Structure and dynamics of dilute suspensions of finite-Reynolds-number settling fibers

Abstract

Many-fiber simulations and a linear stability analysis are used to explore the structure and dynamics that arise in a dilute suspension of sedimenting slender fibers with finite particle Reynolds numbers. Dynamic simulations based on a slender-body treatment of the fibers coupled with a pseudospectral solution of the Navier–Stokes equations reveal an inhomogeneous structure dominated by the largest wavelength that fits in the periodic simulation cell. This structure becomes weaker with increasing fiber Reynolds number and fiber concentration. A linear stability analysis shows that the stability of the homogeneous state of the suspension is determined by the direction of the horizontal migration of a fiber in a weak shear field with vertical streamlines produced by a perturbation to the fiber number density. The lift force on a settling fiber, in a plane transverse to gravity, has two contributions. The first contribution results from a broken symmetry in the presence of shear at finite Reynolds number, and involves the coupled effects of the shear and translational inertial terms. The second contribution is related to the sedimentation-driven drift of an inclined fiber, and is present even in the Stokes limit. Both contributions act to push fibers toward downward flowing, high density regions, and the net transverse drift is therefore of a destabilizing nature. The drift calculation and its implications for the instability of a homogeneous suspension are explored up to a Reynolds number of 10.6. The structure factor, fluid velocity fluctuations, and deviations of the fiber orientation away from the horizontal plane are found to generally decrease with increasing Reynolds number as a result of the increasing dominance of the inertial torque acting to rotate settling fibers toward the horizontal plane.