Experimental and numerical study of anomalous thermocapillary convection in liquid gallium

Thermocapillary Marangoni convection of liquid gallium was studied experimentally and analytically. Using a sophisticated high-vacuum technique, liquid gallium was filled into the container with an optical window. The main idea was to obtain an oxide-free surface. For this purpose the working container was made as small as possible, so as to minimize the number of residual gas molecules. The amount of gallium introduced into the container was such as to form a layer of 2 mm thickness. This finite-volume technique is the principal advantage and innovation versus all other methods used before. It worked so well that no deterioration of the surface quality was noticeable over 6 months after preparation of the facility. This enabled us to monitor the motion of tracer particles along the free surface and to measure the corresponding velocity profiles.
It turned out that the movement along the free surface is directed from the cold toward the hot area for some temperature range just above the melting temperature. This finding was quite unexpected, since it means that surface tension increases with temperature. In the most investigations, however, the surface tension of gallium is found to decrease with increasing temperature.
This anomalous direction of the thermocapillary flow could be explained by the presence of a small amount of a surface-active contaminant. Despite the high purity of the gallium, laser-ablation analysis of the solidified sample of gallium done after opening of the container revealed 0.5% of lead in the layer of 50 microns depth at the free surface, but no lead in the bulk of the sample was found. Lead is known to be strongly surface-active with respect to gallium, and even a very small admixture can significantly change the surface tension of the latter.
A novel physical model was devised for the flow driven by the gradient of the surface tension induced additionally by the concentration of the adsorbed layer of contaminant, which in turn depends on the temperature. The observed anomalous direction of the flow can be explained as follows: In the hot region of the container the adsorbed layer partly dissolves and its concentration decreases, so that the surface tension increases, driving the surface towards the hot region of the container. This centripetal flow advects the adsorbed layer and restores its concentration, and at the same time reduces the gradient of the surface tension. When the surface concentration exceeds its equilibrium level, the surfactant on the surface begins to dissolve, increasing the bulk concentration. The resulting non-uniformity of the latter is smoothed out by diffusion and advection of the impurity in the liquid bulk. Thus there is a balance between contraction and stretching of the adsorbed layer, as well as between adsorption and desorption of the impurity - which is controlled by its diffusion from and to the surface. Since the diffusion of the impurity is much slower than the thermal or even the viscous one, the flow has a very strong feedback on the driving force. This is different from pure thermocapillary convection in low-Prandtl-number fluids where the coupling between the velocity and the driving temperature field is weak. The strong coupling in the present case could account for the heavily concave surface velocity profile observed in the experiment.