Stability Analysis of a Gravity Driven Miscible Two-fluid Flow: Role of Wall Slip

A linear stability analysis of a gravity-driven miscible two-fluid flow with matched density and different viscosities, containing a thin mixed layer between the two fluids, down a slippery inclined plane is considered. Results reveal the stabilizing effects on the surface (S), the overlap (O1 and O2) and the TS (not shown) modes that exist for a configuration with more viscous fluid adjacent to the free surface under overlap conditions. There is a possibility of destabilizing the overlap mode (O1) when the mixed layer is very close to the slippery wall, indicating the dual role played by the wall slip. The stabilizing characteristics of slip can be favourably used to suppress the nonlinear breakdown that may happen due to the coexistence of the unstable modes in a flow over a substrate with no slip.