Flow of fluids with pressure-dependent viscosity down an incline: Long-wave linear stability analysis

In this paper, we investigate the linear stability of a gravity-driven fluid with pressure-dependent viscosity flowing down an inclined plane. The linear stability analysis is formulated using the long-wave approximation method. We show that the onset of instability occurs at a critical Reynolds number that depends on the material and geometrical parameters. Our results suggest that the dependence of the viscosity on pressure can influence the stability characteristics of the flow down an incline.