Fully-resolved simulations of an ellipsoidal particle settling in a Bingham fluid

Abstract

Despite many particle shapes and motion patterns that can be present in viscoplastic settling, the scientific studies are mostly limited to spherical particles and cases in which the solid body motion is purely vertical or rotational. Here we tackle the problem of an ellipsoidal particle settling in Bingham fluid through fully-resolved simulations. Oblate and prolate spheroids of varied aspect ratios and initial orientations are analyzed. We use the Lattice Boltzmann Method (LBM), in which the Bingham constitutive equation is solved exactly. We employ the Immersed Boundary Method (IBM) to delineate the particle boundaries and enforce the no-slip condition over them. For the case of creeping flow around a settling ellipsoid, we benchmark results of the critical yield number for oblate and prolate spheroids against augmented Lagrangian method (ALM) data and provide values for different aspect ratios and initial orientations. Then, we analyze the dynamics of prolate and oblate spheroids settling in Bingham fluid at an inertial flow. We present the evolution of trajectory, orientation, angular momentum, Reynolds number, and drift angle for various aspect ratios and initial orientations.