Smoothed Particle Hydrodynamics for the Rising Pattern of Oil Droplets

The problem of rising droplets in liquids is important in physics and has had many applications in industries. In the present study, the rising pattern of oil droplets has been examined using the smoothed particle hydrodynamics (SPH), which is a fully Lagrangian meshless method. The open-source SPHysics2D code is developed to two phase by adding the effects of surface tension and an added pressure term to the momentum equation. Several problems of droplet dynamics were simulated, and the performance of the developed code is evaluated. First, the still water-oil tank problem was solved to examine the hydrostatic pressure, especially at the interface, for different density ratios. Then, the rising patterns of an oil droplet of different densities are simulated and the time evolutions of the rising velocity and center of mass are shown. It is shown that the shape and behavior of the droplet rising depend on the balance between viscous, surface tension, and dynamic forces. Afterward, the flow morphologies of multiple droplet rising are shown where the density ratio causes negligible effects on the droplet shape, but it has large effects on the dynamics behavior of rising process.