Interface-resolved simulations of a sphere settling in simple shear flows of elastoviscoplastic fluids*

We present the fluid mechanics of a settling sphere in an elastoviscoplastic (EVP) material with and without a simple cross shear flow. The objective is to understand how elasticity, plasticity and inertia affect the flow features and consequently the drag force on the sphere. The EVP material is modeled with the constitutive law proposed by Saramito. The single and rigid particle is discretized on a moving Lagrangian grid while the flow equations are solved on a fixed Eulerian grid. The solid particle is represented by an Immersed Boundary method (IBM) with a computationally efficient direct forcing method. Our results show that for constant elasticity, the total drag force on the sphere increases with the yield stress of the material. We infer from our fully resolved numerical simulations that the viscous stresses are the dominant cause of the increase in the particle drag force, while the least contribution comes from the form drag.