Fluctuation-induced slip of thermal boundary layers at a stable liquid-liquid interface

We report a systematic experimental study of the mean temperature profile θ(δz) and temperature variance profile η(δz) across a stable and immiscible liquid-liquid (water-FC770) interface formed in two-layer turbulent Rayleigh-Bénard convection. The measured θ(δz) and η(δz) as a function of distance δz away from the interface for different Rayleigh numbers are found to have the scaling forms θ(δz/λ) and η(δz/λ), respectively, with varying thermal boundary layer (BL) thickness λ. By a careful comparison with the simultaneously measured BL profiles near a solid conducting surface, we find that the measured θ(δz) and η(δz) near the liquid interface can be well described by the BL equations for a solid wall, so long as a thermal slip length ℓ_T is introduced to account for the convective heat flux passing through the liquid interface.