Vortex-dynamical implications of nonmonotonic viscous dissipation of off-center droplet bouncing

Abstract

In this paper, vortex-dynamical perspectives were adopted to interpret the recently reported observation that the total viscous dissipation of off-center droplet bouncing varies nonmonotonically with the impact parameter [C. He, X. Xia, and P. Zhang, “Non-monotonic viscous dissipation of bouncing droplets undergoing off-center collision,” Phys. Fluids 31, 052004 (2019)]. The particular interest of this study is on analyzing the velocity and vorticity vector fields and their correlations, such as helicity and enstrophy. The helicity analysis identifies a strong interaction between the “ring-shaped” vortices and the “line-shaped” shear layers in the non-axisymmetric droplet internal flow. A general relation between the total enstrophy and the total viscous dissipation rate for an unsteady free-surface flow was theoretically derived and numerically verified. It shows that the equality between the total enstrophy and the total viscous dissipation rate holds for a single-phase flow confined by stationary boundaries but is not satisfied for a gas–liquid two-phase flow due to the interfacial movement. Both the total enstrophy and a defined “half-domain” helicity show the nonmonotonic variation with the impact parameter, implying their interrelation with the nonmonotonic viscous dissipation.