Rise and fall of a multicomponent droplet in a surrounding fluid: Simulation study of a bumpy path

The coupling between mass transfer and hydrodynamic phenomena in two-phase flow is not straightforward due to the different effects that can be encountered. Its description is complex and requires particular efforts, especially in the modeling of the interface between phases. Here, we consider the case of a two-component droplet (one miscible and one immiscible in water) released in a 2D rectangular domain filled with water. Mass transfer occurs between the miscible element and the surrounding water, which leads to a density inversion that directly affects the droplet trajectory through buoyancy. We perform simulations using a ternary Cahn-Hilliard model to capture such coupled phenomena. The Boussinesq approximation for a multicomponent system is used to define the density law and an analytical chemical potential is proposed for the thermodynamic landscape. The effect of the mobility parameter on the flow is highlighted, the solutal Marangoni effect is discussed, and the results are found in good agreement with the dynamics described from an experimental study of the literature.