Numerical study of filament suspensions at finite inertia
Abstract
We present a numerical study on the rheology of semidilute and concentrated filament suspensions of different bending stiffness and Reynolds number, with the immersed boundary method used to couple the fluid and solid. The filaments are considered as onedimensional inextensible slender bodies with fixed aspect ratio, obeying the EulerBernoulli beam equation. To understand the global suspension behavior we relate it to the filament microstructure, deformation and elastic energy and examine the stress budget to quantify the effect of the elastic contribution. At fixed volume fraction, the viscosity of the suspension reduces when decreasing the bending rigidity and grows when increasing the Reynolds number. The change in the relative viscosity is stronger at finite inertia, although still in the laminar flow regime as considered here. Moreover, we find the first normal stress difference to be positive as in polymeric fluids, and to increase with the Reynolds number; its value has a peak for an intermediate value of the filament bending stiffness. The peak value is found to be proportional to the Reynolds number, moving towards more rigid suspensions at larger inertia. Moreover, the viscosity increases when increasing the filament volume fraction, and the rate of increase of the filament stress with the bending rigidity is stronger at higher Reynolds numbers and reduces with the volume fraction. We show that this behaviour is associated with the formation of a more ordered structure in the flow, where filaments tend to be more aligned and move as a compact aggregate, thus reducing the filamentfilament interactions despite their volume fraction increases.
 Publication:

Journal of Fluid Mechanics
 Pub Date:
 January 2020
 DOI:
 10.1017/jfm.2019.794
 arXiv:
 arXiv:1903.12007
 Bibcode:
 2020JFM...882A...5A
 Keywords:

 Physics  Fluid Dynamics;
 Condensed Matter  Soft Condensed Matter
 EPrint:
 26 pages, 20 figures