A Volume of Fluid Method for Three Dimensional Direct Numerical Simulations of Immiscible Droplet Collisions

Abstract: An advanced Volume of Fluid (VOF) method is presented that enables performant three-dimensional Direct Numerical Simulations (DNS) of the interaction of two immiscible fluids in a gaseous environment with large topology changes, e.g., binary droplet collisions. One of the challenges associated with the introduction of a third immiscible phase into the VOF method is the reconstruction of the phase boundaries near the triple line in arbitrary arrangements. For this purpose, an efficient method based on a Piecewise Linear Interface Calculation (PLIC) is shown. Moreover, the surface force modeling with the robust Continuous Surface Stress (CSS) model was enhanced to treat such three-phase situations with large topology changes and thin films. A consistent scaling of the fluid properties at the interfaces ensures energy conservation. The implementation of these methods in the multi-phase flow solver Free Surface 3D (FS3D) allowed a successful validation. A qualitative comparison of the morphology in binary collisions of immiscible droplets as well as a quantitative comparison regarding the threshold velocities that distinguish different collision regimes shows excellent agreement with experimental results. These simulations enable the evaluation of experimentally inaccessible data like the contributions of the kinetic, surface and dissipative energy of both immiscible liquids during the collision process. Furthermore, the comparison with binary collisions of the same liquids highlights similarities and differences between the collisions. Both can support the modeling of the immiscible liquid interaction in the future.