6. Applications

Approximately 400 billion two-piece, all-aluminum cans are produced annually for the purpose of storing beverages for distribution worldwide. The interior of each of these cans must be coated to protect the aluminum from onslaught due to corrosive elements in the contained beverage, and the beverage must be protected from picking up metal ions or other off-flavors from the aluminum substrate. Consequently the coating must be as uniform as possible for thick regions may slough off and thin regions may not offer adequate protection. To achieve a uniform film thickness, spin coating is employed using a spray fan to distribute the coating on the can substrate. But because the can is highly curved due to structural considerations, achieving a uniform final film thickness is much more complicated than for a flat substrate. In this section we will apply the analytical and numerical model we developed in previous sections to determine how the many parameters are influencing the flow of the paint coating. These parameters include the rotation rate, the shape of the can, the coating fluids physiochemical properties, and the geometry and flux of the spray fan, all affecting the final film thickness distribution.

The can body is initially punched from sheet aluminum and then goes through a washing process to produce a substrate suited for the spray coating. The can is then spun at between 2500 and 3500 rotations per minute, and one or two spray guns spray the interior with the liquid paint film. Centrifugal and gravitational forces redistribute this liquid layer as the can continues to spin after the initial spray process. The can is then placed in an oven where the solvent is allowed to evaporate leaving only the hardened resin. Then the can is filled with the beverage and the top of the can is attached in place. This conveyer process can produce as many as 1700 filled cans per minute.

In practice, one or two spray guns are used to coat the interior of the spinning cans. These are oriented at between 5° and 30° with respect to the vertical axis of the can and placed between 0.5 and 1.5 cm vertically from the top of the sidewall [6, 7]. Typically the can is sprayed for between 0.05 and 0.2 s and spun for an additional 0.1–0.5 s [6] so that centrifugal forces can act to redistribute the coating layer.

The industry uses schematic drawings which plot the substrate as a function of circular arcs of radius Ri, and subtended angles φi, as shown in Figure 2. Consequently the slope is always continuous, but there is a discontinuity in the radius of curvature between adjacent segments. Figure 6 shows a profile view of a typical can bottom, as well as a possible coating distribution, during the course of the fast spin with spray phase of the coating process. The functions κð Þs , θð Þs , and r sð Þ were derived from a published schematic drawing of a typical beverage can from a can manufacturer [8]. We define the "dome" of the can as the region from the centerline to the first inflection point, as labeled by the symbol A. The "moat" is defined as the region from A to D, with the inner moat defined as the region from A to B, and

Numerical Simulation of the Spin Coating of the Interior of Metal Beverage Cans DOI: http://dx.doi.org/10.5772/intechopen.90381

#### Figure 6.

Profile of the can substrate in red lines and the coating layer in blue lines at ^<sup>t</sup> <sup>¼</sup> :10, in the middle of fast spin with spray phase. Dimensionless variables are used.

#### Figure 7.

Profile of the can substrate in red lines and coating layer in blue at ^<sup>t</sup> <sup>¼</sup> :20, in the middle of the fast spin phase. Dimensionless variables are used.

the outer portion of the moat from C to D. The intersection of the bottom of the can with the side wall occurs at E. In this study we will consider one phenomenon in the can coating process that can lead to a defect in the final coating layer. As centrifugal forces drive the coating outward along the dome, they can form a "front" which if it reaches the moat can form pendant drops on the inner wall of the moat. If centrifugal forces are sufficiently large, these drops can detach from the substrate and flung horizontally outward to the outer side of the moat. This can create a coating that is too thin on the inner wall of the moat and too thick on the opposite side (Figures 7 and 8).

We will assume that the spray fan has an elliptical cross section with a ratio of the major axis to the length of the minor axis of 10. The parameters determining the placement and orientation of the spray gun are illustrated in Figure 9. For the simulation considered in this work, the nondimensional parameters are listed in

#### Figure 8.

Profile of the can substrate in red lines and coating layer in blue at ^<sup>t</sup> <sup>¼</sup> ^tmax <sup>¼</sup> :45, near the end of the fast spin phase. Dimensionless variables are used.

#### Figure 9.

Profile view of can and spray gun placement and orientation parameters.


#### Table 2.

Nondimensional parameters for this simulation.

Numerical Simulation of the Spin Coating of the Interior of Metal Beverage Cans DOI: http://dx.doi.org/10.5772/intechopen.90381

Table 1, the dimensional parameters in Table 2, and typical properties of the coating liquid in Table 3.

From Eq. (26), we see that the coating applied by the spray gun is an inverse function of the radius of the can substrate r. Consequently, the coating thickness near the centerline will be significantly greater than that far away from the centerline. This effect is illustrated in Figure 6 which shows a profile view of the can substrate and the coating thickness in the middle of the spray phase at time ^<sup>t</sup> <sup>¼</sup> <sup>0</sup>:10. Centrifugal forces are mostly parallel to the substrate in the dome region and act to drive liquid outward toward the moat region, as shown in Figure 7. At the start of the inner wall of the moat, near symbol A in Figure 8, the can substrate becomes perpendicular to the centrifugal force, and the coating liquid tends to accumulate at this point. If the coating becomes too thick in this region, centrifugal forces can overcome surface tension forces and cause a pendant drop of liquid to form, which can detach from the inside of the dome edge and be thrown to the region between D and E. Surface tension forces act against the centrifugal forces in this region and reduce the chance that a pendant drop will detach from the coating. But if a droplet does detach, it will cause a starving of coating liquid in the inner wall region and an excess in the outer wall region, possibly leading to coating irregularities such as blisters after the final bake.

The dimensionless parameter ρR<sup>2</sup> <sup>ω</sup><sup>2</sup>=ð Þ <sup>σ</sup>=<sup>R</sup> expresses the ratio of the pressure drop across the interface due to centrifugal forces versus surface tension forces. The dimensionless characteristic time for droplet detachment is plotted versus this dimensionless parameter in Figure 10. This graph estimates the maximum value of ^t, termed ^tmax, before droplet ejection occurs for a Newtonian liquid. Here we estimate the value of ^t when droplet detachment occurs using the criteria developed in Eq. (5) in Section 5. One can then determine how long the can may remain in the fast spin phase to avoid this coating irregularity.

The surface tension, density, and viscosity of the coating liquid are difficult to significantly alter as they depend on the required organic solvent content and surfactant levels in the paint formula. Similarly, R, the beverage can radius, is fixed by industry production standards. This leaves the rate of rotation as the only significant production parameter for changing the nondimensional (centrifugal force)/(surface tension force) parameter.

The centrifugal ejection of coating liquid from the inner wall of the moat is also predicted to be a strong function of the position and orientation of the spray gun. In the above example, the gun is placed 0.5 to the left of the centerline, is 0.5 cm above the top of the can, and is angled at 28<sup>∘</sup> with respect to the vertical. For our second simulation, the gun is placed 1.5 cm to the left of the centerline, 1.5 cm above the top of the can, and angled at 15<sup>∘</sup> with respect to the vertical. All other parameters are the same as in the previous example. This second spray gun position results in


Table 3.

Dimensional parameters for this simulation.

#### Figure 10.

Critical time for droplet formation, ^tmax, versus centrifugal force parameter. Here dimensionless variables are used.

#### Figure 11.

Critical time for droplet formation, ^tmax, versus centrifugal force parameter for two different spray gun placements. For fan #1, the angle of inclination is 28<sup>∘</sup> , A1 ¼ �0:15, B1 ¼ 0:45. For fan #2, the angle of inclination is 15<sup>∘</sup> , A2 ¼ �0:45, B2 ¼ 0:45. Dimensionless variables are used.

approximately 40% less spray falling on the dome and approximately 10% more coating on the sidewall than the first case. The total liquid volume emitted from the two spray guns is identical. Because the flux parallel to the substrate Qð Þ<sup>s</sup> is a function of the coating thickness cubed, we would expect that it would take longer before the coating is driven off the dome due to centrifugal forces for the second spray gun placement than the first spray gun placement. This is illustrated in Figure 11 where we plot ^tmax versus the dimensionless centrifugal force parameter for the two spray gun positions. With the new gun placement and orientation, one may keep the can in the fast spin phase for between 150 and 190% longer than the original spray gun configuration.

Numerical Simulation of the Spin Coating of the Interior of Metal Beverage Cans DOI: http://dx.doi.org/10.5772/intechopen.90381
