Axisymmetric buoyant–thermocapillary flow in sessile and hanging droplets

The steady axisymmetric incompressible flow in a droplet sitting on or hanging from a flat plate is calculated numerically. In the limit of large mean surface tension the liquid–gas interface is spherical which allows the use of boundary-fitted toroidal coordinates. The flow is driven by thermocapillary and buoyant forces induced by a linear variation of the ambient temperature normal to the perfectly conducting wall. We present benchmark-quality results for the streamfunction and temperature fields, varying the contact angle, the thermocapillary Reynolds number, the Prandtl number, the Grashof number and the interfacial heat-transfer coefficient including the latent heat of evaporation. Scaling laws for the strength of the flow are provided for asymptotically large Marangoni numbers.