In this talk, we demonstrate that miscible two-fluid free surface flows of varying viscosity down an inclined substrate have different stability characteristics from both immiscible two layer flows and flows with viscosity gradients spanning the entire flow. Existence of new instability modes are shown, when the critical layer of the dominant unstable mode is located within the viscosity gradient. At moderate miscibility, a lubricating configuration with less viscous fluid adjacent to the wall is most stable, which is in contrast with the immiscible case, in which lubrication configuration is always destabilizing. The role of simultaneous occurrence of growing overlap modes under certain conditions in triggering nonlinearities is an interesting question for the future.
The talk is based on the results published in Linear Stability of Miscible two-fluid Flow down an Incline R.Usha, Outi Tammisola, Rama Govindarajan,
Physics of Fluids, 2013