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

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.