A numerical study of the water entry of non-rotating and rotating rigid spheres under varying impact angles and Weber numbers is presented. The numerical algorithm uses a finite-volume discretization and the interface between the liquid and the gaseous phase is described by means of a volume-of-fluid method. An appropriate mesh translation allows the boundary condition at the surface of the moving and rotating particle to be accounted for. The simulation results are validated with experiments and found to be in very good agreement both qualitatively (evolution of cavity shape) and quantitatively (motion of particle with respect to time). An investigation of the influence of particle rotation on its water entry behavior is carried out as well as an analysis of the effect of wettability upon cavity formation. Notably, wettability of the sphere plays a role during the penetration of a free liquid surface, even at higher Weber numbers. During impact of small particles at low Weber numbers, the influence of capillary forces rises and the force emerging at the three phase contact line becomes predominant. This force is taken into account and its influence on the impact behavior is presented. It is shown that the interface penetration behavior, either water entry or escaping from water, mostly depends on the Weber number, the solid to liquid density ratio, and the particle’s wettability, while the impact angle has nearly no influence.
We numerically investigate the hydrodynamics of a two-dimensional compound drop in a plane Poiseuille flow under Stokes regime. A neutrally buoyant, initially concentric compound drop is released into a fully developed flow, where it migrates to its equilibrium position. Based on the results, we find that the core–shell interaction affects the dynamics of both the core and the compound drop. During the initial transient period, the core revolves about the center of the compound drop due to the internal circulation inside the shell. At equilibrium, depending upon the nature of the flow field inside the shell, we identify two distinct core behaviors: stable state and limit-cycle state. In the stable state, the core stops revolving and moves outward very slowly. The core in the limit-cycle state continues to revolve in a nearly fixed orbit with no further inward motion. The presence of the core affects both deformation and migration dynamics of the compound drop. A comparison with the simple drop reveals that the core enhances the deformation of the compound drop. The outward moving core in the stable state pushes the compound drop toward the walls, while the revolving core in the limit-cycle state causes the compound drop to oscillate at its equilibrium position. The migration of the compound drop also affects the eccentricity of the core significantly. From the parametric study, we find that the core affects the compound drop dynamics only at intermediate sizes, and an increase in any parameter sufficiently causes a transition from the limit-cycle state to the stable state.
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