## 3 Results
### Analytical Modelling
The contact angle affects the slope of the border between stacked ink lines (Figure 6a), which may affect the flatness of the ink layer before leveling to a plane. However, the printed ink layer only keeps ripple morphology as a processing intermediated state and will tend to flat-plane induced by the leveling. The final flatness after curing is mainly dominated by the evaporation gradient from the interfaces among the adjacent lines into the inner of the lines. In order to reduce the ripples to improve the flatness, we established a model to quantify the relationship for the ripple height with the crucial parameter of line spacing. Using this model, the optimization processing parameters for high flatness printing can be directly determined. In order to simplify the model, some assumptions are put forward according to the observation based on tests: (i) the ink layer is fully leveled before curing; (ii) the lateral dimension of the ink layer will not change after curing; (iii) the angle \(\alpha\) between the circular arc and the vertical line passing through the highest point of the stripe is a constant value; (iv) the solid loading of the ink is not taken into account. Figure 4: Schematic diagram of the process for printing an ink layer using DIW technology. During the printing process, the nozzle moves laterally at a velocity of \(v_{n}\) at a height \(h_{tt}\) from the substrate, while the ink is extruded from the nozzle to print multiple ink lines in parallel with a spacing of \(l_{s}\). These ink lines merge through self-leveling, forming a flat surface. When printing a single ink line, a line with a width of \(l\) and a contact angle of \(\theta\) is formed due to the self-leveling properties. Experimental results have shown that the geometric shape of the stripes formed after ink curing varies slightly with the spacing \(l_{s}\) between ink lines on the printing plane. As shown in Figure 6b, when \(l_{s}\) is less than or equal to a certain value \(l_{s0}\), the vertical cross-sectional profile of the ink-cured surface can be approximated by multiple circular arcs. Figure 5: (**a**) Optical image of the layer surface before curing. (**b**) White light interference image of the layer surface before curing. (**c**) the corresponding cross-sectional profiles of (**b**). (**d**) Optical image of the layer surface after curing. (**e**) White light interference image of the layer surface after curing. (**f**) the corresponding cross-sectional profiles of (**e**). Figure 6: (**a**) Curing process of layer surface after printing. After printing the layer surface, the ink will flatten into a relatively smooth surface. Upon curing, the layer surface will exhibit aligned ripples. (**b**) Schematic diagram of the layer surface geometry model when \(l_{s}\) is less than \(l_{s0}\). (**c**) Schematic diagram of the layer surface geometry model when \(l_{s}\) is greater than \(l_{s0}\). Assuming that the angle \(\alpha\) between the circular arc and the vertical line passing through the highest point of the stripe is a constant value, we can establish a model to describe the profile of the ink-cured surface:  
\[y=r_{c}-\sqrt{r_{c}^{2}-(x-kl_{s})^{2}},-\frac{l_{s}}{2}+kl_{s}<x<\frac{l_{s}}{2} +kl_{s},k=0,\pm 1,\pm 2,\ldots, \tag{1}\]  
where \((x,y)\) are the cartesian coordinate points, representing the cross-sectional profile of the ink layer. The symbol \(k\) represents the number for \(k\)th strip; \(r_{c}=l_{s}/2\)cosat is the radius of the arc. As shown in Figure 6c, when the distance between ink lines on the printing surface \(l_{s}\) is greater than a certain value \(l_{s0}\), the height of the striped protrusions no longer changes, and the radius of the arc \(r_{c}\) also remains unchanged. There is a relatively flat contour between the striped protrusions. Therefore, we can represent the contour model as:  
\[y=\left\{