## 3 Results and Discussion
### Error Analysis of the Predicted Line Width and the Experimental Results  
Based on the rheological properties of the paste measured in Section 2.3, the values of the parameters in Equation (9) in Section 3.3 could be determined, and the flow coefficient of the conductive paste \(n\) was set to 0.6184 and the consistency coefficient \(K\) was set to 49.46. In this paper, the nozzle was chosen to be \(r_{2}=28\) um and \(r_{1}=300\) um, and the length \(l\) was taken as the vertical distance of 3.55 mm at the front end of the glass nozzle with the largest pressure gradient change in the tapered part, which was measured by the step meter. The height to width ratio was measured to be approximately 0.4868, while the feed pressure gradient and speed gradient were set to the same as those of the single-factor experiment. The actual feed pressure calculation value is shown in Appendix B, Figure 10. By introducing these parameters, the theoretical values of the mathematical model of the line width of the extrusion process could be obtained, and the calculated results were compared with the experimental results, as shown in Figure 8.  
The proportion of error in the experimental data was calculated by the following formula:  
\[p=\frac{T_{i}-M_{i}}{M_{i}} \tag{10}\]  
where \(M_{i}\) is the measured value at the substrate moving speed \(v_{i}\), \(T_{i}\) is the theoretical value at the same speed, and p represents the total proportion of error between \(M_{i}\) and \(T_{i}\) relative to the measured value. It could be calculated from Equation (9) that under the condition of feed pressure, the theoretical line width change value decreased with the increase in substrate moving speed. The line width difference decreased at 0.6 MPa from 3.18 um between 100 mm/s and 110 mm/s to 1.95 um between 140 mm/s and 150 mm/s. Although there were some fluctuations in the experimental data changes due to the experimental conditions and other factors, the overall trend was also in line with the maximum drop from 4.07 um to 1.62 um. It was speculated that the reason for the decrease in the line width change value at high speed was the complexity of the paste, and so the outlet flow rate of the paste  
Figure 8: (**a**) Comparison of the experimental and theoretical results. (**b**) Error variation between the theoretical and experimental values. could be regarded as basically unchanged when the feed pressure was constant, and as the substrate moved faster, the speed difference between the two gradually increased. The closer it came to its tensile limit, the more the stretch ability was reduced. The variation range of the line width in the actual experiment was larger than the theoretical value. It was speculated that when the feed pressure increased, the flow rate per unit time at the outlet also increased accordingly, and more paste would be forced to extrude, with the resulting pressure loss being more obvious than the pressure loss when the pressure was low. The result was that the theoretical value of the line width under high pressure was larger than the measured value. When the feed pressure increased to 0.65 MPa and 0.7 MPa, the theoretical difference in the line width under the same speed difference changed from 3.43 \(\upmu\)m to 2.12 \(\upmu\)m and from 3.69 \(\upmu\)m to 2.28 \(\upmu\)m, respectively, and the experimental difference changed from 3.16 \(\upmu\)m to 0.87 \(\upmu\)m and from 2.93 \(\upmu\)m to 2.61 \(\upmu\)m, respectively. The theoretical value showed a slight upward trend with the increase in feed pressure, while the experimental value decreased slightly. The shear stress of the paste at the outlet from the moving direction of the substrate increased, which reduced the viscosity of the paste. The result was that the line width under actual measurement was slightly larger than the theoretical value, and this was more obvious at faster speeds. It can be seen in Figure 8b that the overall error range between the measured value and the theoretically calculated value was within 5%.