*3.2. Observation of Coating Film Formation Process*

In the above section, we focused on one droplet, but in the following, we observe a wider range of coating films using fluorescence. Figure 9 shows a fluorescence image of a painted surface, taken under conditions of injection pressure, *P*in = 0.2 MPa, and paint viscosity, *μ* = 0.033 Pa·s. The area where the paint adheres becomes green, the adhesion area increases with time, and the overall fluorescence intensity increases. The red solid line shown in the image at *t* = 0.2 s represents the measurement position of the cross-sectional fluorescence intensity.

**Figure 9.** Fluorescence image of spray coating.

In the past, the authors changed the injection pressure *P*in to arbitrary values and examined the time change in the area and overlap ratios [12]. In the time change graph of the area and overlap ratios when changing the injection pressure, the increase ratio of the area ratio grows with the increase in the injection pressure. The higher the injection pressure, the shorter the time until *α*(*t*) = 100%. This was due to the increase in the paint flow rate per unit of time caused by the increase in injection pressure. The area ratio *α*(*t*) increases immediately after adhesion for any injection pressure, but increases gradually from around 50%. This was caused by the fact that the paint overlapped and began to adhere. The overlap ratio, *β*(*t*), shows a value close to 0, because there was almost no overlap of droplets at the beginning of the paint adhesion. However, it increased with time. In addition, the overlap ratio in the time (*t* = *T*100) it took for area ratio to reach 100%, with an injection pressure of *P*in = 0.2, 0.3, and 0.4 MPa, was about 200%, 300%, and 350%, respectively. It was found that the paint, which was about 2.3 to 2.8 times the measurement range, had adhered prior to the film formation.

Figure 10 shows the cross-sectional film thickness distribution at each stage, in the case of injection pressure *P*in = 0.2 MPa and viscosity *μ* = 0.033 Pa·s. The cross-sectional coatingthickness distribution was obtained by measuring the fluorescence intensity distribution on the line shown by the red solid line in Figure 9 and calculating the distribution of thickness from the calibration data of the fluorescence intensity and the coating thickness. It can be seen that the variation in coating thickness decreases with time and that a uniform and thick coating is formed. Thus, the temporal change in the coating film thickness can be examined from the distribution of fluorescence intensity.

Figure 11 shows the temporal change in the coating thickness under the conditions of *P*in = 0.2 MPa and *μ* = 0.033 Pa·s. The coating film thickness increased from the start of the spray coating. At the end of the spray coating (*t* = *T*fin), the change in the coating thickness became flat.

## *3.3. Evaluation of Coating Surface Smoothness and Leveling Process*

Leveling phenomena in the spray coating process were analyzed using the intensity distribution of the fluorescence image. To evaluate the surface smoothness, a histogram, or frequency distribution, of the tone values of the fluorescence image was produced. Figure 12 shows the histograms produced under the conditions of injection pressure *P*in = 0.2 MPa and paint viscosity *μ* = 0.033 Pa·s. The horizontal axis of Figure 12 indicates the tone values of fluorescence intensity, which was changed from 0 to 256. The vertical axis indicates the probability density.

**Figure 10.** Fluorescence intensity distribution on a line graph.

**Figure 11.** Evolution of the coating thickness over time.

**Figure 12.** Fluorescence intensity distribution.

At the first stage of spray coating, the histogram has a wide range distribution. This result shows that fluorescence intensities have various tone values because the paint droplets adhered to the coating surface individually. The distribution becomes gradually narrower with an increase in the coating time, *t*. At the final stage, the distribution settles into a monodispersed shape. This means that the coating surface became flat. As described here, leveling phenomena can evaluate the width of the histogram. In this study, the standard deviation, *σ* [-], was used for estimating the coating surface smoothness.

The center of the distribution, *I*M, is shifted to the higher intensity side. This result shows that the average thickness of the coating film increased with the change in distribution shape. Therefore, the change in the average thickness of the coating film can be evaluated using the position of the center value.

The standard deviation of the intensity distribution in the histogram was investigated. Figure 13 shows the temporal change in the standard deviation. As shown in Figure 11, the standard deviation increased after the start of the spray-droplet adhesion (part of (A) in Figure 13) and decreased in part (B) of Figure 13. In this part, the leveling phenomena between adherent droplets occurred via their coalescence. *T*<sup>100</sup> indicates a point in time when the entire surface was covered by paint droplets. At the end of part (B), the coating surface became flat by the finish of leveling. However, in part (C), the standard deviation increased because the paint droplets overlapped on the coating surface. At the final stage of spray coating (in part (D)), the standard deviation decreased, gradually, with the progress of the leveling. In the figure, *T*fin indicates the stop time of spray coating. As described above, the average thickness and smoothness of the coating film could be easily estimated using the fluorescence method. In particular, it was clearly shown that the standard deviation data from the fluorescence intensity distribution provided important information about the smoothness of the coating surface.

**Figure 13.** Standard deviation.

#### *3.4. Influence of Injection Pressure and Paint Viscosity on Film Formation*

Figure 14 shows the average thickness of the coating film, *h* [mm], under various amounts of injection pressure *P*in. The *P*in was changed from 0.1 to 0.5. It can be seen that the coating thickness increased uniformly until the end of injection, *t* = *T*fin. The film thickness of *P*in = 0.2 MPa was thicker than that of *P*in = 0.1 MPa, because the injection flow rate of the former was greater than that of the latter.

In the case of *P*in = 0.5 MPa, a thinner thickness value was maintained, even though the spray coating was sustained. The reason for this characteristic can be explained with reference to the airflow effect. In this study, the two-fluid atomizer was used for the spray formation. Therefore, strong airflow was generated at the coating surface under the high injection pressure condition. When atomized paint is stuck to the paint surface, paint flow is caused by the impact of adhesion and the contact of paint droplets. This flow affected the coating film formation and the quality of the paint surface. In this study, paint flow on the coating surface was visualized using the tracer particles in the paint.

**Figure 14.** Coating film thickness under various injection pressures *P*in.

The first point where paint adhesion was defined as the origin (*X*0, *Y*0) = (0, 0). The length of the particle trajectory, *L*p, and the absolute displacement, *L*d, were measured under several experimental conditions. Figure 15 shows a schematic image of *L*p (the black line) and *L*<sup>d</sup> (the dashed line). *L*<sup>p</sup> is the total distance the particle moved, and *L*<sup>d</sup> is the linear distance from the original point to the end point after being moved by the flow. It was predicted that the flow would show random movement caused by the paint impact and leveling. Therefore, it was expected that *L*<sup>p</sup> and *L*<sup>d</sup> would become different values. If these values indicated almost the same number, then the flow caused by other forces would be generated. In our experiments, the time evolution of *L*<sup>p</sup> and *L*<sup>d</sup> was measured.

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**Figure 15.** Definition of *L*<sup>p</sup> and *L*d.

Figure 16, Figure 17, Figure 18 show the time evolution of the absolute displacement, *L*d, using paint with a viscosity of *μ* = 0.023 Pa·s and an injection pressure of *P*in = 0.1, 0.2, and 0.5 Pa, respectively. The horizontal axis represents the injection time, *t* s, and the vertical axis represents *L*d. The point in time when the droplet starts to adhere is *t* = 0. Each plotline corresponds to one tracer particle.

As shown in Figure 16, the *L*<sup>d</sup> of most droplets that adhered at a relatively early time became 100–150 μm, and, after that, *L*<sup>d</sup> was maintained or decreased. This indicates the flow when the droplets that initially adhered began to coalesce to form a coating film. The paint droplet that first adhered to the surface did not move much. However, it moved when the droplet coalesced with other droplets.

**Figure 16.** Time evolution of *L*<sup>d</sup> with injection pressure of *P*in = 0.1 Pa.

**Figure 17.** Time evolution of *L*<sup>d</sup> with injection pressure of *P*in = 0.2 Pa.

**Figure 18.** Time evolution of *L*<sup>d</sup> with injection pressure of *P*in = 0.5 Pa.

However, the *L*<sup>d</sup> of the droplet that adhered after *t* = 1.5 s increased steadily until *t* = *T*fin. In addition, the *L*<sup>d</sup> of some droplets that initially adhered increased to around *t* = 1.0 s, although the rate of increase was lower than that of the droplets that adhered later. These are the effects of the flow in the coating film. The *L*<sup>d</sup> of the droplets that adhered later increased at the same rate, and a uniform flow occurred on the surface of the entire area.

The fastest flow was generated on the surface of the coating film because the droplets that adhered later had a higher rate of increase of *L*d. In addition, the particles that initially adhered were closer to the wall surface than the particles that adhered later. Therefore, the particles moved at a lower velocity than the surface velocity. Some of the droplets that adhered at the initial stage, whose *L*<sup>d</sup> had a low rate of increase from around *t* = 1.0 s, were caused by this movement.

As shown in Figure 17, the *L*<sup>d</sup> of all the droplets increased steadily until *t* = *T*fin. However, there was a difference in the rate of increase of *L*d. The droplets that adhered later showed a higher rate of increase, and it was confirmed that the particles moved to a point away from the initial position—above *L*<sup>d</sup> = 1200 μm. In accordance with this, a flow faster than *P*in = 0.1 Pa was expected to occur. In addition, the slow flow was generated near the wall because the *L*<sup>d</sup> of all particles increased, regardless of the time of adherence. The initially deposited paint was replaced by the latterly deposited paint as a result of this slow flow.

As shown in Figure 18, the *L*<sup>d</sup> of all the droplets increased at the same rate. Therefore, the *L*<sup>d</sup> of the droplets that initially adhered became larger than that of the droplets that adhered later. According to this result, a uniform flow was generated in the coating film. Even near the wall, the flow moved at the same velocity as the paint on the surface, if it was outside the boundary layer. Moreover, in this case, the replacement of the paint that adhered in the initial stage was performed more actively. The above results suggest that under the condition of a paint viscosity of *μ* = 0.023 Pa·s, a flow occurs in the coating film, and the higher the injection pressure, the greater the replacement of the paint that initially adheres to it. Therefore, we consider that the coating film flowed out of the observation range before it hardened, and the coating thickness did not increase. In addition, we consider this to be because the average film thickness does not increase under the conditions of *μ* = 0.023 Pa·s and *P*in = 0.5 MPa, as shown in Figure 14.
