  The effects of wall velocity slip on the linear stability of a gravity-driven
miscible two-fluid flow down an incline are examined. The fluids have the
matched density but different viscosity. A smooth viscosity stratification is
achieved due to the presence of a thin mixed layer between the fluids. The
results show that the presence of slip exhibits a promise for stabilizing the
miscible flow system by raising the critical Reynolds number at the onset and
decreasing the bandwidth of unstable wave numbers beyond the threshold of the
dominant instability. This is different from its role in the case of a single
fluid down a slippery substrate where slip destabilizes the flow system at the
onset. Though the stability properties are analogous to the same flow system
down a rigid substrate, slip is shown to delay the surface mode instability for
any viscosity contrast. It has a damping/promoting effect on the overlap modes
(which exist due to the overlap of critical layer of dominant disturbance with
the mixed layer) when the mixed layer is away/close from/to the slippery
inclined wall. The trend of slip effect is influenced by the location of the
mixed layer, the location of more viscous fluid and the mass diffusivity of the
two fluids. The stabilizing characteristics of slip can be favourably used to
suppress the non-linear breakdown which may happen due to the coexistence of
the unstable modes in a flow over a substrate with no slip. The results of the
present study suggest that it is desirable to design a slippery surface with
appropriate slip sensitivity in order to meet a particular need for a specific
application.
