Shape of a Ponytail and the Statistical Physics of Hair Fiber Bundles

Phys. Rev. Lett. 108, 078101
volume 108, issue 7, pages 078101
DOI: http://dx.doi.org/10.1103/PhysRevLett.108.078101
Published 13 February 2012

Raymond E. Goldstein [1], Patrick B. Warren [2], and Robin C. Ball [3]

[1] Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
[2] Unilever R&D Port Sunlight, Quarry Road East, Bebington, Wirral, CH63 3JW, United Kingdom
[3] Department of Physics, University of Warwick, Coventry, CV4 7AL, United Kingdom

Abstract

A general continuum theory for the distribution of hairs in a bundle is developed, treating individual fibers as elastic filaments with random intrinsic curvatures. Applying this formalism to the iconic problem of the ponytail, the combined effects of bending elasticity, gravity, and orientational disorder are recast as a differential equation for the envelope of the bundle, in which the compressibility enters through an “equation of state.” From this, we identify the balance of forces in various regions of the ponytail, extract a remarkably simple equation of state from laboratory measurements of human ponytails, and relate the pressure to the measured random curvatures of individual hairs.

http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.078101