Study on the formation mechanism of viscoplastic line deposition for predicting filament width

• Established a comprehensive simulation model for predicting the width of extrusion-based 3D printed Herschel-Bulkley filaments, validated experimentally. • The study analyzed the morphology, pressure–velocity field distribution, and contact line dynamics of filament formation in simulations to elucidated the influence of inertia, gravity, and surface tension on filament formation mechanism during printing. • High non-Newtonian Reynolds numbers during hydrogel ink extrusion cause “over-spreading” near the nozzle, with filaments gradually transitioning to equilibrium under surface tension and yield stress. • Bond values indicate the effect of gravity: higher values result in finer filaments printed upwards and coarser filaments printed downwards. • Surface tension and rheological characteristics govern filament width in low-speed, small-scale printing, with shear-thinning fluids’ outcomes dependent on K and τ y . Currently, all popular 3D printing inks exhibit Herschel-Bulkley (HB) fluid characteristics. However, the filament spreading, which reduces printing precision, decelerates the development of complex hydrogel models for engineered tissues or organs. In this study, a finite element model (FEM) is established to investigate the impact of processing and fluid parameters on the spreading of the HB inks. The non-dimensional numbers Re (ratio of inertia to viscosity) and Bo (ratio of gravity to surface tension) are used to analyze the influence of parameters on filament formation. When Re > 0.077 and Bo > 0.15, inertial and gravitational forces significantly alter the pressure gradient near the nozzle, thereby affecting the final spreading width of the filament. Additionally, when the spreading is dominated by surface tension, the ranges of rheological parameters of materials as well as the process parameters in 3D printing can be determined by Re and Bo . Under this parameter range, the error between predicted filament widths and that of the printed filament can be controlled to less than 6.7 %. The spreading of HB inks during printing is accurately predicted.