Modeling of the high-viscosity fluid transient flow for material deposition in direct ink writing

Abstract

A transient flow model is developed to predict the flow of high-viscosity fluid dispensing for precision direct ink writing (DIW) in additive manufacturing. Models for pump deformation and fluid friction to accurately predict flow of a high-viscosity non-Newtonian fluid through a progressive cavity pump, static mixer, and a tapered nozzle are created. Inside the progressive cavity pump, the effect of elastic deformation on modeling high-viscosity fluid transient flow is included. Based on the Characteristic Method (CM) and boundary conditions for DIW, the continuity and momentum equations are numerically solved. Using deformation modeling and CM, the transient response of the DIW system to the input volumetric flow rate is modeled for both a pipe and static mixer. The transient response of the DIW output volumetric flow rate is recorded using flow and pressure sensors and found to match the flow model. The deformation and CM models are applied to predict the swelling of a 90° corner DIW tool path from trapezoidal motion planning with accelerations from 100 to 2000 mm/s². Predicted corner swelling is matched with the actual corner swelling via image processing of the 90° corner. The corner swelling is significant, ranging from 0.76 to 0.37 mm for a line width of 0.25 mm and a height of 0.15 mm, and represents the model’s ability to quantify print errors. This study demonstrates that the flow model can accurately predict the transient response of the DIW volumetric flow rate, which is foundational to high-fidelity flow control and compensation in precision DIW.