Improving Coating Stability Using Slip Conditions: An Analytical Approach to Curtain Coating

Curtain deflector coating is a widely employed technique for producing thin, uniform films in numerous industrial applications. The flow dynamics in curtain coating become complex near the corner region due to the interaction of the moving substrate and the falling liquid curtain. In this study, an analytical investigation is conducted for the steady, in-compressible, and creeping flow of a Maxwell fluid, under the Navier slip condition at the substrate. The mathematical model is derived from the conservation of mass and momentum representing the nonlinear system which is solved using the Langlois recursive technique in combination with the inverse method. The inclusion of the Navier slip boundary condition in this research makes it novel and remove the singularity which produce the unstable stresses at a sharp corner due to no slip, but the Navier slip gives a stable solution for the stresses at a sharp corner. The analysis demonstrates that substrate slip significantly reduces tangential stresses and enhances the stability of the coating flow. Residual error analysis is also performed to verify the accuracy and convergence of the analytical solutions. The results provide a deeper understanding of how slip effects can be utilized to improve coating uniformity and optimize the operational performance of curtain deflector coating systems.