Numerical Interpretation to the Roles of Liquid Viscosity in Droplet Spreading at Small Weber Numbers

Droplet impacting a free-slip plane at small Weber numbers (We < 30) was numerically investigated by a front tracking method, with particular emphasis on clarifying the roles of the liquid viscosity and the "left-over" internal kinetic energy in droplet spreading. The most interesting discovery is that there exists a certain range of We in which the maximum diameter rate, D_m, shows a nonmonotonic variation with the Reynolds number, Re. This non-monotonic variation is owing to the dual role of liquid viscosity in influencing droplet spreading. Specifically, when the initial surface energy is comparable to the initial kinetic energy (the corresponding We is around 10-30), the high strain rates of the droplet internal flow dominate its viscous dissipation at a relatively large Re, while the liquid viscosity dominates the viscous dissipation at a relatively small Re. Furthermore, to unravel the influence of droplet attachment and detachment on droplet spreading, we considered two limiting situations such as full attachment (with no gas film throughout droplet spreading) and full detachment (with a gas film throughout droplet spreading). The results show that the droplet with a gas film tends to generate a stronger vortical motion in its rim, results in a larger left-over kinetic energy, and hence causes a smaller spreading.