## 3 Results and Discussion
### Arrayed Nozzle Print Model  
As discussed in Section 3.1, the diameter and velocity of the droplet leaving the nozzle can be controlled in the experiment. Based on the results in Section 3.2, the spreading radius of the droplet can be calculated based on the controlled size of the droplet. In the following subsection, we will be able to calculate the droplet size required by an arbitrary jetting process based on the geometric model.  
As shown in Figure 8a,b, gaps will form between the neighboring droplets if all the injected droplets have the same sizes. In this case, the droplets will not be able to connect with each other. Figure 8c below shows the printing model calculated based on a simple geometric model. As shown in the figure, as the distance between the nozzle and the substrate increases, the larger the droplet size is required to ensure that all the droplets are connected to each other must increase.  
To quantify this defect, we used profilometer measurements to demonstrate the existence of the problem. As shown in Figure 9a below, owing to the large distance between the droplets, when the droplets are not fully fused, the heating of the substrate will lead to the evaporation of the solvent of the ink. Thus, only the solid silver nanoparticle residue will remain. Therefore, this will cause the antenna resistance to become higher (or will lead to a lower conductivity) that will ultimately affect the performance of the antenna. Figure 9b shows the outcomes in the case at which the droplets are completely fused.  
Using a nozzle number of \(N_{count}=394\) and a spacing of \(\text{L}_{Stap}=0.0854\) mm in the arrayed nozzle, the printing condition on a quarter of a circle can be calculated theoretically, as shown in the figure below. Based on experimental measurements, the droplets will be affected by the airflow and the air drift when the fall height \(h\) becomes greater than 3.5 mm. Based on the experiment, when the jetting distance \(h\) is greater than 3.5 mm, the droplets will not float to the predetermined substrate position owing to airflow, as shown in Figure 10b below. The smaller the kinetic energy, the more significant will be the effects of the external airflow.  
Figure 7: (**a**) The printing process from the arrayed nozzle recorded by the camera; (**b**) droplets deposited on the substrate; and (**c**) theoretical calculation and actual measurement results.  
Figure 8: Simplified model for printing on the conformal surface using the arrayed nozzle: (**a**) formation of gaps between neighboring droplets during the printing process from the arrayed nozzle when all droplets share the same size; (**b**) droplet size calculated based on the geometric model; and (**c**) the printing model proposed in this study. (**d**) Actual effect of direct printing on the surface; and (**e**) actual effects of printing with the method proposed in this article.  
Figure 10: (**a**) Theoretical calculation model on a quarter of a circle with a radius of \(N_{\text{court}}\)+\(L_{\text{Stip}}\).(**b**) When the ejection distance is greater than 3.4 mm, it will be disturbed by the airflow, which will cause the droplets to fall on the substrate incorrectly. N\({}_{\text{count}}\), nozzle number; L\({}_{\text{Stip}}\), spacing.  
Figure 9: Difference between the defect phenomenon measured by the profilometer and uniform printing. (**a**) Drawback measured by the step instrument. (**b**) Results generated in the case in which the droplets are uniformly fused.  
The theoretical model shown in Figure 10a was obtained. In this theoretical model, the maximum droplet radius required was 1.15 mm. This radius cannot be achieved by the spreading of a single droplet. Based on the previous model, the maximum spreading radius was calculated to be 80 \(\upmu\)m. In this case, the minimum fall height is 3.4 mm. Therefore, the maximum boundary conditions are calculated to be the maximum spreading radius of 80 \(\upmu\)m and the maximum fall height of 3.4 mm.