Droplet Spreading Dynamics upon Impact and Freezing Tip Offset on Inclined Cold Surfaces

Droplet impact-freezing on inclined cold surfaces produces asymmetric ice accretion. Existing studies focus on qualitative ice morphology and freezing time, while quantitative analysis of hydrodynamic-phase-transition evolution at three-phase interfaces under inclined and supercooling surfaces was relatively less. In this work, experiments of droplet impacting on cold copper substrates were performed under varied substrate temperatures (-10, -20, -30 °C) and inclination angles (0, 23, 30, 45°). By analyzing the stage hydrodynamic and phase-transition behaviors of droplets during spreading, sliding, and freezing, this work clarified how the inclination angle and supercooling dominate droplet motion, contact line evolution, and solidification dynamics. The results reveal that droplet impact evolution undergoes five sequential stages (spreading, sliding, receding, oscillation, and steady infiltration), presenting two final modes of complete adhesion and partial rebound. The dimensionless time parameter Π effectively characterizes the evolution of sliding contact angle and solid-liquid contact line. Decreasing substrate temperature advances heterogeneous nucleation from the late steady infiltration stage to the early postspreading sliding stage. A refined Padé model with a correction coefficient of A = 1.657 is proposed by correcting cold liquid thermophysical properties. A theoretical model based on the principle of force equilibrium is used to predict the sliding distance of a droplet on an inclined cold surface. Freezing tip offset is governed by the competition between gravity-driven sliding and solidification retardation, and the established dimensionless power-law scaling correlation quantitatively describes its variation with key control parameters. The findings provide fundamental insights and design references for optimizing anti-icing strategies of engineering equipment operating in cold and high-altitude environments.