In the present study, the transient thermocapillary migration of a small liquid droplet on a horizontal solid surface is numerically investigated. The droplet has a large static contact angle and a high aspect ratio of the maximum height of the droplet to its footprint. The Navier–Stokes and energy equations for both the droplet and surrounding air are solved through the finite element method. The evolution of the isotherms, the flow fields and the contact angle hysteresis are presented. Two asymmetric thermocapillary vortices appear inside the droplet. The variation of the size of the thermocapillary vortex during the migration process causes the speed of the droplet to first increase significantly, and then decrease gradually to approach a constant value. The higher imposed temperature gradient causes the droplet velocity to reach its maximal value earlier and have a higher final speed. If the static contact angle of the droplet is less than (or higher) than 90°, the droplet speed is lower (or higher) since the net thermocapillary momentum in the horizontal direction is diminished (or enhanced) by the presence of capillary force. The present results for the migration velocity and the contact angle hysteresis for a squalane droplet are also in good agreement with the previous experimental results.

Numerical computations have been performed to study the effects of thermocapillary convection and buoyancy convection, and free surface deformation induced by gravity on the migration behavior of a liquid droplet on a horizontal solid surface subjected to a uniform temperature gradient. Investigations are carried out by solving the Navier-Stokes equations coupled with the energy equation through the finite element method. The combined thermocapillary and buoyancy force driven convection produces complex dynamic behavior of fluid motion inside the droplet. The net momentum generated by a pair of asymmetric thermocapillary convection vortices inside the droplet drives the droplet to move in both small and middle droplet sized regimes. In the small sized regime, the quasisteady migration speed of the droplet is mostly linearly proportional to its size because of the stronger net thermocapillary momentum. When the droplet is in the middle sized regime, its quasisteady migration speed reaches a maximum, but this is gradually reduced as the droplet size increases due to the suppression of the net thermocapillary momentum by the buoyancy force. In the large droplet sized regime, two pairs of convection vortices exist inside the droplet as a result of the appearance of the buoyancy-driven convection accompanying the thermocapillary convection. The quasisteady migration speed quickly diminishes mainly due to the reduction of the net thermocapillary momentum from the stronger buoyancy convection.

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