Three-dimensional numerical simulation and theoretical model of a hollow droplet impacting on a solid surface

The phenomenon of a hollow droplet impacting on a solid surface is widely found in various fields. The dynamic characteristics of hollow diesel droplets impacting on a solid surface are studied by combining numerical simulation and theoretical analysis. The dynamic contact angle model presented in this paper couples the advantages of existing dynamic contact angle models for simulating both the spreading and retracting stages. It also considers the continuous variation of the contact angle during the maximum spreading state. Compared to existing models, the maximum error has been reduced from 14.9% to 4.6%. The effects of impact velocity, impact angle, and volume ratio of a hollow droplet on the spreading and jetting characteristics are investigated by three-dimensional numerical simulations. It is found that air entrainment occurred in the counter-jet, and the presence of the impact angle increased the asymmetry of the counter-jet and spreading liquid film, promoting fingerlike splashing at the front liquid film. Based on energy conservation law, the theoretical prediction models of the maximum spreading coefficient of the hollow droplet impacting on the surface and the velocity of the counter-jet at the maximum spreading state are established using the multi-regional modeling method and the energy distribution principle. Compared with existing hollow droplet theoretical models, the proposed theoretical models exhibit a more concise expression, higher accuracy, and wider applicability range.