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High-frequency viscosity of a dilute suspension of elongated particles in a linear shear flow between two walls

Published online by Cambridge University Press:  23 December 2014

François Feuillebois ,
Maria L. Ekiel-Jeżewska ,
Eligiusz Wajnryb ,
Antoine Sellier  and
Jerzy Bławzdziewicz
François Feuillebois*
Affiliation:
LIMSI-CNRS, UPR 3251, Rue John von Neumann Campus Universitaire d’Orsay Bât 508, 91405 Orsay CEDEX, France
Maria L. Ekiel-Jeżewska
Affiliation:
Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5b, 02-106 Warsaw, Poland
Eligiusz Wajnryb
Affiliation:
Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawińskiego 5b, 02-106 Warsaw, Poland
Antoine Sellier
Affiliation:
LadHyX, École Polytechnique, 91128 Palaiseau CEDEX, France
Jerzy Bławzdziewicz
Affiliation:
Department of Mechanical Engineering, Texas Tech University, Lubbock, TX 79409, USA
*
†Email address for correspondence: [email protected]
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Abstract

A general expression for the effective viscosity of a dilute suspension of arbitrary-shaped particles in linear shear flow between two parallel walls is derived in terms of the induced stresslets on particles. This formula is applied to $N$-bead rods and to prolate spheroids with the same length, aspect ratio and volume. The effective viscosity of non-Brownian particles in a periodic shear flow is considered here. The oscillating frequency is high enough for the particle orientation and centre-of-mass distribution to be practically frozen, yet small enough for the flow to be quasi-steady. It is known that for spheres, the intrinsic viscosity $[{\it\mu}]$ increases monotonically when the distance $H$ between the walls is decreased. The dependence is more complex for both types of elongated particles. Three regimes are theoretically predicted here: (i) a ‘weakly confined’ regime (for $H>l$, where $l$ is the particle length), where $[{\it\mu}]$ is slightly larger for smaller $H$; (ii) a ‘semi-confined’ regime, when $H$ becomes smaller than $l$, where $[{\it\mu}]$ rapidly decreases since the geometric constraints eliminate particle orientations corresponding to the largest stresslets; (iii) a ‘strongly confined’ regime when $H$ becomes smaller than 2–3 particle widths $d$, where $[{\it\mu}]$ rapidly increases owing to the strong hydrodynamic coupling with the walls. In addition, for sufficiently slender particles (with aspect ratio larger than 5–6) there is a domain of narrow gaps for which the intrinsic viscosity is smaller than that in unbounded fluid.

JFM classification

Complex Fluids: Complex Fluids Low-Reynolds-number flows: Low-Reynolds-number flows Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 764 , 10 February 2015 , pp. 133 - 147
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© 2014 Cambridge University Press 

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