Hydrodynamic Elastocapillary Morphing of Hair Bundles

Featured in Physics
Editors' Suggestion

Hydrodynamic Elastocapillary Morphing of Hair Bundles

Jonghyun Ha, Yun Seong Kim, Kaiying Jiang, Ryan Siu, and Sameh Tawfick

Phys. Rev. Lett. 125, 254503 – Published 16 December 2020

See synopsis: Hair Styling with Physics

Abstract

We report polymorphic self-assembly of hair arranged in hollow bundles driven by capillarity, hydrodynamics, and elasticity. Bundles emerging from a liquid bath shrink but remain hollow at slow drainage due to the negative pressure of the menisci trapped between the hairs. The timescale allows the collective stiffening of the fibers to resist closure. At fast drainage, the bundles fully close before the liquid can drain through the hair. A liquid column trapped in the hole closes the bundle while the lubricated hairs still behave softly. Scaling laws predict this reversible hair polymorphism.

Received 18 March 2020
Revised 30 June 2020
Accepted 11 November 2020
Corrected 13 January 2021

DOI:https://doi.org/10.1103/PhysRevLett.125.254503

Physics Subject Headings (PhySH)

Actuating materials Imbibition & injection Liquid bridges Stimuli-responsive materials Wetting

Fluid DynamicsPolymers & Soft Matter

Corrections

13 January 2021

Correction: The name of the second author in Ref. [13] was processed improperly during the prepublication stage and has been fixed.

synopsis

Hair Styling with Physics

Published 16 December 2020

Experiments show that hair-like bundles form different shapes depending on the speed at which they are dried.

See more in Physics

Authors & Affiliations

Jonghyun Ha ¹, Yun Seong Kim ¹, Kaiying Jiang¹, Ryan Siu¹, and Sameh Tawfick ^1,2,*

¹Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
²The Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

^*tawfick@illinois.edu

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 125, Iss. 25 — 18 December 2020

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Hydrodynamic elastocapillarity-induced polymorphism of hairy tubes. (a) Schematics of hairy tubes. $R_{0}$ , $w$ , $r$ , $d$ , and $ℓ$ correspond to the inner radius, the thickness of the tubes, fiber radius, spacing, and length, respectively. (b) Top views of the hairy tubes ( $R_{0} = 7 mm$ , $ℓ = 25 mm$ ). The middle image indicates the shape of the initial state. The left and right images indicate the final shape of the partial closure (slow drainage, $u = 0.1 mm / s$ ) and the complete closure (fast drainage, $u = 20 mm / s$ ), respectively.
Reuse & Permissions
Figure 2
Evolution of tube closure. (a) Side view of hairy tubes ( $R_{0} = 7 mm$ , $ℓ = 25 mm$ ). The ring-shaped images are captured by a top camera. (b) Drainage distance evaluation of tube closure. Top and bottom images correspond to slow ( $u = 0.1 mm / s$ ) and fast drainage ( $u = 20 mm / s$ ), respectively. $h$ and $R$ correspond to the drainage distance and the contracted radius, respectively. Movie S1 [12] shows the reversibility between partial and complete closure. (c) Fiber densification and shrinking regimes of partial closure at slow drainage. The left side from the dashed line indicates fiber densification, and the right side indicates shrinking (partial closure). (d) Diameter evolution during complete closure at fast drainage. Empty and filled symbols correspond to the partial and complete closure, respectively. Orange circle markers correspond to the average radius between outer and inner radii. Upper and lower black circle markers correspond to the outer and inner radius, respectively.
Reuse & Permissions
Figure 3
Capillarity-driven partial closure at slow drainage. (a) Schematics of a side view of slow-drainage mechanism. The drainage process goes from left to right. (b) Experimentally measured tube radii versus drainage distance for various bundle geometries. (c) Nondimensional $\bar{R}$ versus drainage distance $η_{h} λ$ , where $λ$ is the aspect ratio. The experimental data collapse onto a single line when plotted against our scaling law, Eq. (1).
Reuse & Permissions
Figure 4
Hydrodynamic-driven full closure at fast drainage. (a) Schematics of a side view of fast-drainage mechanism. The black box corresponds to the control volume of mass conservation. The drainage process goes from left to right. (b) Regime map of hair morphing where $λ$ is the aspect ratio. Empty and filled symbols correspond to the partial and complete closure, respectively. (c) Universal regime map where $ζ$ is the dimensionless dynamic rise and $η λ$ is the dimensionless drainage height with respect to $ℓ_{ec}$ . The black line corresponds to the transition from partial to complete closure according to the theoretical model, Eq. (3). According to the theoretical line, the lower and upper regions indicate partial and complete closure, respectively. The markers for different geometries are listed in Fig. 3.
Reuse & Permissions

Physical Review Letters