Linear stability analysis of a film flowing down a wall with different surface corrugated amplitudes — a long wave approximation approach

Instability features of a liquid film flowing along an inclined wall for different corrugated amplitudes have been studied with the long wave approximation methods. It has been derived in the rectangular and orthogonal curve coordinates. Results reveal that the present theoretical calculations coincide better with the previous experimental data for the small Reynolds number cases. The liquid film thickness on a small corrugated wall is consistent with that of a flat wall while it would be promoted by the larger corrugated amplitude cases. Besides, it illustrates that the small corrugated surface amplitudes have a limited impact on the flow neutral stability. The larger surface corrugated amplitude cases suppress the surface instability when the surface Taylor-Rayleigh instability is not induced. The corresponding suppression impact would be more pronounced when the inclined angle becomes smaller.