Exploiting nozzle geometry to predict resolution in extrusion-based bioprinting: mathematical modelling of a power-law fluid

Extrusion-based additive manufacturing is a popular technique used in the fabrication of three-dimensional constructs. Owing to the non-linear manner in which process parameters impact resolution and printability, the optimal combination remains platform- and material-specific. This study proposes a user-friendly, adaptable model to predict the diameter of a printed line of material through extrusion-based bioprinting. Exploiting the geometry of an arbitrary, axisymmetric nozzle, and assuming a power-law fluid, the model generated determines a relationship between the printed filament diameter and the pressure drop, nozzle travel speed, nozzle geometry, and material flow properties. Employing the model prior to printing enables engineers to restrict process parameter space and minimise the dependence on the current print-and-test methodology before an optimal combination of process parameters is determined. Two materials (a poly(vinyl alcohol)-based hydrogel and Nivea Crème), two temperature conditions, and three nozzle sizes were used for model validation, presenting good agreement with model predictions. When the shear-thinning property is included, R2 > 0.97. This model provides context and direction for future optimisation-driven design research for this advancing manufacturing technology.