We examine the thermocapillary-driven flow of a droplet on a nonuniformly heated patterned
surface. Using a sharp-interface scheme, capable of efficiently modeling the flow over
complex surfaces, we perform 2D and 3D finite element simulations for a wide range of
substrate wettabilities, ie, from hydrophilic to superhydrophobic surfaces. Our results
demonstrate that the contact angle hysteresis, due to the presence of the solid structures, is
responsible for the appearance of a critical thermal gradient beyond which droplet migration …