Phase-field modeling of solidification resistance and droplet spreading dynamics under low-velocity impact

Prediction of the droplet spreading process on a supercooled wall surface is important for advancing engineering applications. However, the complexity of this issue is exacerbated by multiple factors, including initial kinetic energy, wettability, physical properties of droplet, and the resistance force generated during the solidification process under wall supercooled conditions. After considering the phase field method, equivalent heat capacity model, and Kistler’s approach, we establish a numerical model to track the droplet spreading evolution bottomed on laminar flow governing equations in this paper. The droplet sectional shape and spreading length under various conditions are systematically investigated, with a focus on the evolution of solidification resistance and its dissipative effects on the spreading dynamics. Results reveal a distinct morphological evolution of the droplet spreading process, transitioning sequentially from a “spherical shape” to a “rounded cap”, followed by “pancake/cylinder” configurations, and ultimately stabilizing as a “shallow-tray” morphology. Solidification resistance dissipation critically modulates these transitions, with elevated supercooling suppressing droplet retraction kinetics while amplifying maximum spreading lengths and prolonged spreading durations. Under the interaction effect of solidification rate and velocity, the solidification resistance and dissipation first increase, then gradually decrease, ultimately approaching zero along with droplet spreading. Besides, reduced initial impact velocities also attenuate the sensitivity of spreading dynamics to variations in supercooled temperature. Notably, a total solidification resistance dissipation computation method assisted by numerical results is developed. Quantitative result demonstrates its efficacy in modifying the isothermal spreading length prediction model, achieving a maximum error of 10% and an average error of 4.8%.