Thermocapillary droplet migration and instability

The spreading and migration of a thin liquid droplet on a horizontal, nonuniformly heated solid surface is investigated. The droplet dynamics is simulated for small capillary numbers using a quasi-static evolution equation developed from lubrication theory and a constitutive equation for the contact-line motion. The results show that the non-uniform heating drives a thermocapillary flow in the droplet that alters the contact angle everywhere along the contact line, thereby modifying the droplet spreading process. With no contact-angle hysteresis, the droplet evolves to a state of steady migration down the temperature gradient. We also find that fbr some heating cases, an instability develops in the form of a dimple on the top of the droplet.