In this thesis, a computational tool has been developed to study multiphase interactions, more precisely ternary phase systems where a solid and a drop phase interact in a common incompressible Newtonian carrier fluid, considering the immersed solid phase properties (including wetting effects), the type of drops and the characteristics of the carrier fluid as controlling parameters. We use an Eulerian-Lagrangian methodology where the continuity and the Navier-Stokes equations are solved numerically by using a pseudo-spectral method for the carrier fluid. The drop phase is modelled by the Phase Field Method (PFM) and the solid phase is described using the Direct Forcing Immersed Boundary approach (DFIB) and inserted to the carrier fluid in the form of a virtual force. The approaches taken in this work consider the solid-fluid and fluid-drop interfaces as smooth transition layers represented by a continuous hyperbolic function. In order to generate a ternary phase system, the solid phase is coupled to the binary-fluid-phase by introducing a single well potential in the free-energy density functional, which can also control the solid surface wetting property. The implemented tool is proven to give reliable results in the studied applications, which are divided into three categories. The first one consists of a 2D and a 3D validation case study of a solid settling in a quiescent fluid. The second category shows solid interactions with a binary-fluid interface and the effects of surface wetting in the submergence of a quasi-buoyant body. Finally, the third category shows the equilibrium configuration of solid-drops pairs at different contact angles and the relative rotation of two solids (bridged by a drop), induced by shear fluid flow deformations on the drop's interface.
