Engineering Parameter Window for Filament Formation and Early-Stage Evolution in Embedded Printing of Gelatin/Alginate Hydrogels Within Carbomer Support Baths

Embedded 3D printing of hydrophilic hydrogels in aqueous support baths often suffers from filament deformation, positional deviation, and diffusion before complete cross-linking, while practical parameter-selection guidelines for specific material systems remain limited. In this work, an integrated engineering evaluation method was developed to characterize filament formation and early-stage evolution during embedded printing of gelatin/sodium alginate inks in Carbomer support baths. Filament quality was assessed using cross-sectional geometry, contour irregularity, deposition position, and early-stage diffusion ratio. The effects of printing kinematics and material rheology are systematically examined to establish a practical process window for this hydrophilic ink–bath system. The results show that the speed ratio between substrate and ink is a primary factor controlling filament geometry and deposition position, and a ratio close to 1 yields the most balanced cross-sectional morphology without position shift from the printed nozzle. Ink with high viscosity maintains contour irregularity within a narrow range of 0.005–0.009 and suppresses early diffusion, whereas a support bath with high viscosity and ink with high viscosity combination further slows diffusional evolution by about 70%. Based on the identified process window, several three-dimensional hydrogel structures were fabricated successfully. The proposed workflow provides a practical route for process evaluation and parameter selection in hydrophilic embedded printing, especially for continuous filament and tubular structures, and offers engineering guidance for bio-soft material fabrication in applications.