Numerical study of filament suspensions at finite inertia

Arash Alizad Banaei, Marco Edoardo Rosti, Luca Brandt

Published 2019-03-28Version 1

We present a numerical study on the rheology of semi-dilute and concentrated filament suspensions for different bending stiffness and Reynolds number, with the immersed boundary method used for the coupling between fluid and solid. The filaments are considered as one-dimensional inextensible slender bodies with fixed aspect ratio, %${1}/{16}$ obeying the Euler-Bernoulli beam equation. At fixed volume fraction, the suspensions are found to be shear-thinning where the relative viscosity decreases by decreasing the non-dimensional bending rigidity. The relative viscosity increases when increasing the Reynolds number due to the larger contribution of the fluid-solid interaction stress to the total stress; moreover the shear-thinning increases at finite inertia, yet in the laminar regime considered here. The first normal stress is positive as in polymeric and other shear-thinning fluids, and increases with the Reynolds number. However, it has a peak for a certain value of the filament bending stiffness, which varies with the Reynolds number, moving towards more rigid suspensions at larger inertia. When increasing the filament volume fraction, we observe that the viscosity increases. On the other, the shear-thinning behavior with respect with deformability is stronger at lower volume fraction and decreases with the number of filaments. This is due to the formation of a more ordered structure in the flow, where filaments tend to be more aligned and move as an aggregate, which reduces the filament-filament interactions.