Departure Velocity of Rolling Droplet Jumping

Droplet jumping phenomenon widely exists in the fields of self-cleaning, antifrosting, and heat transfer enhancement. Numerous studies have been reported on the static droplet jumping while the rolling droplet jumping still remains unnoticed even though it is very common in practice. Here, we used the volume of fluid (VOF) method to simulate the droplet jumping induced by coalescence of a rolling droplet and a stationary one with corresponding experiments conducted to validate the correctness of the simulation model. The departure velocity of the jumping droplet was the main concerned here. The results show that when the center velocity of the rolling droplet (V₀ = ωR, where ω is the angular velocity of the rolling droplet and R is the droplet radius) is fixed, the vertical departure velocity satisfies a power law which can be expressed as V_z,depar = aR^b. When the droplet radius is fixed, the vertical departure velocity first decreases and then increases if the center velocity exceeds a critical value. Interestingly, the critical center velocity is demonstrated to be approximately 0.76 times the capillary-inertial velocity, corresponding to a constant Weber number of 0.58. Different from the vertical departure velocity, the horizontal departure velocity is basically proportional to the center velocity of the rolling droplet. These results deepen the understanding of the droplet jumping physics, which shall further promote related applications in engineering fields.