Mass transfer in drop-laden turbulent flow

We employ direct numerical simulation coupled with a volume-of-fluid method to investigate mass transfer in drop-laden turbulent flows. In this set-up, drops initially saturated with a specific chemical species are injected into a turbulent channel flow where the species is initially absent. This configuration leads to mass transfer from the drops to the surrounding flow. Two distinct sets of numerical simulations are conducted. In the first set, we vary the Schmidt number (Sc) of the carrier fluid while maintaining a unity diffusivity ratio between the carrier fluid and the drops. In the second set, we keep the Schmidt number inside the drops constant and systematically vary the diffusivity ratio, Dr . Our results show that, regardless of the value of the diffusivity ratio Dr , the mass-transfer velocity K (or equivalently, the Sherwood number Sh, which represents the ratio of convective to diffusive mass-transfer rates), with K ∝ Sh/Sc, scales as K ∼ Sc−1/2. This result, which is consistent with many theoretical, experimental and numerical predictions found in the literature and covering a broad spectrum of instances (i.e. gas–liquid and liquid–liquid flows), seems to highlight a universal nature of the mass-transfer process across fluid interfaces. Interestingly, while the diffusivity ratio Dr does not influence the scaling K ∼ Sc−1/2, it does influence the magnitude of the mass-transfer velocity. In particular, and for the range of Dr considered here (1 < Dr < 400), we show that KDr >1/KDr =1≃1.75. These findings are further explained using a simple lumped-parameter model of the process. We anticipate that these insights will contribute to the development of more accurate models and parametrisations in the field of mass transfer in turbulent dispersed flows.