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In this paper, we present an Eulerian-Lagrangian methodology to simulate theinteraction between a fluid-fluid interface and a solid particle in thepresence of wetting effects. The target physical problem is represented byternary phase systems in which a solid phase and a drop phase interact insidean incompressible Newtonian carrier fluid. The methodology is based on anEulerian-Lagrangian approach that allows for the numerical solution of theContinuity and Navier-Stokes equations by using a pseudo-spectral method,whereas the drop phase is modelled by the Phase Field Method, in which a smoothtransition layer represented by an hyperbolic function is considered bothacross 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 DirectForcing Immersed Boundary approach. The properties of the immersed solid phase(including wetting effects), the deformability of the drops and thecharacteristics of the carrier fluid flow are the main controlling parameters.To simulate a ternary phase system, the solid phase is coupled to thebinary-fluid phase by introducing a single well potential in the free-energydensity functional, which can also control the solid surface wetting property.The capabilities of the methodology are proven by examining first 2D and 3Dvalidation cases in which a solid particle is settling in a quiescent fluid.Then, the interaction of solid particles with a binary-fluid interface and theeffects of surface wetting on the submergence of a quasi-buoyant body arediscussed. Finally, the equilibrium configuration for a solid particleinteracting with an equally-sized drop at different contact angles and therelative rotation of two solid particles bridged by a drop are examined in thecase the interaction is induced by shear fluid flow deformations on the dropinterface.

Particle interaction with binary-fluid interfaces in the presence of wetting effects