Fluid dynamics and mass transfer at single droplets in liquid/liquid systems

The design of contact apparatuses in which one liquid phase is dispersed into another is a challenging task with regard to fluid dynamics and mass transfer. To disentangle the complexity in these multiphase polydispersed systems with all their coupled mutual interactions, one first step towards a reliable prediction is to reduce the system to a single droplet problem, where a single droplet is moving in a quiescent ambient phase. Commonly, one is interested in the mass transfer coefficient (or Sherwood number) in case of the transfer of a soluble component, and the drop velocity of fall/rise. In order to save time and money, one objective is to predict the behaviour of a given system as reliable as possible to minimise the own experimental (and numerical) effort. However, although the issue is “only” to understand the single droplet, merely in a few basic cases analytical equations are available and applicable, and results based on CFD methods have to be judged with care. Additionally, in most cases experimental or numerical data for a given system may not be available at all, hence the practitioner has to select the best suitable empirical or semi-empirical approaches for the corresponding system which itself is a challenging task. This paper aims to help to make the required decisions and to enable the reader to characterise and confine a given extraction system regarding fluid dynamics and mass transfer. Thereto, a chart is presented to initiate a selection process starting from simpler cases to cases with increasing complexity, especially addressing the behaviour of systems dominated by Marangoni instabilities.