## 3 Results and Discussion
### The Instabilities of Inkjet-Printed Lines
The requisite for the bulging instability is that liquids should have a zero \(\theta_{\text{r}}\) and an initial CA (\(\theta_{\text{i}}\)) larger than \(\theta_{\text{a}}\). Generally a colloidal suspension containing small-sized particles is said  
Figure 5: Microscopic images of inkjet-printed lines with 200 Hz printing frequency for various types of substrates and droplet overlaps at room temperature when using continuous printing procedure. to have a zero \(\theta_{\rm r}\) because its contact line can advance but can't retreat due to the contact line pinning by particle deposition during solvent evaporation. For that reason, ink on a substrate spreads until the \(\theta_{\rm i}\) decreases down to the \(\theta_{\rm a}\) due to capillary force, forming an outward-moving contact line. Going back to Figures 5 and 6 with the above explanation, the inkjet lines on \(S\) 30 substrate do not wet the substrate surface, breaking up into separate circular droplets and forming inward-moving contact lines. It occurs because the ink has both the \(\theta_{\rm i}\) and the non-zero \(\theta_{\rm r}\), which are close to \(\theta_{\rm a}\). However, the ink on \(S\) 50 to \(S\) 70 substrates was initially expected to have a zero \(\theta_{\rm r}\) and the \(\theta_{\rm i}\) larger than \(\theta_{\rm a}\), since the substrates yielded the liquid lines with a series of bulges. However the ridges observed from the lines have a smaller width than a single droplet diameter because of the liquid dewetting (Figure 7). It indicates that the Ag colloidal ink on the substrates had a non-zero \(\theta_{\rm r}\) at the initial stage of the line formation, and the non-zero \(\theta_{\rm r}\) resulted in bulge formation. This shows that bulging phenomenon can occur even with a non-zero \(\theta_{\rm r}\) for a relatively long time until the contact line is pinned and the \(\theta_{\rm r}\) becomes zero. It caused the inconsistency of bulge formation process with the previous researches, like confirmed in Figures 5 and 6. Figure 8 shows the growth of bulges and ridges on \(S\) 50 substrate with the number of printed droplets (\(n\)). The experiment was performed by providing ink droplets toward right direction with 40% droplet overlap at room temperature. First, note that all cases in the figure are the results obtained from separate printings. The end of a liquid line, where ink droplets are deposited, moves continuously toward right side as \(n\) increases. This brings a different end effect in each printed line. When \(n\leq 3\)  
Figure 6: Microscopic images of inkjet-printed lines on the \(S\) 50 substrate for various printing frequencies and droplet overlaps at room temperature. Figure 7: Variation of ridge width according to substrate types and droplet overlaps at room temperature. the second and third droplets retreat from their initial landing positions toward the first droplet site, immediately after the deposition. Then, they form the liquid pattern in a large elliptical dome shape, minimizing their surface energy. Here the first bulge is initiated. Next, the ridge of the liquid pattern starts to pull out from when depositing the fourth droplet (\(n=4\)). The length of the ridge increases steadily till printing the fourteenth droplet on the substrate. At the same time with the growth of the ridge, the first bulge also develops with \(n\) until reaching the equilibrium width determined by \(\theta_{\mathrm{a}}\). The primary cause of the bulge growth is in pressure-driven fluid transport between the bulged front and the end of the narrow liquid line. The amount of the fluid delivered to the bulge through the ridge decreases as the length of the liquid line increases by printing, because the pressure difference between the two approaches to zero gradually. However after the routine landing of the droplets, fluidic disturbance arises due to the large curvature which is made at the end of the line and which in turn leads to the creation of a second bulge.