Effects of confinement on the motion of a single sphere in a sheared viscoelastic liquid

The motion of a single, inertialess, non-Brownian sphere immersed in a suspending fluid is studied in a confined geometry. A simple shear flow is imposed as external flow field and the impact of the gap between the particle and the wall on the flow fields is investigated. The suspending fluid is considered both Newtonian and viscoelastic, using for the latter case two different constitutive equations in order to separately highlight the influence of typical non-linear phenomena of non-Newtonian fluids. The rotation rate of the sphere is investigated for different Deborah numbers and gap sizes, with the sphere always at the cell center. The study is carried out through full 3D numerical simulations. We solve the balance equations by means of a finite element method. The particle rigid-body motion is imposed through constraints on the sphere surface. Therefore, the unknown particle rotation is recovered by solving the full system of equations. Simulations for a Newtonian suspending liquid show a slowing down of the particle if the gap decreases, in quantitative agreement with other numerical results in literature. For a viscoelastic matrix, this effect is even more pronounced since the nature of the fluid leads itself to a slower rotation, even in unconfined geometries. Finally, the streamlines around the particle show the existence of a recirculation zone even in Newtonian suspending fluids. Such a zone is larger and closer to the sphere as the viscoelasticity of the suspending fluid increases.