Heat transfer and mixing in turbulent water-in-oil and oil-in-water emulsions

We numerically investigate turbulent heat transfer in water-in-oil (W/O) and oil-in-water (O/W) emulsions using direct numerical simulations coupled with a phase-field method. Heat is treated as a passive scalar, initially confined within the dispersed phase and subsequently transferred to the carrier fluid. The two emulsions share identical density and thermal diffusivity, while the oil phase is four times more viscous than water. To isolate convective effects, the same Péclet number (Pe = 2400) is imposed in both configurations. Viscosity contrast strongly affects local flow and scalar dynamics, producing enhanced velocity fluctuations and mixing in the water phase and reduced activity in the oil phase. Reversing the dispersed and carrier phases redistributes these local mixing mechanisms between the drop interior and the surrounding fluid. This redistribution leads to similar global heat-transfer rates and comparable thermal transient in both emulsions, despite fundamentally different phase-conditioned flow and mixing dynamics.