Diagnostic tools of particle rotation anisotropy

Abstract

Anisotropies of rotation of inertia-free spheroidal particles have been studied by means of invariants of a rotation correlation tensor. Anisotropy invariant maps (AIMs), supplemented by flatness and axisymmetry parameters F and A, represent a new approach to characterize rotations of non-spherical particles. To demonstrate the attractive features of these diagnostic tools we examined the rotation of spheroidal point-particles suspended in an asymmetric turbulent channel flow with typical mean shear at one side and shear-free conditions at the other side. The AIMs showed that spheroidal particles rotate differently from the local fluid rotation even in the absence of inertia and also that prolate and oblate spheroids rotate differently. The particles generally achieve different modes of rotation near the sheared and shear-free walls. The most aspherical particles, however, exhibited the same pancake-shaped mode (A=−1) of axisymmetric rotation at both sides. Next to the shear-free wall, particles with similar magnitude of asphericity, be it disks or rods, attained the same mode of rotation. The present results suggest that AIMs, supplemented by the axisymmetry measure A, can serve as a versatile tool to characterize the complex rotation modes of non-spherical particles embedded in a turbulent flow. Although the present study was concerned only with inertia-free spheroids, exactly the same approach can be used for inertial spheroids or tri-axial ellipsoidal particles.