Spreading of low-viscosity ink filaments driven by bath viscoelasticity in embedded printing

Inks deposited in conventional direct ink writing need to be able to support their own weight and that of the upper layers with minimal deformation to preserve the structural integrity of the three-dimensional (3D) printed parts. This constraint limits the range of usable inks to high-viscosity materials. Embedded printing enables the use of much softer inks by depositing the materials in a bath of another fluid that provides external support, thus diversifying the types of 3D printable structures. The interactions between the ink and bath fluids, however, give rise to a unique type of defect: spreading of the dispensed ink behind the moving nozzle. By printing horizontal threads made of dyed water in baths of Carbopol suspensions, we demonstrate that the spreading can be attributed to the pressure field generated in the viscous bath by the relative motion of the nozzle. As the pressure gradient increases with the viscosity of the bath fluid while the viscosity of the ink resists the flow, a larger bath-to-ink viscosity ratio results in more spreading for low-concentration Carbopol baths. For high-concentration, yield-stress-fluid baths, we find that the steady-state viscosity alone cannot account for the spreading, as the elastic stress becomes comparable to the viscous stress and the bath fluid around the dispensed ink undergoes fluidization and resolidification. By parameterizing the transient rheology of the high-concentration Carbopol suspensions using a simple viscoelastic model, we suggest that the ink spreading is exacerbated by the elasticity, but is mitigated by the yield stress as long as the yield stress is low enough to allow steady injection of the ink. These results help illuminate the link between the bath rheology and the printing quality in embedded 3D printing.