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Inertial torques and a symmetry breaking orientational transition in the sedimentation of slender fibres

Published online by Cambridge University Press:  22 July 2019

Anubhab Roy ,
Rami J. Hamati ,
Lydia Tierney ,
Donald L. Koch Open the ORCID record for Donald L. Koch [Opens in a new window]  and
Greg A. Voth Open the ORCID record for Greg A. Voth [Opens in a new window]
Anubhab Roy
Affiliation:
Department of Applied Mechanics, Indian Institute of Technology Madras, Chennai 600036, India
Rami J. Hamati
Affiliation:
Department of Physics, Wesleyan University, Middletown, CT 06459, USA
Lydia Tierney
Affiliation:
Department of Physics, Wesleyan University, Middletown, CT 06459, USA
Donald L. Koch
Affiliation:
Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY 14853, USA
Greg A. Voth*
Affiliation:
Department of Physics, Wesleyan University, Middletown, CT 06459, USA
*
†Email address for correspondence: gvoth@wesleyan.edu
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Abstract

Experimental measurements of the force and torque on freely settling fibres are compared with predictions of the slender-body theory of Khayat & Cox (J. Fluid Mech., vol. 209, 1989, pp. 435–462). Although the flow is viscous dominated at the scale of the fibre diameter, fluid inertia is important on the scale of the fibre length, leading to inertial torques which tend to rotate symmetric fibres toward horizontal orientations. Experimentally, the torque on symmetric fibres is inferred from the measured rate of rotation of the fibres using a quasi-steady torque balance. It is shown theoretically that fibres with an asymmetric radius or mass density distribution undergo a supercritical pitch-fork bifurcation from vertical to oblique settling with increasing Archimedes number, increasing Reynolds number or decreasing asymmetry. This transition is observed in experiments with asymmetric mass density and we find good agreement with the predicted symmetry breaking transition. In these experiments, the steady orientation of the oblique settling fibres provides a means to measure the inertial torque in the absence of transient effects since it is balanced by the known gravitational torque.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Multiphase and Particle-laden Flows: Particle/fluid flow Low-Reynolds-number flows: Slender-body theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 875 , 25 September 2019 , pp. 576 - 596
Copyright
© 2019 Cambridge University Press 

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References

Batchelor, G. K. 1970 Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44 (3), 419–440.Google Scholar
Bragg, G. M., van Zuiden, L. & Hermance, C. E. 1974 The free fall of cylinders at intermediate Reynold’s numbers. Atmos. Environ. 8 (7), 755–764.Google Scholar
Candelier, F. & Mehlig, B. 2016 Settling of an asymmetric dumbbell in a quiescent fluid. J. Fluid Mech. 802, 174–185.Google Scholar
Cox, R. G. 1970 The motion of long slender bodies in a viscous fluid. Part 1. General theory. J. Fluid Mech. 44 (4), 791–810.Google Scholar
Goldfriend, T., Diamant, H. & Witten, T. A. 2017 Screening, hyperuniformity, and instability in the sedimentation of irregular objects. Phys. Rev. Lett. 118, 158005.Google Scholar
Guazzelli, L. & Hinch, J. 2011 Fluctuations and instability in sedimentation. Annu. Rev. Fluid Mech. 43 (1), 97–116.Google Scholar
Gustavsson, K., Jucha, J., Naso, A., Lévêque, E., Pumir, A. & Mehlig, B. 2017 Statistical model for the orientation of nonspherical particles settling in turbulence. Phys. Rev. Lett. 119, 254501.Google Scholar
Jayaweera, K. O. L. F. & Mason, B. J. 1965 The behaviour of freely falling cylinders and cones in a viscous fluid. J. Fluid Mech. 22 (4), 709–720.Google Scholar
Jayaweera, K. O. L. F. & Mason, B. J. 1966 The falling motions of loaded cylinders and discs simulating snow crystals. Q. J. R. Meteorol. Soc. 92 (391), 151–156.Google Scholar
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 715.Google Scholar
Keller, J. B. & Ward, M. J. 1996 Asymptotics beyond all orders for a low Reynolds number flow. In The Centenary of a Paper on Slow Viscous Flow by the Physicist HA Lorentz, pp. 253–265. Springer.Google Scholar
Khayat, R. E. & Cox, R. G. 1989 Inertia effects on the motion of long slender bodies. J. Fluid Mech. 209, 435–462.Google Scholar
Koch, D. L. & Shaqfeh, E. S. G. 1989 The instability of a dispersion of sedimenting spheroids. J. Fluid Mech. 209, 521–542.Google Scholar
Kramel, S.2018 Non-spherical particle dynamics in turbulence. PhD thesis, Wesleyan University, Middletown, CT.Google Scholar
Lamb, H. 1911 On the uniform motion of a sphere through a viscous fluid. Lond. Edin. Phil. Mag. J. Sci. 21 (121), 112–121.Google Scholar
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.Google Scholar
Lauga, E. & Powers, T. R. 2009 The hydrodynamics of swimming microorganisms. Rep. Progr. Phys. 72 (9), 096601.Google Scholar
Lopez, D. & Guazzelli, É. 2017 Inertial effects on fibers settling in a vortical flow. Phys. Rev. Fluids 2 (2), 024306.Google Scholar
Newsom, R. K. & Bruce, C. W. 1994 The dynamics of fibrous aerosols in a quiescent atmosphere. Phys. Fluids 6 (2), 521–530.Google Scholar
Oseen, C. W. 1910 Stokes’ formula and a related theorem in hydrodynamics. Ark. Mat. Astron. Fys. 6, 20.Google Scholar
Parsa, S., Calzavarini, E., Toschi, F. & Voth, G. A. 2012 Rotation rate of rods in turbulent fluid flow. Phys. Rev. Lett. 109, 134501.Google Scholar
Shin, M. & Koch, D. L. 2005 Rotational and translational dispersion of fibres in isotropic turbulent flows. J. Fluid Mech. 540, 143–173.Google Scholar
Shin, M., Koch, D. L. & Subramanian, G. 2006 A pseudospectral method to evaluate the fluid velocity produced by an array of translating slender fibers. Phys. Fluids 18 (6), 063301.Google Scholar
Shin, M., Koch, D. L. & Subramanian, G. 2009 Structure and dynamics of dilute suspensions of finite-Reynolds-number settling fibers. Phys. Fluids 21 (12), 123304.Google Scholar
Siewert, C., Kunnen, R. P. J., Meinke, M. & Schröder, W. 2014 Orientation statistics and settling velocity of ellipsoids in decaying turbulence. Atmos. Res. 142, 45–56.Google Scholar
Stokes, G. G. 1851 On the Effect of the Internal Friction of Fluids on the Motion of Pendulums, vol. 9. Pitt Press.Google Scholar
Tomotika, S. & Aoi, T. 1951 An expansion formula for the drag on a circular cylinder moving through a viscous fluid at small Reynolds numbers. Q. J. Mech. Appl. Maths 4 (4), 401–406.Google Scholar
Voth, G. A. & Soldati, A. 2017 Anisotropic particles in turbulence. Annu. Rev. Fluid Mech. 49 (1), 249–276.Google Scholar