Influence of rotary inertia on the fiber dynamics in homogeneous creeping flows

The rotation of an inertialess ellipsoidal particle in a Newtonian fluid has been firstly analyzed by Jeffery [1]. He found that in the shear flow the particle rotates such that the end of its axis of symmetry describes a closed periodic orbit. The aim of this paper is to discuss the effects of particle inertia on the rotary motion of a fiber in uniform flow fields. We recall the equations of motion and the constitutive equation for the hydrodynamic moment in the case of a slender fiber. These equations are solved numerically for several flow fields. We demonstrate that for the plane flow fields with dominant vorticity (elliptic and rotational flows) the effect of inertia is the slow particle drift toward the flow plane.