7. Conclusion

In this work we have used scaling arguments and perturbation theory to derive the lubrication form of the governing fluid mechanical equations for a thin liquid film coating an arbitrarily curved, axisymmetric, rotating substrate. Our main purpose has been to develop mathematical model that can be employed to numerically simulate the application of a paint film to the interior of beverage cans, though the basic algorithm may be useful in other applications. We have used our algorithm to predict the time of centrifugal ejection of coating from the inner moat wall as a function of several input parameters: the physiochemical properties of the coating liquid, the rotation rate, and the spray gun placement. The model can also be used to predict other coating defects and how the input parameters can be used to avoid them. The effect of solvent evaporation during the drying phase, when gravity and surface tension forces affect the coating distribution as the viscosity increases until only a final, hard, film remains, may also be modeled. With so many parameters regulating the final coating thickness, using experiments to model the coating evolution and measure the final, dry, film thickness is an almost impossible task. Instead we can utilize the power and versatility of computer simulation to predict the coating profile as a function of input parameters. This understanding will be useful in optimizing the current application process. It may also be essential in acquiring a satisfactory coating when environmental regulations require a change to high solids and latex paints.
