The role of wall slip on soluto-Marangoni instability in inertial two-fluid channel flows: A linear stability analysis

The impact of wall slip on soluto-Marangoni instability in a two-dimensional inertial flow is analyzed using the Orr-Sommerfeld and species transport equations. While previous studies explored similar instability, their scope was limited. This study extends Picardo et al., “Solutal Marangoni instability in layered two-phase flows,” J. Fluid Mech. 793, 280–315 (2016), who considered only no-slip condition, and Agrawal et al., “Impact of wall-slip on the soluto-Marangoni instability in a two-fluid system in a channel–Creeping flow scenario,” Int. J. Multiphase Flow 175, 104813 (2024), who considered wall slips but only for creeping flow. By incorporating wall-slip effects, we examine three scenarios: S1 (slip at the upper wall), S2 (slip at the lower wall), and S1S2 (symmetric slip at both walls). Stability is assessed by identifying unstable and stable regions in the n–m (depth ratio–viscosity ratio) plane through asymptotic analysis of long-wave disturbances. Numerical simulations using the Chebyshev spectral collocation method reveal two distinct modes (M1 and M2), with stability characteristics presented for typical values of the Marangoni number, Reynolds number, n, m, and slip lengths. The exchange of the dominance between inertial and Marangoni stresses under different wall-slip conditions is highlighted through energy budget analysis. Under inertial flow, in a channel with a less viscous fluid adjacent to the upper wall and mass transfer occurs downward, the system becomes unstable at lower Marangoni numbers. In such configurations, S2 slip stabilize both M1 and M2 modes at higher slip lengths. Conversely, for a more viscous upper layer with the same mass transfer direction, S1 slip conditions provide better stability compared to the no-slip condition. The study presents methods for stabilizing or destabilizing inertial channel flow by designing channel walls with appropriate slip conditions for the specific application.