Gravity-Driven Film Flow of a Power-Law Fluid over a Wavy Substrate with Slip Condition

Abstract In the current manuscript, the flow of a thin film of a power-law fluid over a slippery topographical substrate is discussed.The von Karman–Pohlhausen method is used to develop the integral boundary layer (IBL)—model for the film thickness using an analytical approach.The findings are supported by earlier research on the resonance phenomena in gravity-driven Newtonian films with and without slippery properties. The novelty of this study lies in the influence of the slip condition at various power-law index n values.The study of the linear and non-linear resonance interactions between the free surface and the slippery undulating substrate yields expressions for the resonant Reynolds number for the largest free-surface amplitudes. The effects of shear-thinning and shear-thickening on the model system’s stability are taken into account when treating the slippery offer. The free surface amplitude is significantly affected by the slip length parameter’s rise, which has a major passive effect on the model system’s instability.