Development of an Immersed Boundary Method for the Simulation of Moving Bodies at Fluid-fluid Interfaces

Particles interacting with interfaces in multiphase flows appear in many scenarios of industrial interest, including bitumen extraction, mineral recovery via froth flotation, soil remediation, and many others. This thesis presents the development of Immersed Boundary Methods (IBMs) coupled to a two-phase incompressible flow solver. The phases are treated as immiscible, and are modelled using the Volume-of-Fluid (VOF) method. The methods developed to include the effects of surface tension and contact lines are presented. A detailed description of the numerical methods, as well as their implementation into a new software framework, are presented. Details regarding the solution of the resulting large systems of sparse equations in parallel are briefly described. The accuracy of the proposed models are demonstrated in three chapters; test cases range from validation of the correct contact angle for droplets sitting on curved surfaces, to more complex Fluid-Structure Interaction (FSI) problems involving moving objects at fluid-fluid interfaces. Stationary IBMs were coupled with a VOF multiphase solver, with the effects of surface tension included via the Continuum Surface Force (CSF) method. The domain was separated into fluid and solid regions, with coupling between them achieved through a ghost-cell interpolation procedure, which in effect prescribed the desired boundary conditions for the velocity and pressure fields. A new method was developed to include the effects of contact angle/wetting for moving boundary problems. For these problems, a unified momentum equation for both the fluid and solid phases was solved, and the effect of the boundary was introduced into the momentum equation via a body force term. Solutions to FSI problems involving strong capillary forces are presented and compared to experiments. Finally, an application of the proposed numerical methods to simulating porous media injection is shown. The algorithm's ability to predict an interface's transition between stable displacement, viscous fingering and capillary fingering is demonstrated.Ph.D