Impact of wall-slip on the soluto-marangoni instability in a two-fluid system in a channel–Creeping flow scenario

Abstract

The role of wall-slip on the soluto-Marangoni instability that emerges in a two-fluid creeping two-dimensional Poiseuille flow is assessed within the framework of Orr-Sommerfeld analysis and species-transport system. Different wall-slip scenarios, namely S1 (slip at the upper wall), S2 (slip at the lower wall), S1S2 (symmetric slip at the upper and lower walls) are considered. The system instability is characterized by identifying unstable and stable zones in the m-n (viscosity ratio - depth ratio) plane for each of the slip conditions at the wall using asymptotic analysis for long-wave disturbances. Numerical simulations based on Chebyshev spectral collocation method reveals the emergence of two modes (M1 and M2) and corresponding stability features are displayed for typical values of Marangoni numbers, n, m and slip lengths. The occurrence of short-wave modes and the features of exchanging dominance between the short-wave modes in the presence of wall-slip for different slip condition are elucidated and the physical mechanism responsible for triggering the instability in the system are revealed through energy budget analysis. The channel system hosting less viscous fluid adjacent to the upper wall demonstrates interesting characteristics such as (among other things): stabilizing/destabilizing the emerging M1/M2 modes in system with no-slip by imposing S1/S2/S1S2 wall conditions and increasing the slip length; exchange of dominance of unstable modes beyond a threshold slip length for S1 slip type. The study thus presents possible means of stabilizing/destabilizing a creeping channel flow system by designing the walls of the channel with appropriate slip type relevant to the application.