Steady and oscillatory thermocapillary convection in liquid columns with free cylindrical surface

Abstract

In liquid columns (Prandtl number 8·9) with free cylindrical surface heated from above, strong thermocapillary convection (TC) has been observed. Stationary thermocapillary convection exists in the form of a single axially symmetric roll bound to the free surface. For aspect ratios l/a < 1 the radial extension of the roll equals the zone length. The stream velocities and the temperature distribution were measured.The influence of buoyant forces due to horizontal temperature gradients in the experiments was also studied. Buoyant forces become obvious for a contaminated free surface and in bulk regions far from the cylinder surface.The thermocapillary convection shows a transition to time-dependent oscillatory motion when a critical Marangoni number Ma_c is exceeded. A unique Ma_c = 7 × 10³ has been found for zones with lengths l < 3·5 mm. The oscillatory state of thermocapillary convection has experimentally been proved to be a distortion of the laminar state in form of a wave travelling in the azimuthal direction. A unique non-dimensional wavenumber ≈ 2·2 (near Ma_c) of the distortion has been found. The non-dimensional frequency of the temperature oscillations is independent of zone size if the aspect ratio is held constant. However, the non-dimensional frequency of temperature oscillations increases linearly with the aspect ratio of the zone. This result is interpreted as a dependence of the phase velocity of the running disturbance on the aspect ratio.