Simplified volume-averaged models for liquid–liquid dispersions: Correct derivation and comparison with other approaches

Although many investigations have been carried out in liquid–liquid dispersions, new questions still emerge related to the treatment of mathematical simulations for such systems, which would be useful as a complement to experimental scaled-down practices with the aim of predicting the behavior of real industrial full-scale systems. In order to simulate these processes, three different models characterized by different levels of details are analyzed in this work for a stirred tank. They are mainly divided in two types: two zero-dimensional (0D) models, in which spatial homogeneity and perfect mixing of the disperse and continuous phases is assumed, and three-dimensional (3D) models, where the inhomogeneous mixing and spatial distribution of the phases is considered. One of the 0D models considers the spatial distribution of the turbulent dissipation rate (homogeneous model), while the other one employs only the average value of this variable in the tank (lumped model). The 3D model is instead based on the Eulerian–Eulerian two-fluid approach, implemented in computational fluid dynamics codes. The comparison of the results obtained imposing the very same operating conditions between the simplest 0D models (implemented in MATLAB), which are computationally very cheap, and the complex 3D models (implemented in OpenFOAM-2.2.x), which are computationally intensive, highlights their range of validity, allowing to establish a priori which level of details or approach is needed to simulate a particular system.