Lattice Boltzmann simulations of sedimentation of a single fiber in a weak vertical shear flow

Instability of a suspension is directly related to the problem of the cross-stream migration of a particle relative to its neighboring particle suspension. Such cross-stream or lateral migration of a single non-spherical particle (fiber) settling in a bounded weak shear flow with vertical streamlines produced by a perturbation to the fiber number density is studied using lattice Boltzmann simulations. The present simulation results demonstrate that at a given shear rate, the lateral migration can be divided into three phases depending on settling Reynolds number Rsd and particle aspect ratio κ. At a low settling Reynolds number Rsd, the suspension becomes more stable in phase 1. As Rsd increases and excesses a critical settling Reynolds number Rsd1, the fiber suspension becomes unstable in phase 2. In phase 3, at an enough large Rsd, the inertia dominates the weak shear flow and it may have little effect on stability. A mechanism of the instability induced by an inertial fiber orientation drift and a shear induced cross-streamline drift, recently proposed by Shin, Koch, and Subramanian [“Structure and dynamics of dilute suspensions of finite reynolds number settling fibers,” Phys. Fluids 21, 123304 (2009)], is examined and confirmed.