  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.
