## 2 Materials and Methods
### Extrusion Process Theory and Simulation Model of Printing Process
#### 2.3.2 Extrusion Process Simulation Model  
The scaffold printing process was simulated and analyzed by using Fluent, and the relationships among the variables in the model were explored. The flow coefficient \(n\) of the composite solution was set to 0.5 and the consistency coefficient \(K\) was set to 18.5. In this paper, needles \(r_{2}\) of 2.5 mm, and \(r_{0}\) of 0.2 mm and the length L is 30 mm, were selected. \(\theta\) was nearly 4 degrees, and the slip layer thickness approximated 9.9 \(\upmu\)m, and \(K_{\text{cf}}\) was set to 0.8. By introducing these parameters, the simulation model of extrusion process could be constructed, as shown in Figure 4.  
Pressure and platform movement speed are also important factors which affect the line width of the printing material. At the same time, air pressure also determines the flow of extruded gel, so the pressure and velocity were selected as variables to explore its effect on line width. In order to obtain different extrusion flow rates, 1.2 bar, 1.5 bar, 1.8 bar, 2.1 bar and 2.4 bar were selected as pressure variables to compare the line width of the needle in the range of 0-20 mm/s. As shown in Figure 5, as the pressure and movement increased, the line width narrowed quickly. When the pressure  
Figure 4: The extrusion process simulation model. (**a**) flow velocity distribution simulation; (**b**) different expansion under different pressure conditions.  
increased to above 2.4 bar and the movement speed increased to above 20 mm/s, the line width became stable. From the dotted line of 0.4 mm red contour line in Figure 5, it can be seen that the needle moving speed of the optimum linewidth (the same linewidth as the inner diameter of the conical needle outlet) was different under different pressure variables, which were 4.77 mm/s, 7.45 mm/s, 10.73 mm/s, 14.6 mm/s and 19.08 mm/s, respectively, which were all higher than the extrusion flow velocity under their respective pressures and conformed to the mathematical model of the linewidth prediction. When printing, the speed could be set to the needle speed corresponding to different pressure variables to obtain the optimal linewidth. Under the same pressure variable, too fast and too slow needle movement would lead to problems such as stretching and material accumulation, which would seriously affect the accuracy and formability of extrusion lines. To sum up, it was more appropriate to choose the needle moving speed between 10 and 16 mm/s by linear width mathematical model (13).  
For extrusion lines with the same line width, the porosity of scaffolds varied with different fiber spacing. Setting the fiber interval in the range of 0.4-4 mm, other variables are maintained unchanged to simulate the printing conditions and parameters. Using a conical needle with an outlet diameter of 0.4 mm and setting the pressure of 1.8 bar and the needle speed of 10.7 mm/s, the relationship between the porosity of the scaffold and the fiber interval was obtained, as shown in Figure 6.  
As shown in Figure 6, the larger the fiber spacing, the larger the porosity of the scaffold. When the fiber interval was less than 0.4 mm, the porosity of the scaffold was zero or even negative, and the scaffold accumulation was serious. In addition, when the interval was small, a slight change made the size of the scaffold porosity fluctuate greatly. When the interval was set to 1 mm, the porosity was about 60%. When the porosity interval needed to be greater than 60%, it needed to be greater than 1 mm. According to the requirement of cell growth on scaffold pore; the interval can be between 1-1.5 mm.  
Figure 5: The line width with different nozzle moving in different pressures and moving speeds.