Dynamic pattern selection in polymorphic elastocapillarity

Abstract

Drying of fine hair and fibers induces dramatic capillary-driven deformation, with important implications on natural phenomena and industrial processes. We recently observed peculiar self-assembly of hair bundles into various distinct patterns depending on the interplay between the bundle length and the liquid drain rate. Here, we propose a mechanism for this pattern selection, and derive and validate theoretical scaling laws for the polymorphic self-assembly of polygonal hair bundles. Experiments are performed by submerging the bundles into a liquid bath, then draining down the liquid. Depending on the interplay between the drain rates and the length of the fibers, we observe the bundles morphing into stars (having concave sides), polygons (having straight edges and rounded corners), or circles. The mechanism of self-assembly at the high drain regime is governed by two sequential stages. In the first stage of the high drain rate regime, the liquid covers the outside of the bundles, and drainage from inside the bundle does not play a role in the self-assembly due to the high viscous stress. The local pressure at the corners of the wet bundles compresses the fibers inward blunting the corners, and the internal lubrication facilitates fiber rearrangement. In the second stage, the liquid is slowly draining from within the fiber spacing, and the negative capillary pressure at the perimeter causes the fibers to tightly pack. In the slow drainage regime, the first stage is absent, and the fibers slowly aggregate without initial dynamic rearrangement. Understanding the mechanism of dynamic elastocapillarity offers insights for studying the complicated physics of wet granular drying.