Interaction of Marangoni and buoyancy effects during mass transfer at liquid interfaces

Complex flow patterns frequently emerge when a surface active substance undergoes mass transfer between an organic and an aqueous phase. At the same time, density effects can play a major role, e.g. during the partial dissolution of floating organic droplets \cite{cejkova2019dancing}. The resulting droplet ensemble dynamics can be understood by highly resolved measurements of the transient velocity field via particle image velocimetry (PIV). At bubbles in a shear flow, the interaction of the Marangoni effect with the surrounding bulk flow leads to the formation of a circulating flow at the bubble surface \cite{eftekhari2021interfacial}. Bubbles or droplets which are placed in a vertical concentration gradient of a surface-active solute show an intriguing interaction of solutal Rayleigh and Marangoni convection in the form of relaxation oscillations \cite{mokbel2018information}. Depending on the distance between multiple droplets, convective interaction can lead to collective relaxation oscillations over the whole ensemble.

A repeated coupling of Rayleigh and Marangoni effects likewise can occur during mass transfer of a solute at a planar interface between two liquid layers. Solutal Rayleigh instability is able to provoke intense Marangoni-driven spreading motions at the interface, even if the mass transfer system is primarily stable towards stationary Marangoni convection \cite{koellner2016eruptive}. A more detailed study \cite{koellner2023eruptive} unravels the underlying mechanisms by a defined variation of key parameters: the layer height and the initial concentration of the solute. The flow structures are analyzed in detail by experiments and elaborate three-dimensional simulations of the two liquid layers. The flow in the interfacial region decouples from the bulk volume flow since for deep layers, the interfacial velocity gets invariant under a change of the nondimensional layer height. Due to the additional convection, mass transfer is strongly enhanced in comparison to the purely diffusive process. This can significantly increase the efficiency of liquid-liquid extraction processes.

\bibitem{cejkova2019dancing} J.~{\v{C}}ejkov{\'a}, K.~Schwarzenberger, K.~Eckert, S.~Tanaka, Colloids and Surfaces A, 566, 141 (2019)
\bibitem{mokbel2018information} M.~Mokbel, K.~Schwarzenberger, S.~Aland, K.~Eckert, Soft Matter, 14, 9250 (2018)
\bibitem{eftekhari2021interfacial} M.~Eftekhari, K.~Schwarzenberger, S.~Heitkam, K.~Eckert, Journal of Colloid and Interface Science, 599, 837 (2021)
\bibitem{koellner2016eruptive} T.~K{\"o}llner, K.~Schwarzenberger, K.~Eckert, T.~Boeck, Journal of Fluid Mechanics, 791, R4 (2016)
\bibitem{koellner2023eruptive} T.~K{\"o}llner, K.~Schwarzenberger, K.~Eckert, T.~Boeck, in progress (2023)