficiently deep cavity produces two bursting jets that are self-similar in terms of jet radius and velocity. A phase diagram of $We$ vs $\tilde{R}=R_0/{\ell }_c$ is presented for categorizing the three different cavity collapse behaviors.