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Nonlinear disturbance growth during sedimentation in dilute fibre suspensions

Published online by Cambridge University Press:  19 February 2013

Feng Zhang ,
Anders A. Dahlkild  and
Fredrik Lundell
Feng Zhang
Affiliation:
Linné FLOW Centre, KTH Mechanics, Royal Institute of Technology, Stockholm S-100 44, Sweden
Anders A. Dahlkild*
Affiliation:
Linné FLOW Centre, KTH Mechanics, Royal Institute of Technology, Stockholm S-100 44, Sweden
Fredrik Lundell
Affiliation:
Linné FLOW Centre, KTH Mechanics, Royal Institute of Technology, Stockholm S-100 44, Sweden Wallenberg Wood Science Centre, KTH Mechanics, Royal Institute of Technology, Stockholm S-100 44, Sweden
*
†Email address for correspondence: [email protected]
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Abstract

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.

JFM classification

Instability: Instability Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 719 , 25 March 2013 , pp. 268 - 294
Copyright
©2013 Cambridge University Press

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Zhang et al. supplementary movie

Time evolution of Ψ only with translational diffusion.

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