Energetic analysis of spreading of impacting drops on cold surfaces

The mechanism restricting an advancing contact line remains debated for drop impacts on cold solid substrates while a lamella is spreading and solidifying simultaneously. We conducted experiments involving hexadecane drops impacts on cold solid substrates at different temperatures below liquid freezing temperature with various impact velocities to observe spreading and contact line dynamics. Due to the similarity in temporal growth of viscous and freezing boundary layers, an effective boundary layer thickness is introduced to estimate dissipation in the shear layer. As the contact line is caught up by freezing front, driven by non-equilibrium kinetic solidification, lamella spreads over solidified volume at contact line region. An additional dissipative friction at proximity to contact line is therefore proposed, which can be incorporated to account freezing-induced dissipative mechanisms at contact line in any prognostic model for maximum solidification-limited spreading ratio. In an energetic argument, we assess relative dissipation of energy in the parameter space of Weber and Stefan numbers and propose a nondimensional number Di to characterize whether solidification-induced energy dissipation basally in the shear layer or laterally at the contact line dominates to limit droplet spreading.