Correction

Fluid ‘rope trick’ investigated

L. Mahadevan, W. S. Ryu, A. D. T. Samuel

Nature 392, 140 ( 1998)

We wish to amend a small mistake in our calculations, although this does not affect the basic idea in our paper, particularly by comparison with experiment. As the longitudinal viscous stress σ in the filament scaled as ∼μ Ur/R² varies linearly across the cross-section, the integrated stress resultant ∫σdA vanishes. However, the net bending torque due to this viscous stress does not vanish and scales as ∫σrdA∼μ Ur⁴/R². The force per unit volume on the fluid due to centripetal and Coriolis accelerations scales as f∼ρΩ²R, so that the bending torque on the whirling filament in the vicinity of the coil scales as fr²R²∼ρΩ²r² R³. Torque balance, together with the ancillary continuity relations, leads to a scaling law for the coiling frequency

which is slightly different from the result given in our paper, where an erroneous argument confuses the transverse and longitudinal timescales in the filament. Equation (1) can be derived directly using an analogy to the coiling of an elastic rope by simply replacing the elastic bending modulus Er⁴ in ref. 1 with the ‘viscous bending modulus’ μr⁴U/ R. A reconsideration of the experimental results leads to data collapse with a power law Ω/Q^1.33∼ r^{−3.45±0.10}, in agreement with our argument.