Simulated extrusion of filaments into support baths

Embedded direct ink writing, wherein continuous filaments are extruded into a support bath, has enabled the fabrication of soft materials including living cell scaffolds. Inks and support baths have consisted of Newtonian and non-Newtonian fluids, across a wide viscosity range. Additionally, previous works have used both hydrophobic and hydrophilic materials for inks and support baths. In order to guide material selection for more reliable prints, we use numerical simulations in OpenFOAM to directly probe the effects of viscous dissipation, viscoelasticity, and interfacial energy on the three-dimensional shape and position of the printed filament within the support bath. These simulations indicate that when both the ink and support are Newtonian fluids, their surface tension and the ratio of their viscosities control the cross-sectional shape of the filament. Further, surface tension and support viscosity can both be used to suppress Plateau-Rayleigh instabilities. Introducing a Hershel-Bulkley support bath can stabilize a Newtonian filament and improve the positional accuracy of the print, but it can also introduce new cross-sectional shape irregularities. Printing a Herschel-Bulkley filament into a Newtonian support bath can lead to positioning errors.