Binary droplet interactions under Marangoni convection: A new combined level-set & film-drainage model

In process engineering, liquid–liquid extraction is used in a range of different applications. Because of the large number of droplets, collisions occur repeatedly, ending in either coalescence or rebound. The detailed mechanisms of droplet interactions have not yet been sufficiently investigated and understood. Furthermore, in real systems, concentration-induced Marangoni convection caused by surface tension gradients is encountered. A reliable design of an extraction apparatus requires process modeling methods that can reproduce the behavior of real systems with respect to fluid dynamics and mass transport. CFD simulations give a possibility to consider the mutual influence of different phenomena (e.g., Marangoni convection and coalescence) and thus to gain a fundamental understanding of fluid dynamics and mass transport. Along these lines, droplet interactions are investigated numerically taking account of Marangoni convection. The focus is on binary droplet interactions. An extension to an arbitrary number of droplets is possible. An extended level-set (LS) method is used to localize the droplet interface. Compared to the conventional LS approach, the extended method allows merging of two interfaces to be avoided. In order to determine the coalescence onset, the CFD model is coupled with a film-drainage (FD) model. In the case of offset collisions, the centrifugal force and the Marangoni force are combined. Various systems are investigated in order to validate the successively extended versions of the model. Finally, a typical extraction test system (toluene/water with the transition component acetone) exhibiting Marangoni convection is investigated. • Numerical analysis of binary droplet coalesce in liquid–liquid systems. • A combination of a CFD-based model with film drainage models. • An extended level-set method allowing merging of two interfaces to be avoided. • A typical extraction test system exhibiting Marangoni convection was investigated. • The model was successfully validated against existing numerical and experimental data.