On the use of a diffuse-interface model for the simulation of rigid particles in two-phase Newtonian and viscoelastic fluids

Abstract

For the simulation of particles in two-phase flows, the diffuse-interface model is frequently employed to describe the fluid-fluid interface. The diffuse-interface model can naturally handle moving contact lines and topological changes, but the thickness of the interface is in general chosen larger than the physical one. We systematically investigated the effect of both the interface thickness and the diffusion of the fluids on the motion of rigid particles in two-phase flows, using a diffuse-interface model for the fluid-fluid interface. A sharp-interface model is considered for the fluid-fluid interface as well, which is expected to behave as the limiting case of the interface thickness going to zero.The first case that was investigated is a spherical particle in a closed cylindrical container filled with two Newtonian fluids, where the particle is moved toward the fluid-fluid interface by a force. The second case that was investigated is that of the migration of a rigid particle in a two-phase viscoelastic shear flow. The migration of the particle is due a contrast in the viscoelastic properties of the fluids, a phenomenon that was not reported before in the literature. For both cases, the results for the diffuse-interface model converge to the sharp-interface model when the interface thickness is decreased. However, it is shown that both the interface thickness and the diffusion of the fluids play crucial roles in the resulting dynamics of a particle interacting with a diffuse fluid-fluid interface.