Thermocapillary and centrifugal-buoyancy-driven motion in a rapidly rotating liquid cylinder

Abstract

The thermocapillary flow field in a uniformly rotating liquid cylinder heated from above is calculated using linear boundary-layer theory appropriate for small values of the Ekman number. The results show that the thermocapillary flow is confined to a thin layer at the liquid-gas interface if the temperature difference across the cylinder is sufficiently small. The interior flow is a uniform rotation with the endplates.The flow due to centrifugal buoyancy is also analysed using the same theory. The magnitude of this flow compared with the thermocapillary motion is small in typical circumstances. However, it does influence the temperature field in the interior of the cylinder, whereas the thermocapillary motion does not. Full details of these flows and the first-order corrections to the interface shape are presented.