Particle-resolved simulations of the wall effect on the sedimentation of a single sphere in yield-stress fluids

We perform high-fidelity numerical simulations to investigate the confinement effect on the sedimentation of a single spherical particle in an otherwise quiescent yield stress fluid. The simulations are performed in the presence of finite elasticity and weak inertia. The carrier fluid is modeled utilizing the elastoviscoplastic constitutive laws proposed by Saramito (2009). The additional elastic stress tensor is fully coupled with the flow equation, while the rigid particle is represented by an immersed boundary method. The particle-resolved simulations demonstrate the faster relaxation of the fluid velocity and the progressive translation of the location of the negative wake downstream of the sphere as the bounding walls are brought closer to the particle. Furthermore, the drag force exerted from the surrounding fluid on the particle decreases by escalating the particle-wall distance. We show that the confinement ratio (ratio of the gap between rigid confining walls and the sphere radius) reaches a critical value beyond which the wall-effect on the particle and flow dynamics becomes negligible. The key finding here is that the critical confinement ratio and the maximum variation of the Stokes drag with confinement ratio are weakly dependent on the level of material elasticity and plasticity for a certain range of material parameters. Finally, we propose an expression for the Stokes drag coefficient, as a function of material plasticity and confinement ratio.