On the migration of a droplet driven by thermocapillary action in a wettability-confined track

We report a study of the thermocapillary migration of droplets under a radial thermal gradient and in a wettability-confined track. A three-dimensional mathematical model is established based on the lubrication approximation. By considering the contact-line dynamics, a method for determining the velocity of the contact line in different directions is proposed for a three-dimensional droplet. Numerical simulations are performed to investigate the variations in the droplet profile, contact angle, and contact line. Three substrate-wettability cases are considered: uniform, temperature-dependent, and track-dependent wettability. The results show that when the substrate wettability is uniform, the droplet height initially decreases rapidly, and its center becomes concave and then gradually evolves into a ring-like morphology. Reducing the temperature sensitivity of the liquid-gas interfacial tension or increasing the temperature sensitivity of the liquid-solid interfacial tension decreases the equilibrium contact angle and accelerates thermocapillary migration. When a droplet spreads in a wettability-confined track, a wave-like peak is formed on each side of the droplet along the track direction until it finally separates into two distinct parts. As the track width is decreased, the time taken for a droplet to split into two smaller droplets advances, and the separation time presents a linear relationship with the track width.