Effects of inertia and viscoelasticity on the orientation dynamics of axisymmetric particles

The talk will focus on the analytical investigation of the effects of weak inertia and fluid viscoelasticity on the orientation dynamics of a spheroidal particle in two canonical flow situations: 1. A spheroid sedimenting in a quiescent fluid, and 2. A neutrally buoyant spheroid rotating in a simple shear flow. The spheroidal geometry is taken as representative of the general effects of particle anisotropy in disperse multiphase systems. The orientation distribution of a non-Brownian spheroidal particle remains indeterminate in both sedimentation and shear flow in the Stokes limit. Either of inertia or viscoelasticity remove this indeterminacy. The above problems are analyzed using a novel approach based on the formalism of vectorial spheroidal harmonics together with the generalized reciprocal theorem. We obtain closed-form expressions for the \textit{O(Re)} inertial and \textit{O(De)} viscoelastic torques in sedimentation, and the \textit{O(Re)} angular velocity in simple shear flow, valid for an arbitrary aspect ratio. The present results highlight errors in earlier theoretical and numerical calculations.