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Influence of small inertia on Jeffery orbits

Part of: JFM Notebooks

Published online by Cambridge University Press:  19 January 2024

Davide Di Giusto Open the ORCID record for Davide Di Giusto [Opens in a new window] ,
Laurence Bergougnoux Open the ORCID record for Laurence Bergougnoux [Opens in a new window] ,
Cristian Marchioli Open the ORCID record for Cristian Marchioli [Opens in a new window]  and
Élisabeth Guazzelli Open the ORCID record for Élisabeth Guazzelli [Opens in a new window]
Davide Di Giusto*
Affiliation:
Aix Marseille Université, CNRS, IUSTI, 13453 Marseille, France Dipartimento Politecnico di Ingegneria e Architettura, University of Udine, 33100 Udine, Italy
Laurence Bergougnoux
Affiliation:
Aix Marseille Université, CNRS, IUSTI, 13453 Marseille, France
Cristian Marchioli
Affiliation:
Dipartimento Politecnico di Ingegneria e Architettura, University of Udine, 33100 Udine, Italy
Élisabeth Guazzelli
Affiliation:
Université Paris Cité, CNRS, Matière et Systèmes Complexes, UMR 7057, 75013 Paris, France
*
†Email address for correspondence: digiusto.davide@spes.uniud.it
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Abstract

We experimentally investigate the rotational dynamics of neutrally buoyant axisymmetric particles in a simple shear flow. A custom-built shearing cell and a multi-view shape-reconstruction method are used to obtain direct measurements of the orientation and period of rotation of particles having oblate and prolate shapes (such as spheroids and cylinders) of varying aspect ratios. By systematically changing the viscosity of the fluid, we examine the effect of inertia (which may be originated from either phase) on the dynamical behaviour of these suspended particles up to a particle Reynolds number of approximately one. While no significant effect on the period of rotation is found in this small-inertia regime, a systematic drift among several rotations toward limiting stable orbits is observed. Prolate particles are seen to drift towards the tumbling orbit in the plane of shear, whereas oblate particles are driven either to the tumbling or to the vorticity-aligned spinning orbits, depending on their initial orientation. These results are compared with recent small-inertia asymptotic theories, assessing their range of validity, as well as to numerical simulations in the small-inertia regime for both prolate and oblate particles.

JFM classification

Multiphase and Particle-laden Flows: Particle/fluid flow Complex Fluids: Suspensions Low-Reynolds-number flows: Slender-body theory

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 979 , 25 January 2024 , A42
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© The Author(s), 2024. Published by Cambridge University Press

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Supplementary material: File

Di Giusto et al. supplementary movie 1

Jeffery orbits for a fibre with equivalent aspect ratio r_eq=7.4 at small particle Reynolds number Re_p=0.08, run 5 of panel (a) of Figure 6;
Download Di Giusto et al. supplementary movie 1(File)
File 3 MB
Supplementary material: File

Di Giusto et al. supplementary movie 2

Jeffery orbits for a fibre with equivalent aspect ratio r_eq=7.4 at small particle Reynolds number Re_p=0.08, run 6 of panel (a) of Figure 6;
Download Di Giusto et al. supplementary movie 2(File)
File 1.8 MB
Supplementary material: File

Di Giusto et al. supplementary movie 3

Jeffery orbits for a fibre with equivalent aspect ratio r_eq=7.4 at small particle Reynolds number Re_p=0.08, run 8 of panel (a) of Figure 6;
Download Di Giusto et al. supplementary movie 3(File)
File 1.8 MB
Supplementary material: File

Di Giusto et al. supplementary movie 4

Jeffery orbits for a fibre with equivalent aspect ratio r_eq=7.4 at large particle Reynolds number Re_p=1.0, run 13 of panel (b) of Figure 6;
Download Di Giusto et al. supplementary movie 4(File)
File 1.9 MB
Supplementary material: File

Di Giusto et al. supplementary movie 5

Jeffery orbits for a fibre with equivalent aspect ratio r_eq=7.4 at large particle Reynolds number Re_p=1.0, run 14 of panel (b) of Figure 6;
Download Di Giusto et al. supplementary movie 5(File)
File 1.5 MB
Supplementary material: File

Di Giusto et al. supplementary movie 6

Jeffery orbits for a fibre with equivalent aspect ratio r_eq=7.4 at large particle Reynolds number Re_p=1.0, run 3 of panel (b) of Figure 6;
Download Di Giusto et al. supplementary movie 6(File)
File 1.3 MB
Supplementary material: File

Di Giusto et al. supplementary movie 7

Jeffery orbits for a spheroid with aspect ratio r=0.6 at small particle Reynolds number Re_p=0.02, run 1 of panel (c) of Figure 6;
Download Di Giusto et al. supplementary movie 7(File)
File 5.2 MB
Supplementary material: File

Di Giusto et al. supplementary movie 8

Jeffery orbits for a spheroid with aspect ratio r=0.6 at small particle Reynolds number Re_p=0.02, run 3 of panel (c) of Figure 6;
Download Di Giusto et al. supplementary movie 8(File)
File 7.6 MB
Supplementary material: File

Di Giusto et al. supplementary movie 9

Jeffery orbits for a spheroid with aspect ratio r=0.6 at small particle Reynolds number Re_p=0.02, run 4 of panel (c) of Figure 6;
Download Di Giusto et al. supplementary movie 9(File)
File 9 MB
Supplementary material: File

Di Giusto et al. supplementary movie 10

Jeffery orbits for a spheroid with aspect ratio r=0.6 at moderate particle Reynolds number Re_p=0.43, run 10 of panel (d) of Figure 6;
Download Di Giusto et al. supplementary movie 10(File)
File 6.6 MB
Supplementary material: File

Di Giusto et al. supplementary movie 11

Jeffery orbits for a spheroid with aspect ratio r=0.6 at moderate particle Reynolds number Re_p=0.43, run 8 of panel (d) of Figure 6;
Download Di Giusto et al. supplementary movie 11(File)
File 7.9 MB
Supplementary material: File

Di Giusto et al. supplementary movie 12

Jeffery orbits for a spheroid with aspect ratio r=0.6 at moderate particle Reynolds number Re_p=0.43, run 5 of panel (d) of Figure 6;
Download Di Giusto et al. supplementary movie 12(File)
File 7.7 MB
Supplementary material: File

Di Giusto et al. supplementary movie 13

Jeffery orbits for a disk with equivalent aspect ratio r=0.18 at small particle Reynolds number Re_p=0.05, run 1 of panel (e) of Figure 6;
Download Di Giusto et al. supplementary movie 13(File)
File 2.4 MB
Supplementary material: File

Di Giusto et al. supplementary movie 14

Jeffery orbits for a disk with equivalent aspect ratio r=0.18 at small particle Reynolds number Re_p=0.05, run 2 of panel (e) of Figure 6;
Download Di Giusto et al. supplementary movie 14(File)
File 950.3 KB
Supplementary material: File

Di Giusto et al. supplementary movie 15

Jeffery orbits for a disk with equivalent aspect ratio r=0.18 at small particle Reynolds number Re_p=0.05, run 5 of panel (e) of Figure 6;
Download Di Giusto et al. supplementary movie 15(File)
File 2.2 MB
Supplementary material: File

Di Giusto et al. supplementary movie 16

Jeffery orbits for a disk with equivalent aspect ratio r=0.18 at large particle Reynolds number Re_p=1.32, run 1 of panel (e) of Figure 6;
Download Di Giusto et al. supplementary movie 16(File)
File 1.3 MB
Supplementary material: File

Di Giusto et al. supplementary movie 17

Jeffery orbits for a disk with equivalent aspect ratio r=0.18 at large particle Reynolds number Re_p=1.32, run 2 of panel (e) of Figure 6;
Download Di Giusto et al. supplementary movie 17(File)
File 1.4 MB
Supplementary material: File

Di Giusto et al. supplementary movie 18

Jeffery orbits for a disk with equivalent aspect ratio r=0.18 at large particle Reynolds number Re_p=1.32, run 9 of panel (e) of Figure 6;
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File 1.6 MB
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Di Giusto et al. supplementary movie 19

Five different Jeffery Orbits for a spheroid of aspect ratio r=10, see Figure 1.
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File 9.2 MB
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Di Giusto et al. supplementary material 20

Di Giusto et al. supplementary material
Download Di Giusto et al. supplementary material 20(File)
File 111.7 KB