Behavior of small water droplets in a highly viscous flow in a converging and diverging channel

Understanding the evolution of water droplets moving in a highly viscous bulk flow (e.g., bitumen) has attracted increasing attention in the context of numerous separation technologies due to various issues relating to the environment (re-use of water) and engineering failures (corrosion of pipelines). With this in mind, the main objectives of this work are to explore the dynamics of water droplets with a diameter of seven micrometers, moving in highly viscous bitumen flowing through a smoothly converging and diverging 11-micron channel using three-dimensional (3D) and two-dimensional (2D) droplet-resolved simulations and to adjust an existing population balance model (PBM) to predict geometry-driven coalescence for different flow rates. The Eulerian-Eulerian (EE) method coupled with a new PBM is used to predict the behavior of water droplets with a diameter of 7 mu m. Numerical simulations were carried out for various capillary numbers ( 0.1 < C a < 3) and compared with the volume of fluid method combined with the level-set function (CLSVOF). Adaptive mesh refinement (up to six levels) was used in 3D and 2D CLSVOF simulations, producing interface cells measuring up to 30 nm. Good agreement was observed between EE-PBM and CLSVOF models. For comparison, we show the results of 2D CLSVOF simulations. This new PBM model can be used to predict water-oil separation in new cascade-formed geometries to enhance the coalescence of water droplets in highly viscous bulk flows.