Validation of the pressure drop–flow rate relationship predicted by lattice Boltzmann simulations for immiscible liquid–liquid flows through SMX static mixers

Abstract

Single-phase and two-phase flows through SMX static mixers were modeled using the color-gradient multiphase lattice Boltzmann method and the results were compared with experimental data from the scientific literature. In particular, the relationship between pressure drop and flow rate was investigated for single-phase and immiscible liquid–liquid interfacial systems in laminar and transitional flow regimes. The hydrodynamic simulations of immiscible liquid–liquid flows at various volume fractions accounted for interfacial effects such as coalescence and breakage. Every simulation was performed at a prescribed pressure drop corresponding to the one observed experimentally, and the resulting dimensionless Reynolds number was predicted and compared to the experimental one. Good agreement between simulations and experiments were obtained. From a practical standpoint, it is also shown that the addition of a more viscous dispersed phase in a continuous phase increases the pressure drop at a given Reynolds number in the laminar flow regime. In the transitional flow regime, the results suggest that the addition of a small fraction of the dispersed phase could actually reduce the pressure drop.