Theoretical analysis, numerical simulation and experimental validation on the side-by-side multi-material simultaneous 3D printing process

Side-by-side multi-material simultaneous 3D printing via direct ink writing (DIW) can efficiently fabricate integrated functional devices by depositing multiple inks simultaneously. However, achieving flow simultaneity of multiple inks with different rheological properties remains a critical challenge. This study conducts theoretical analysis, numerical simulations, and experimental validation to address this issue. The flow behavior of printable inks conforming to the Herschel-Bulkley model in circular micro-channels is theoretically analyzed, and analytical solutions for flow rate and velocity are derived. One-At-a-Time (OAT) and Sobol' sensitivity analyses are conducted to examine the individual and interactive effects of rheological parameters and pressure gradient on the flow rate. It is revealed that it is viable to realize the flow simultaneity of inks with different rheological parameters by regulating the pressure gradient. Computational fluid dynamics (CFD) and experimental observations are performed to investigate the flow simultaneity of side-by-side multi-material simultaneous 3D printing process, and optimal pressure gradients are determined. Finally, experimental validation is conducted using dielectric elastomer and electrode inks to fabricate various complex multi-material patterns on both planar and curved substrates. Results show that simultaneous flow of multiple inks can be achieved to obtain multi-material structures with excellent structural integrity and filament continuity. This study provides comprehensive guidance for coordinating flow rates of inks with different rheological properties to realize flow simultaneity and obtain high-quality multi-material structures.