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The instability of a sedimenting suspension of weakly flexible fibres

Published online by Cambridge University Press:  09 September 2014

Harishankar Manikantan ,
Lei Li ,
Saverio E. Spagnolie  and
David Saintillan
Harishankar Manikantan
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, San Diego, CA 92093, USA
Lei Li
Affiliation:
Department of Mathematics, University of Wisconsin–Madison, 480 Lincoln Drive, Madison, WI 53706, USA
Saverio E. Spagnolie
Affiliation:
Department of Mathematics, University of Wisconsin–Madison, 480 Lincoln Drive, Madison, WI 53706, USA
David Saintillan*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, San Diego, CA 92093, USA
*
†Email address for correspondence: [email protected]
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Abstract

Suspensions of sedimenting slender fibres in a viscous fluid are known to be unstable to fluctuations of concentration. In this paper we develop a theory for the role of fibre flexibility in sedimenting suspensions in the asymptotic regime of weakly flexible bodies (large elasto-gravitation number). Unlike the behaviour of straight fibres, individual flexible filaments rotate as they sediment, leading to an anisotropic base state of fibre orientations in an otherwise homogeneous suspension. A mean-field theory is derived to describe the evolution of fibre concentration and orientation fields, and we explore the stability of the base state to perturbations of fibre concentration. We show that fibre flexibility affects suspension stability in two distinct and competing ways: the anisotropy of the base state renders the suspension more unstable to perturbations, while individual particle self-rotation acts to prevent clustering and stabilizes the suspension. In the presence of thermal noise, the dominant effect depends critically upon the relative scales of flexible fibre self-rotation compared to rotational Brownian motion.

JFM classification

Instability: Instability Low-Reynolds-number flows: Low-Reynolds-number flows Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 756 , 10 October 2014 , pp. 935 - 964
Copyright
© 2014 Cambridge University Press 

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