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.

Marine oil spills can cause serious damage to the marine ecological environment. In the numerical modeling of oil plume rising and its advection, a better understanding of the oil plume transport may be effective on the sea pollution reduction and removing pollutants. In this paper, the effects of waves are investigated on the oil plume convection-diffusion pattern using smoothed particle hydrodynamics (SPH). Firstly, the rising patterns of an oil plume of different densities are simulated and the results are compared with the analytical solution. Then, the concentration distribution is shown for the oil plume rising problem. Afterwards, the suitability of the SPH method is examined by a cnoidal wave on shore effect. Finally, the plume of different conditions is located in waves and the advection of pollutant is studied with a fixed boom and different angles. It will be concluded that using a boom with a zero diversion angle would lead to minimum passing pollutant.