  In this paper, we present an Eulerian-Lagrangian methodology to simulate the
interaction between a fluid-fluid interface and a solid particle in the
presence of wetting effects. The target physical problem is represented by
ternary phase systems in which a solid phase and a drop phase interact inside
an incompressible Newtonian carrier fluid. The methodology is based on an
Eulerian-Lagrangian approach that allows for the numerical solution of the
Continuity and Navier-Stokes equations by using a pseudo-spectral method,
whereas the drop phase is modelled by the Phase Field Method, in which a smooth
transition layer represented by an hyperbolic function is considered both
across the solid-fluid interface and across the drop-fluid interface. Finally,
the solid phase is described in the form of a virtual force using the Direct
Forcing Immersed Boundary approach. The properties of the immersed solid phase
(including wetting effects), the deformability of the drops and the
characteristics of the carrier fluid flow are the main controlling parameters.
To simulate 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 capabilities of the methodology are proven by examining first 2D and 3D
validation cases in which a solid particle is settling in a quiescent fluid.
Then, the interaction of solid particles with a binary-fluid interface and the
effects of surface wetting on the submergence of a quasi-buoyant body are
discussed. Finally, the equilibrium configuration for a solid particle
interacting with an equally-sized drop at different contact angles and the
relative rotation of two solid particles bridged by a drop are examined in the
case the interaction is induced by shear fluid flow deformations on the drop
interface.
