Eulerian/Lagrangian formulation for the elasto-capillary deformation of a flexible fibre

The capillary-induced bending of flexible fibres, a process also known as elasto-capillary deformation, is central to a variety of industrial and non-industrial applications, among which stand out textile flotation, stabilization of emulsions, micro-folding of elastic structures, and clogging of feather fibres by oil droplets. A consistent formulation for the direct numerical simulation of a flexible fibre interacting with a fluidic interface is presently suggested. The fibre is geometrically decomposed into a chain of spherical beads, which undergo stretching, bending, and twisting. interactions. The capillary force, acting at the three-phase contact line, is calculated using a ternary diffuse-interface model. In a first stage, the fibre deformation model and the ternary diffuse-interface model are validated against theoretical solutions. In a second stage, the two- and three-dimensional elasto-capillary bending of a fibre by an immersed droplet are numerically investigated. Partial wrapping and complete encapsulation could be simulated. The results show that the fibre curvature increases linearly with the square of the elasto-capillary length, for both low and large structural deformation.