Thermal boundary layer slip at a stable liquid-liquid interface

We report a systematic experimental study of the mean temperature profile θ (δ z) and temperature variance profile η(δ z) across a stable and immiscible liquid-liquid (water-FC770) interface formed in two-layer turbulent Rayleigh-Bénard convection. The measured θ (δ z) and η(δ z) as a function of distance δ z away from the interface for different Rayleigh numbers are found to have the scaling forms θ (δ z/λ ) and η(δ z/λ ), respectively, with varying thermal boundary layer (BL) thickness λ . By a careful comparison with the simultaneously measured BL profiles near the solid conducting surface, we find that the measured θ (δ z) and η(δ z) 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. Direct numerical simulation results further confirm that the turbulent thermal diffusivity κ_t near a stable liquid interface has a complete cubic form, κ_t(ξ )/κ ∼ (ξ +ξ0)^3, where κ is the molecular thermal diffusivity of the convecting fluid, ξ = δ z/λ is the normalized distance away from the liquid interface, and ξ0 is the normalized slip length associated with ℓ_T .