Bio-inspired flexible fiber brushes that keep liquids in a controlled manner by closing their ends

Abstract

When brushes of flexible fibers are removed from liquid baths, these brushes sometimes show unwanted droplets at their ends, depending on the length, rigidity and shape of their fibers. Capillary forces arising from the varying cross-sections of conical fiber tips have been thought to eliminate the droplets. However, these forces may not operate with water, which fills the entire space between the fibers of a brush. Here, we theoretically show that brushes eliminate unwanted droplets with a physical mechanism that is significantly different from a single conical fiber by ‘closing’ their ends. We analyze the hydrostatics of water in a brush when it is removed from a bath, and we identify the condition under which the end of the brush is closed, emphasizing the roles played by the elastic deformation of the flexible fibers owing to interfacial forces. Moreover, this theory predicts that the volume of water that is captured by brushes is a non-monotonic function of the length of their fibers because the fibers show excluded volume interactions when their ends are ‘closed’. This theory may guide the design of liquid-transfer devices that can retain liquids in a controlled manner. An artist’s paint brush that prevents paint droplets forming at its tip is mathematically modelled by researchers in China and Japan. When a single fibre is withdrawn from a fluid, surface tension creates a small bridge of liquid between its tip and the liquid surface. As the fibre moves further away, the bridge collapses and a droplet can form at the end of the fibre. Tetsuya Yamamoto and co-workers from Beihang University, China, Chinese Academy of Sciences and Nagoya University, Japan, show that when many fibres are combined — as they are in a brush — hydrostatic pressures, capillary forces, and material elasticity combine to force the outside fibres into the centre. This creates a pointed, closed tip to the brush, which eliminates droplet formation. When brushes are removed from an ink bath, they sometimes show unwanted droplets, which may accidentally drop on surfaces. Our theory predicts that Chinese calligraphic brushes eliminate the unwanted droplets by closing their ends. The ends of the brushes are closed when the length L of their fibers is longer than a critical length Lclo. This principle may be applicable to the design of liquid-transfer devices.