Skip to main content Accessibility help

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

  • Anubhab Roy (a1), Rami J. Hamati (a2), Lydia Tierney (a2), Donald L. Koch (a3) and Greg A. Voth (a2)...


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.


Corresponding author

Email address for correspondence:


Hide All
Batchelor, G. K. 1970 Slender-body theory for particles of arbitrary cross-section in Stokes flow. J. Fluid Mech. 44 (3), 419440.
Bragg, G. M., van Zuiden, L. & Hermance, C. E. 1974 The free fall of cylinders at intermediate Reynold’s numbers. Atmos. Environ. 8 (7), 755764.
Candelier, F. & Mehlig, B. 2016 Settling of an asymmetric dumbbell in a quiescent fluid. J. Fluid Mech. 802, 174185.
Cox, R. G. 1970 The motion of long slender bodies in a viscous fluid. Part 1. General theory. J. Fluid Mech. 44 (4), 791810.
Goldfriend, T., Diamant, H. & Witten, T. A. 2017 Screening, hyperuniformity, and instability in the sedimentation of irregular objects. Phys. Rev. Lett. 118, 158005.
Guazzelli, L. & Hinch, J. 2011 Fluctuations and instability in sedimentation. Annu. Rev. Fluid Mech. 43 (1), 97116.
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.
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), 709720.
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), 151156.
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102, 715.
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. 253265. Springer.
Khayat, R. E. & Cox, R. G. 1989 Inertia effects on the motion of long slender bodies. J. Fluid Mech. 209, 435462.
Koch, D. L. & Shaqfeh, E. S. G. 1989 The instability of a dispersion of sedimenting spheroids. J. Fluid Mech. 209, 521542.
Kramel, S.2018 Non-spherical particle dynamics in turbulence. PhD thesis, Wesleyan University, Middletown, CT.
Lamb, H. 1911 On the uniform motion of a sphere through a viscous fluid. Lond. Edin. Phil. Mag. J. Sci. 21 (121), 112121.
Lamb, H. 1932 Hydrodynamics. Cambridge University Press.
Lauga, E. & Powers, T. R. 2009 The hydrodynamics of swimming microorganisms. Rep. Progr. Phys. 72 (9), 096601.
Lopez, D. & Guazzelli, É. 2017 Inertial effects on fibers settling in a vortical flow. Phys. Rev. Fluids 2 (2), 024306.
Newsom, R. K. & Bruce, C. W. 1994 The dynamics of fibrous aerosols in a quiescent atmosphere. Phys. Fluids 6 (2), 521530.
Oseen, C. W. 1910 Stokes’ formula and a related theorem in hydrodynamics. Ark. Mat. Astron. Fys. 6, 20.
Parsa, S., Calzavarini, E., Toschi, F. & Voth, G. A. 2012 Rotation rate of rods in turbulent fluid flow. Phys. Rev. Lett. 109, 134501.
Shin, M. & Koch, D. L. 2005 Rotational and translational dispersion of fibres in isotropic turbulent flows. J. Fluid Mech. 540, 143173.
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.
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.
Siewert, C., Kunnen, R. P. J., Meinke, M. & Schröder, W. 2014 Orientation statistics and settling velocity of ellipsoids in decaying turbulence. Atmos. Res. 142, 4556.
Stokes, G. G. 1851 On the Effect of the Internal Friction of Fluids on the Motion of Pendulums, vol. 9. Pitt Press.
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), 401406.
Voth, G. A. & Soldati, A. 2017 Anisotropic particles in turbulence. Annu. Rev. Fluid Mech. 49 (1), 249276.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification

Related content

Powered by UNSILO

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

  • Anubhab Roy (a1), Rami J. Hamati (a2), Lydia Tierney (a2), Donald L. Koch (a3) and Greg A. Voth (a2)...


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.