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

## TL;DR

This paper presents a mathematical model to predict the resolution of extrusion-based bioprinting by considering nozzle geometry and material properties.

## Contribution

The novelty lies in the development of a user-friendly model that predicts printed filament diameter using nozzle geometry and fluid properties.

## Key findings

- The model accurately predicts filament diameter with an R2 value greater than 0.97 when shear-thinning is considered.
- The model was validated using two materials, three nozzle sizes, and two temperature conditions.
- The model helps reduce reliance on trial-and-error methods by narrowing down optimal process parameters.

## Abstract

Extrusion-based additive manufacturing (AM) is a popular technique used in the fabrication of three-dimensional constructs. Owing to the nonlinear manner in which process parameters affect 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 minimize 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 (PVA-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, the coefficient of determination, R2, is greater than 0.97. This model provides context and direction for future optimization-driven design research for this advancing manufacturing technology.