Simulation of collisions of two droplets containing two different liquids using incompressible smoothed particle hydrodynamics method

The present study aims to simulate a collision of two droplets containing immiscible liquids by employing a three- dimensional incompressible smoothed particle hydrodynamics (SPH) method, with models implemented for the computation. The simulation of a head-on collision of two droplets, both of which contain the same glycerol solution, showed that the droplet behavior agrees very well with that observed in an experiment by Qian and Law (J Fluid Mech 331:59-80, 1997. 10.1017/S0022112096003722). The simulation of a head-on collision of a silicone oil droplet and a glycerol solution droplet showed that the droplet behavior agrees fairly well with that observed in the experiment by Planchette et al. (J Fluid Mech 702:5-25, 2012. 10.1017/jfm.2012.94). However, the oil only partially wraps the glycerol solution in the simulation, whereas in the experiment, the oil completely encapsulates the glycerol solution. The shape of the coalesced droplet at the early stage of the collision quantitatively agrees with that observed in the experiment. In the case of an offset collision of a droplet of silicone oil and a droplet of glycerol solution, the two droplets separate again, and small satellite droplets are formed after the collision; this behavior agrees well with that observed experimentally by Planchette et al. (2012). The feasibility of using simulations to estimate droplet liquid composition ratios is also presented. It is shown that the models implemented for the incompressible SPH simulation work reasonably well, and that this method can be a useful tool for studying the droplet collision phenomena.