Simulated filament shapes in embedded 3D printing

Embedded 3D printing, wherein fluid inks are extruded into support baths, has enabled the manufacture of complex, custom structures ranging from cell-laden tissue analogues to soft robots. This method encompasses two techniques: embedded ink writing (EIW), where filaments are extruded, and embedded droplet printing (EDP), where droplets are suspended. Materials for embedded 3D printing can be Newtonian, but often both the ink and the support bath are yield stress fluids, following elastic behavior below the yield stress and shear-thinning, viscous behavior above the yield stress. The effect of surface tension on print quality has been debated, as inks have been printed into supports at high and low surface tensions. In order to guide material selection for embedded 3D printing and identify key scaling relationships that influence print quality, this study investigates the role of ink rheology, support rheology, and surface tension on the morphology of single filaments. Numerical simulations in OpenFOAM demonstrate that at low viscosities, surface tension controls the filament morphology. Where capillarity is suppressed, the ratio of the local ink and support viscosities and the shape of the yield surface in the support control the filament shape. Herschel-Bulkley support fluids (yield stress fluids) produce more stable, accurately positioned filaments than Newtonian supports. In the short term, non-zero surface tensions can suppress filament shape defects in EIW and are essential for producing droplets in EDP.