Wetting of flexible fibre arrays

Fibrous media are functional and versatile materials, as demonstrated by their ubiquity both in natural systems such as feathers(1-4) and adhesive pads(5) and in engineered systems from nanotextured surfaces(6) to textile products(7), where they offer benefits in filtration, insulation, wetting and colouring. The elasticity and high aspect ratios of the fibres allow deformation under capillary forces, which cause mechanical damage(8), matting(5,9) self-assembly(10,11) or colour changes(12), with many industrial and ecological consequences. Attempts to understand these systems have mostly focused on the wetting of rigid fibres(13-17) or on elastocapillary effects in planar geometries(18) and on a fibre brush withdrawn from an infinite bath(19). Here we consider the frequently encountered case of a liquid drop deposited on a flexible fibre array and show that flexibility, fibre geometry and drop volume are the crucial parameters that are necessary to understand the various observations referred to above. We identify the conditions required for a drop to remain compact with minimal spreading or to cause a pair of elastic fibres to coalesce. We find that there is a critical volume of liquid, and, hence, a critical drop size, above which this coalescence does not occur. We also identify a drop size that maximizes liquid capture. For both wetting and deformation of the substrates, we present rules that are deduced from the geometric and material properties of the fibres and the volume of the drop. These ideas are applicable to a wide range of fibrous materials, as we illustrate with examples for feathers, beetle tarsi, sprays and microfabricated systems.