Improving Coating Stability Using Slip Conditions: A Maxwell Fluid Analysis via the Langlois Recursive Method

Curtain deflector coating is a widely employed technique for producing thin, uniform films in numerous industrial applications. Near the corner region created by the interaction of the moving substrate and the falling liquid curtain, the flow dynamics are more complex. In this study, an analytical investigation is conducted for the steady, incompressible, and creeping flow of a Maxwell fluid, incorporating the Navier slip condition at the substrate. The governing nonlinear equations, derived from the conservation of mass and momentum, are solved using the Langlois recursive technique in combination with the inverse method, yielding an approximate third-order solutions for velocity, pressure, and stress fields. Finite and physically consistent stress distributions are produced by the slip condition that removes the singularity connected to the traditional no-slip boundary condition. 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.