3D Printing of soft fibers in complex trajectories: achieving minimum feature sizes

Nature employs hairy and fibrous structures for sensing and structural functions, as seen in beetle hairs, mammalian whiskers, and spider silks. Replicating these intricate, high aspect ratio geometry has been a longstanding challenge. Embedded 3D printing, which suspends extruded ink in a non-Newtonian yield-stress fluid bath, enables the fabrication of delicate structures not achievable by other means. While interfacial capillary effects theoretically limit the minimum feature size, discrepancies exist between the theoretical plasto-capillary length d = 2Γ/σ_y and observed minimum feature sizes. We hypothesize that the critical diameter is determined by the dimensionless Plasto-Capillary number Pl = σ_yd/(2Γ), with a non-trivial critical value different than one. Our experiments across this wide parameter space, show a critical value of Pl = σ_yd/(2Γ) = 0.21±0.03 explained by analogies to other critical dimensionless groups in yield stress fluids. These findings offer a new method to determine the minimum feature size in embedded 3D printing, given by d = 0.42 (Γ/σ_y). Furthermore, we explore an alternative approach based on viscosity criteria. By rapidly increasing the ink's viscosity before capillary forces can pinch off the filament, smaller feature sizes can be obtained. We verified this by demonstrating 3D printing of fine hairs with diameters as small as 1.5 µm and continuous lengths, using 3D printing by solvent exchange (3DPX) in a microgranular gel bath. Rapid radial solidification of extruded polymer solutions at 2.33 μm/s increases the elastic plateau modulus, preventing capillarity-induced breakage. We rationalize the smallest filament diameter achievable by 3DPX by comparing the capillary breakup and solidification timescales. These advancements not only push the boundaries of embedded 3D printing but also demonstrate the potential to replicate nature-inspired fibrous structures.