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 (～10^-2 torr) in the experiments of Ginde et al. (1989). The magnitude of the ΔT_c across the layer of liquid tin required for the onset of convection depends on the ratios of the thermal conductivities and thicknesses of the supporting layers of boron nitride and copper to those of the tin.

According to our theory surface tension contributes more than buoyancy to the instability observed experimentally. The critical ΔT_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 was uncontaminated, or a significantly larger observed critical ΔT_c would be expected.

The boundary condition on the thermal fluctuations 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.