Stability of two-layer flows past slippery surfaces. II. Inclined channels

In this paper, the linear stability characteristics of a two-layered liquid–liquid flow in an inclined channel with slippery walls are investigated. Previous studies on two-layered inclined channel flows have observed the presence of multiple base state flow profiles, two for countercurrent flow and up to three base states for co-current flow. The role of wall slip on the multiple base states associated with each holdup solution is analyzed here. Subsequently, a linear stability analysis, using a combination of a long-wave asymptotic analysis and finite wavenumber numerical calculation, is carried out with the slip boundary condition. Neutral stability boundaries are presented for each base state, with comparisons made with the previous results obtained for the no-slip boundary condition. It was found that the wall slip could have both stabilizing and destabilizing effects depending on the flow rates and the value of holdup—the location of an interface.