Turbulent thermal convection across a stable liquid-liquid interface

We report a systematic study of turbulent thermal convection across two vertically stacked layers of immiscible fluids, FC770 and water, with a stable liquid-liquid interface even when each fluid layer is under turbulent convection. The normalized mean temperature profile θ(z) and temperature variance profile ω(z), as a function of distance z away from the interface, are measured along the central vertical axis of the cylindrical convection cell with varying temperature difference Δ across the cell. From the measured mean temperature and temperature variance profiles, we find a unique twin-boundary-layer structure across the liquid interface with one of the twin boundary layers (BLs) residing on each side of the interface. The measured θ(z) and ω(z) in each fluid layer are found to have the scaling forms θ(z/λ) and ω(z/λ), respectively, with varying BL thickness λ, and their functional forms are well described by the equations for a BL attaching to a solid conducting plate, so long as a thermal slip length ℓT is introduced to account for the convective heat flux passing through the liquid interface. While the obtained θ(z/λ) and ω(z/λ) for the twin BLs share the same scaling forms, they nevertheless have different BL thickness λ and slip length ℓT in the two fluid layers. Furthermore, three characteristic temperatures are found as response parameters in the two-layer convection, namely, the mean temperature T0 of the interface, the mean bulk temperature TF of the FC770 layer, and the mean bulk temperature TW of the water layer. By combining the scaling result of heat transport across the entire cell and the effects of broken symmetry between the BL near the conducting plate and that near the liquid interface, we obtain three quantitative relations that link the three characteristic temperatures to the normalized slip length ζ0=(1+λ/ ℓT)-1 and the temperature difference Δ. The theoretical predictions are found in good agreement with the experimental results.