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

We report a systematic experimental study of the mean temperature profile theta (delta z) and temperature variance profile eta(delta z) across a stable and immiscible liquid-liquid (water-FC770) interface formed in two-layer turbulent Rayleigh-Benard convection. The measured theta(delta z) and eta(delta z) as a function of distance delta z away from the interface for different Rayleigh numbers are found to have the scaling forms theta(delta z/lambda) and eta(delta z/lambda), respectively, with varying thermal boundary layer (BL) thickness lambda. By a careful comparison with the simultaneously measured BL profiles near a solid conducting surface, we find that the measured theta(delta z) and eta(delta 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 kappa(t) near a stable liquid interface has a complete cubic form, kappa(t)(xi)/kappa similar to (xi + xi(0))(3), where kappa is the molecular thermal diffusivity of the convecting fluid, xi = delta z/lambda is the normalized distance away from the liquid interface and xi(0) is the normalized slip length associated with l(T).

Automated summary

This study systematically investigates the mean temperature profile and temperature variance profile across a stable liquid-liquid interface formed in two-layer turbulent Rayleigh-Benard convection. The experimental results show that the temperature and variance profiles near the liquid interface can be well described by boundary layer equations meant for solid surfaces, with the introduction of a thermal slip length. Direct numerical simulation results further confirm that the turbulent thermal diffusivity near a stable liquid interface exhibits a complete cubic form.