Rotation of an isolated triaxial ellipsoid suspended in slow viscous flow

Abstract

A freely suspended triaxial ellipsoid, or particle with two perpendicular symmetry planes, orients in a creeping flow at a rate given by differential equations in the three Euler angles, derived here for simple shear flow. The parameters for a given particle are three components of Bretherton's tensor; observations along two directions in space suffice to determine these. Any ellipsoid's two axis ratios can be chosen with the second deviating from unity less than the square root of the first. Numerical integration shows that, in contrast to the orbits of Jeffery, the particle has no fixed period of rotation about the fluid's vorticity axis. The longest axis of a rod-like triaxial particle crosses the plane perpendicular to the fluid vorticity, a motion impossible for an axisymmetric particle. In typical graphs for a quarter rotation, times required and changes in orientation are shown. Lack of axial symmetry implies that a suspension of such particles can be more disoriented.