Effects of curvature on hydrothermal waves instability of radial thermocapillary flows Effets de courbure sur l’instabilité en ondes hydrothermales d’un écoulement thermocapillaire radial

The stability of a thermocapillary flow in an extended cylindrical geometry is analyzed. This flow occurs in a thin liquid layer with a disk shape when a radial temperature gradient is applied along the horizontal free surface. Besides the aspect ratio, a second parameter related to the local curvature is introduced to describe completely the geometrical effects. We recover classical hydrothermal waves as predicted by Smith and Davis [1] but the properties of these waves are shown to evolve with the curvature parameter, thus leading to a non uniform pattern over the cell. Moreover, it is shown that the problem is not invariant with respect to the exchange of the hot and cold sides.