Counting droplets: A solver for the droplet population balance equation

Liquid-Liquid-Extractions is one of the fundamental operations in chemical engineering. At this, one or more components are being separated from a liquid mixture. However, this work restricts to a two component mixture. The most common used extractors in this field are liquid-liquid-extraction columns. For such extraction columns there exist many executions, however they share their functional principle. A vertically aligned column is being fed at the top by the mixture of components to be separated. On the contrary, the column is getting filled by a specifically lighter solvent at the bottom. With the help of appropriate installations (stirrer, sieve) an intensive mixing of these two phases is achieved. This process makes the solvent form many tiny droplets, which are going to rise along the extraction column due to the difference in the densities of the two phases. While the droplets are rising an exchange of material happens (mass transfer) whereby components of the mixture are getting separated. This work presents a numerical method to resolve the hydrodynamic model of the droplets