Thermocapillary migration mechanism of molten silicon droplets on horizontal solid surfaces

Effective lubrication under extreme conditions such as high temperature is of considerable importance to ensure the reliability of a mechanical system. New lubricants that can endure high temperatures should be studied and employed as alternatives to traditional oil-based lubricant. In this paper, a thermocapillary model of a silicone-oil droplet is developed by solving the Navier–Stokes and energy equations to obtain the flow, pressure, and temperature fields. This is accomplished using a conservative microfluidic two-phase flow level set method designed to track the interface between two immiscible fluids. The numerical simulation accuracy is examined by comparing the numerical results with experimental results obtained for a silicone-oil droplet. Hence, the movement and deformation of molten silicon droplets on graphite and corundum are numerically simulated. The results show that a temperature gradient causes a tension gradient on the droplet surface, which in turn creates a thermocapillary vortex. As the vortex develops, the droplet migrates to the low-temperature zone. In the initial stage, the molten silicon droplet on the corundum substrate forms two opposite vortex cells, whereas two pairs of opposite vortices are formed in the silicone fluid on the graphite substrate. Multiple vortex cells gradually develop into a single vortex cell, and the migration velocity tends to be stable. The greater the basal temperature gradient, the stronger the internal thermocapillary convection of the molten silicon droplet has, which yields higher speeds.