Receding Dynamics of Droplet Deposition on a Smooth Surface from a Central Jet to Secondary Droplet Emission

A droplet impacting a solid surface undergoes deposition, splashing, or rebounding, depending on the properties of the droplet and impacted surface. The deposition pattern attracts lots of attention for the reasons of its predictable behavior on wetting and dewetting. The phenomenon of the central jet, even breaking up into a secondary droplet, is observed during gentle deposition on partially wettable surfaces. The mechanism behind the central jet is addressed by the dual role of the inertia force. In this paper, the dynamic characteristics of droplet deposition are analyzed with a focus on the receding process from jetting to secondary droplet emission. The jet is pinched off into a small secondary droplet when the impacting Weber (We) number is within the range of approximately 26-54. The secondary droplet is then ejected because of the collision with the upward jet. The convergence of capillary waves on the liquid film is employed to explain the two-stage upward jet. The jet tip is pinched off because of Rayleigh-Plateau instability, leading to the generation of the secondary droplet. A geometric model of a two-floor cylinder is further proposed to describe the equivalent recession of the capillary wave. The equivalent radius of the receding wave is linear with time, and the jet height exhibits a scaling law of D_jet ∼ (t - 0.8)^1/2 with normalized time. Additionally, the dynamic characteristics are investigated from time and size views. With various Weber numbers, the normalized receding, jetting, and tip times are found to remain almost constant. A piecewise relationship with the Weber number is revealed for the normalized receding wave and the tip height. The wave recedes at the characteristic velocity of 0.23 m/s. Moreover, the normalized jet height and tip diameter, as well as secondary droplet diameter, are independent of the inertia force. The emission velocity and kinetic energy of the secondary droplet are found to reach the maximum at We ∼ 41.6.