Nonlinear disturbance growth during sedimentation in dilute fibre suspensions

Authors: Zhang, F.Z., Dahlkild, A. A., Lundell, F.
Document Type: Article
Pubstate: Published
Journal: Journal of Fluid Mechancis
Volume: 719   268-294
Year: 2013


Disturbances in a dilute fibre suspension are studied with an Eulerian approach. Based on a linear stability analysis, it is shown that inertia and hydrodynamic diffusion damp perturbations at long wavelengths and short wavelengths, respectively, leading to a wavenumber selection. For small but finite Reynolds number of the fluid bulk motion, the most unstable wavenumber is a finite value, which increases with Reynolds number. Furthermore, the diffusion narrows the range of unstable wavenumbers. Numerical simulations of the full nonlinear evolution in time of a normal-mode perturbation show that the induced flow may either die out or saturate on a finite amplitude. The character of this long-time behaviour is dictated by the wavenumber and the presence or absence, as well as nature, of the translational and rotational diffusivities.