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Nonlinear disturbance growth during sedimentation in dilute fibre suspensions

  • Feng Zhang (a1), Anders A. Dahlkild (a1) and Fredrik Lundell (a1) (a2)

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.

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Email address for correspondence: ad@mech.kth.se

References

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Time evolution of Ψ only with translational diffusion.

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