Numerical simulation of droplet solidification on a cold plate

We proposed a solidification model based on the Front-Tracking method to simulate the freezing of liquid droplets on a cold substrate. The model is validated through comparison with existing numerical and experimental results, demonstrating agreement and improved mass conservation relative to previous approaches. Subsequently,the model is employed to investigate droplet solidification dynamics by varying key parameters, including the initial contact angle (${\theta }_0$), growth angle (${\theta }_{gr}$), Stefan number ($St$), Bond number ($Bo$), solid–liquid density ratio (${\chi }_{sl}$) and solid–liquid thermal conductivity ratio (${\kappa }_{sl}$). The results reveal that, on hydrophobic surfaces, increasing the growth angle enhances circulation near the three-phase contact line, promoting upward liquid motion and yielding taller, more slender solidified morphologies. A higher Stefan number and ${\kappa }_{sl}$ accelerate solidification by driving faster interface propagation, while an increased Bond number facilitates horizontal spreading, enlarging the solidification interface and improving heat transfer with the substrate. The solid–liquid density ratio is found to significantly influence both solidification rate and morphological development. These insights offer valuable guidance for controlling droplet solidification on hydrophobic surfaces and have direct implications for anti-icing technologies in power systems and aerospace applications.