Linear stability analysis of miscible two-fluid flow in a channel with velocity slip at the walls

The linear stability characteristics of pressure-driven three-layer flow of two miscible liquids with same density and varying viscosity in a channel with velocity slip at the wall are examined.The flow system is destabilizing when a more viscous fluid occupies the region closer to the wall with slip. For this configuration, a new mode of instability,namely,the overlap mode, similar to the one which appears in the corresponding flow in a rigid channel, occurs for high mass diffusivity of the two fluids,when the critical layer of the disturbance overlaps the viscosity stratified layer.The co-existence of several overlap modes, TS mode are also observed under certain circumstances.The flow is unstable at low Reynolds numbers for a wide range of wave numbers for low mass diffusivity.A configuration with less viscous fluid adjacent to the wall is stabilizing at moderate miscibility. It is possible to achieve stabilization or destabilization of miscible two-fluid flow in a channel with wall slip by appropriately choosing the viscosity of the fluid layer adjacent to the wall. In addition, the velocity slip at the wall has a dual role in stabilizing the flow system.The flow system can be either stabilized or destabilized by designing the walls of the channel as hydrophobic surfaces.