Sedimentation of a spheroidal particle in an elastoviscoplastic fluid

Abstract

The sedimentation dynamics of a prolate spheroidal particle in an unbounded elastoviscoplastic (EVP) fluid is studied by direct finite element simulations under inertialess flow conditions. The Saramito–Giesekus constitutive equation is employed to model the suspending liquid. The arbitrary Lagrangian–Eulerian formulation is used to handle the particle motion. The sedimentation, lift, and angular velocities of spheroids with aspect ratio between 1 and 8 are computed as the initial orientation, Bingham, and Weissenberg numbers are varied. Similar to the purely viscoelastic case, a spheroid in an EVP fluid rotates up to align its major axis with the applied force. As the Bingham number increases, the settling rate monotonically reduces, while the angular velocity first increases and then decreases. The initial orientation has a relevant effect on the particle stoppage because of the different drag experienced by the spheroid as its orientation is varied. The yielded and unyielded regions around the spheroid reveal that, for particle oriented transversely to the force, the yielded envelope shrinks near the tips due to the fast spatial decay of the stresses, and unyielded regions appear along the surface of the particle, similar to the solid caps observed at the front and back of a sphere. Fluid plasticity enhances the negative wake phenomenon that is observed at Weissenberg numbers significantly lower than the purely viscoelastic case. The results of the drag correction coefficient for particles aligned with longest axis along the force are presented.