Numerical simulation of the unsteady hydrodynamics of a water droplet in paraffin oil

This work reports on numerical simulations of the unsteady hydrodynamics occurring in droplets of pure water in a continuous paraffin oil phase. The considered droplets have varying initial position and are confined in a 1 cm × 1 cm square box. The systems are two-dimensional, submitted to gravity and surface tension effects are fully accounted for. Such systems are typical examples of two phases, unsteady, free interface problems. The full Navier–Stokes equation for incompressible fluids is solved and a volume of fluids technique without interface reconstruction is used. The time evolution of the droplets as well as their hydrodynamics is investigated. Influence of the initial condition and the bifurcations occurring in the velocity field inside the droplets are discussed. Besides droplets unsteady evolution, this work also aims to propose numerical techniques for the simulation of the hydrodynamics of complex fluids systems like emulsions.