Predicting Extensional Behaviors of Colloidal Inks from Shear-Based Models for Direct Ink Writing

Abstract Colloidal-based inks have immense potential to be used in direct ink writing 3D printing if their printability can be evaluated, which is typically difficult. In this work, the extrudability of colloidal-based inks of moderate volume fraction for direct ink writing is characterized using the dripping-onto-substrate method and compared to predictions derived from a piecewise power-law model based on simple shear rheology. In extension, filaments from the colloidal ink exhibited elasto-capillary thinning that can be modeled as a power-law fluid. However, the model inks exhibit a much greater degree of thinning than is predicted from the shear-based model. This disagreement occurs due to the different flow regimes between the shear-based measurements and extensional measurements based on different Deborah numbers calculated using a Brownian time scale for the fluid relaxation time. The Deborah numbers of the extensional experiments are several orders of magnitude higher than shear values. This indicates that in extension, the particles within the ink do not have time to relax, resulting in variation of volume fraction within the filament. Despite the mismatch between the shear and extensional behavior, this method still can be utilized to predict the filament breakup time, extensional viscosities, and optimal printing height for printing without breakup or clean filament breakup.