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Moving contact line dynamics calculations include two models: precursor film models and slip models. The lubrication approximation method is used to establish a three-dimensional mathematical model to analyze the droplet thermocapillary migration behavior on a non-uniformly heated solid substrate with a wettability track. The contact line dynamics in the slip model and the disjoining pressure effect in the precursor model are proposed to regulate the substrate wettability. Both models are numerically implemented to investigate droplet spreading for three cases: free spreading on an isothermal substrate, thermocapillary migration on a uniform wettability substrate, and thermocapillary migration on a wettability-confined track. For the case of free spreading on an isothermal substrate, the three-dimensional results of the slip and precursor contact line models are essentially consistent with two-dimensional slip model results. For the case of thermocapillary migration on a uniform wettability substrate, the results of the two models essentially agree with the experimental results. Decreasing the thermal gradient reduces the discrepancies between the two models that result from the coordinate transformation method used in the slip model, which reduces the contact angles measured in the y-direction and enlarges the advancing contact angle in the migration direction. For the case of thermocapillary migration on a wettability-confined track, the slip model gradually shows a "dynamic-pinning" behavior with increasing equilibrium contact angle in the hydrophobic region. By contrast, the precursor film model maintains a stationary pinning behavior but separates a residual liquid outside the track. The precursor film model is preferred over the slip model in lubrication approximations for three-dimensional fluids when calculating complex moving contact dynamics caused by wettability differences. However, the precursor film model must be further optimized to prevent numerical instability. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]