Modulating 3D-printability with nanocellulose hydrogels

Three-dimensional (3D) printability with hydrogels can be engineered from first principles by modelling their viscoelastic and interfacial behaviour. Printability is defined as the ability of a gel to maintain shape during and after unsupported extrusion. We hypothesized that the quality and resolution of 3D gel printing can be predicted and therefore, optimized from the material viscoelastic response in the shear relaxation test. Mechanical properties of hydrogels with varying ratios of cellulose nanofibrils (CNF) and cellulose nanocrystals (CNC) ionically crosslinked with CaCl₂ were characterized using rheology, and their printability was tested using a filament sag test. A predictive model based on the Euler-Bernoulli beam-bending theory was developed to estimate the maximum critical span length that limits the filament sag below a desired threshold using the linear viscoelastic relaxation modulus. The proposed model accurately predicted the maximum span length required to limit filament sag across different hydrogel compositions spanning 2-3 orders of magnitude in mechanical properties, as confirmed by a close agreement between the predicted and measured printability boundaries. By reformulating control variables into dimensionless parameters, the framework removes dependence on specific geometry and hydrogel composition enabling generalization to any soft colloidal gels. This study establishes a quantitative platform for engineering, from first colloidal, interfacial, and continuum mechanics principles, the 3D-printability of hydrogels beyond nanocellulose systems.