SURFACE-TENSION AND BUOYANCY-DRIVEN INSTABILITIES IN A LAYER OF LIQUID-TIN HEATED FROM BELOW

The linear theory of Pearson (1958) and Nield (1964) is modified here to study liquid tin and include the finite thermal resistances of the bounding layers of boron nitride, copper and air (approximately 10(-8) torr) in the experiments of Ginde et al. (1989). The magnitude of the DELTAT(c) across the layer of liquid tin required for the onset of co nvection depends on the ratios of the thermal conductivities and thick nesses of the supporting layers of boron nitride and copper to those o f the tin. According to our theory surface tension contributes more th an buoyancy to the instability observed experimentally. The critical D ELTAT(c) observed required for the onset of convection in the layer of tin, is up to 25% lower than that predicted, which shows the layer is less stable than the theory indicates. Thus the surface of the tin wa s uncontaminated, or a significantly larger observed critical DELTAT(c ) would be expected. The boundary condition on the thermal fluctuation s at the base of the supporting layer of copper does not appear to be important in these experiments. However, the thermal resistance of the boron nitride would have to be assumed to be unrealistically large to obtain agreement within experimental error with the theory.