# Simulations of Extrusion 3D Printing of Chitosan Hydrogels
## 4 Results and Discussion
### Chitosan-Based Ink Characterization in 3D Printing Modeling
Thus, the densities of ink were set to 960.0 [kg/m\({}^{3}\)], and the dynamic viscosities of ink were equal to 25 [Pa-s]. The surface tension coefficient was 0.7 [N/m]. Furthermore, the variables used to demonstrate the velocity and viscosity were similar to those of the experimental test. Figure 6 demonstrates the velocity magnitude and volume fraction of ink in the 3D printing model. The velocity increases from inside to outside the filament formation of ink (as shown in stages 5--7), where the volume fraction and velocity of the fluid are similar to those obtained via experimental printing. Figure 4: Influence of the viscosity on the behavior of the extruding hydrogel ink; (**A**) Constant viscosity = 1 Pa-s; (**B**) Constant viscosity 15 Pa-s; (**C**) Constant viscosity = 25 Pa-s; (**D**) Shear rate-dependent viscosity. The simulation results show the filament formation and the ink extrusion shape in Figure 7 for different velocity parameters. Figure 7 presents the whole generation process, including the filament formation process of the 3D printing model. Figure 7A, step (1) presents the start of the filament formation process. At this stage, the dispersed phase (ink) completely enters the nozzle channel and begins to squeeze out of it. When the ink is squeezed out of the nozzle channel, the filament's size increases, the ink pushes itself into the main channel, and the pressure decreases. In the second step of the filament formation process (cf. Figure 7), the filament is elongated, and the size also increases. When the pressure reaches its maximum value, a filament is formed, and the pressure returns to a small value. Generally, surface tension and viscosity dominate the filament formation process dynamics. In Figure 7, step (3), no droplet formation occurs. However, the ink flows are in air phase distance, representing the filament formation and die swelling after extrusion from the nozzle. Figure 7 at stages 1 to 3 shows the step by step generation of the filament. Figure 5: (**A**) Illustrated is the volume fraction and viscosity during chitosan 3D printing; (**B**) description of the mass fluid ink during simulation of chitosan 3D printing. Figure 6: Filament formation in extrusion chitosan 3D printing device with the COMSOL software. The variations in the filament length are presented in Figure 7A-C; the ink's flow rate (velocity) is changed to another constant parameter when the filament length is short. The figures illustrate a gradual increase in the ink's velocity rate that changes the filament's length. The general conclusion is that the filament length increases at a corresponding scale. Furthermore, when the velocity of ink is increased from 5 [m/s] to 10 [m/s], it can be inferred from Figure 7, Step 3, that ink can easily be formed after extruding from the nozzle, showing the filament deposition shape properly. The distance between the nozzle and filament formation is important in 3D printing. We kept this distance constant in the simulation design, as shown in Supplementary Information SI1, owing to the crosslink characteristics of novel chitosan ink. The novel chitosan inks should be printed in deionized hot water for better crosslink. However, the preparation of this environment in COMSOL Multiphysics is not feasible. Therefore, the distance between the nozzle and filament formation was 2 cm. The formation of hydrogel extrusion in the 3D printing technique is presented. Simulations were conducted using the two-phase level set method; the ink flow from the nozzle was regulated by controlling the velocity during simulation. Thus, the velocity magnitude of the numerical simulations is demonstrated in Figure 8. The findings revealed that the size of the filaments was determined based on counting the pixels using the COMSOL software (Hangzhou, China). Figure 8 presents the surface of the velocity magnitude. The effect of the velocity on the shape of the extruded is determined from 0 m/s to 1.6 m/s.